Answer:
(i) R = 4.70g
(ii) R = $35.25
Step-by-step explanation:
(i) R ∞ g
Removing the proportionality symbol, we have
R = kg, where k is the constant of proportion
56.40 = k(12)
Divide both sides by 12
56.40/12 = k(12)/12
$4.70 = k
k = $4.70
So, R = 4.70g (which is the linear equation relating Revenue, R to number of gallons, g)
(ii) When g = 7.5,
R = 4.70 * 7.5 = 35.25
R = $35.25
The revenue R at a gas station varies directly with the number of gallons of gasoline sold g. The linear equation relating R to g is R = 4.7g. The revenue when the number of gallons sold is 7.5 is $35.25.
Explanation:
In this particular scenario, we're dealing with a problem of direct variation. In a direct variation, as one quantity increases, the other increases proportionally. This can be represented by a linear equation of the form y = kx, where y is the dependent variable, x is the independent variable, and k is the constant of variation (the ratio of y to x).
Here, the Revenue (R) varies directly with the number of gallons of gasoline sold (g). We can calculate the constant of variation (k) by dividing the given Revenue (R) by the given number of gallons (g): k = 56.4 ÷ 12 = 4.7. So, the linear equation relating R to g is: R = 4.7g.
To find the revenue R when the number of gallons of gasoline sold is 7.5, substitute g = 7.5 into the equation: R = 4.7 * 7.5 = $35.25
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Help meh!
Which is the BEST estimate of the average rate of change for the function graphed, over the interval 1 ≤ x ≤ 3?
A) 2
B) 3
C) 4
D) 6
Answer:
The answer is B) 3
Step-by-step explanation:
The reason why is because 1 is less than OR equal to x and 3 is less than or equal to x and is x = 3 then it fits both descriptions the best.
Answer:
-3
Step-by-step explanation:
3 is the average rate of change for the exponential graph shown over the interval 1 ≤ x ≤ 3.
Start by determining the two distinct points: (1, 2) and (3, −4).
Therefore,
Δf(x)
Δx
=
−4 − 2
3 − 1
=
−6
2
= −3
A jar contains 11 green marbles, 7 red marbles, and 6 blue marbles. A marble is selected at random, not replaced, and then a second marble is selected. What is the probability of selecting a blue marble followed by a green marble?
Write In a fraction.
Answer:
11/92
Step-by-step explanation:
G = 11
R = 7
B = 6
P(b) = 6/24 = 1/4
P(g) = 11/23
P(blue first and then green(without replacement)) = 1/4 * 11/23
= 11/92
The probability of randomly selecting a blue marble followed by a green marble from a jar of 24 marbles (6 blue, 7 red, 11 green) is 11/92.
Explanation:The number of outcomes considered favorable or desired is compared to the total number of outcomes possible. In this situation, we're interested in choosing a blue marble first, then a green marble. The total number of marbles is 11 green + 7 red + 6 blue = 24 marbles.
Initially, the probability of selecting a blue marble is 6/24 = 1/4
because there are 6 blue marbles out of a total of 24.
After taking one marble out (assuming it's blue), you have 23 marbles left, with 11 of them being green. So, the probability of selecting a green marble next is 11/23.
Therefore, the probability of both of these events happening (selecting a blue marble followed by a green marble) is found by multiplying these two probabilities together, which gives (1/4) * (11/23) = 11/92.
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A company that sells seeds wants to check that at least 90% of its corn seeds are viable. An independent testing lab plants 1000 randomly chosen seeds and observes that 903 of them germinate. What does this data imply about the claim that 90% of the seeds are viable?
Answer:
The data claims that 90% of the seeds are viable meaning that 90% of the seeds are likely to germinate and grow into healthy plants under good conditions.90% 0f 1000seeds gives 900seeds,and 903seeds germinated so the claim is true
Step-by-step explanation:
Total number of seeds=1000
Seeds that germinate =903
90% of 1000=>90/100×1000 =900seeds.
You are designing a staircase to reach a second floor that is 113" above the ground floor of a building. The owner of the building wants you to make a staircase as close as possible to a 7.25" rise to meet their specifications
Answer:
Step-by-step explanation:
total height, H = 113 inches
height of each stair case, h = 7.25 inches
Number of stair case, n = total height / height of each stair case
n = 113 / 7.25 = 15.6
Let M be the midpoint of side \overline{AB} of \triangle ABC. Angle bisector \overline{AD} of \angle CAB and the perpendicular bisector of side \overline{AB} meet at X. If AB = 40 and MX = 9, then how far is X from line {AC}?
Final answer:
To find the distance from X to line AC, we can use the angle bisector theorem and the fact that M is the midpoint of AB. By substituting the known values, we can solve for the distance d and find that X is 12 units away from line AC.
Explanation:
We are given that M is the midpoint of side AB of triangle ABC. Angle bisector AD of angle CAB and the perpendicular bisector of side AB meet at X. We are also given that AB = 40 and MX = 9.
To find the distance from X to line AC, we can use similar triangles. Let's denote the distance from X to line AC as d. According to the angle bisector theorem, we have:
AD/CD = AB/CB
Since M is the midpoint of AB, we have:
MD = MB = AB/2 = 40/2 = 20
Therefore, we can rewrite the angle bisector theorem as:
AD/(AD + CD) = AB/CB
Substituting the known values, we get:
9/(9 + d) = 40/20
Cross multiplying, we have:
20 * 9 = 40 * (9 + d)
Simplifying, we find:
d = 12
Therefore, X is 12 units away from line AC.
If you were going to apply statistical methods to analyze teacher evaluations, which question form, A or B, would be better? Form A: In your own words, tell how this teacher compares with other teachers you have had. Form B: Use the following scale to rank your teacher as compared with other teachers you have had.a. Form B would be better because statistical methods can be applied to the ordinal data. b. Form B would be better because statistical methods can be applied to the nominal data. c. Form A would be better because statistical methods can be applied to the nominal data. e. Form A would be better because statistical methods can be applied to the ordinal data.
Answer:
a. Form B would be better because statistical methods can be applied to the ordinal data.
Step-by-step explanation:
Ordinal data can be ranked. This teacher evaluation can be ranked on a scale of 1-10 for example. Ordinal data can provide good information about the choice of the person who is responding. And these informations are quantitative in nature.
Please help, I was absent for this day so I don't know how to do this.
Answer:
Step-by-step explanation:
An arc is a portion of the circle's circumference bounded by 2 radii
The formula for determining the length of an arc is expressed as
Length of arc = θ/360 × 2πr
Where
θ represents the central angle or angle which the 2 radii subtends at the center of the circle.
r represents the radius of the circle.
π is a constant whose value is 3.14
From the information given,
Radius, r = 5 inches
θ = 170 degrees
Therefore,
Length of arc = 170/360 × 2 × π × 5
Length of arc = 4.7222π feet
rounding up to 2 decimal places, it becomes
4.72π feet
PLZ HURRY IT'S URGENT!!
Which fraction represents the ratio 9 to 6 in simplest form?
1/6
6/9
3/2
9/2
Answer:
3/2
Step-by-step explanation:
Answer:
3/2
Step-by-step explanation:
9 to 6 means
[tex]\dfrac{9}{6}[/tex]
Now we will cancel that fraction - we will divide numerator and denominator both by 3:
9 divided by 3 equals 3
6 divided by 3 equals 2
Hence,
[tex]\dfrac{9}{6} = \dfrac{3\cdot 3}{2\cdot 3} = \dfrac{3}{2}[/tex]
Use differentiation to show that the given function is a solution of the equation for all values of the constants. (Enter your answers in terms of x.) equation: x'' + x = 2et, function x = C1 sin(t) + C2 cos(t) + et
Answer with Step-by-step explanation:
We are given that
DE
[tex]x''+x=2e^t[/tex]
Function:[tex]x=C_1sint+C_2cost+e^t[/tex]
We have to show that given function is a solution of the equation for all values of the constants.
If given function is solution of DE then it satisfied the given DE.
Differentiate function w.r.t.t
[tex]x'=C_1cost-C_2sint+e^t[/tex]
Again differentiate w.r.t. t
[tex]x''=-C_1sint-C_2cost+e^t[/tex]
Substitute the values in the given DE
[tex]-C_1sint-C_2cost+e^t+C_1sint+C_2cost+e^t=2e^t[/tex]
LHS=RHS
Given function satisfied the given DE.Therefore, it is solution of given DE for all values of the constants.
In the context of data patterns in a time series, a(n) _____ is a one-time variation that is explainable.
Final answer:
In a time series, an explainable one-time variation is known as an outlier. Outliers can be important for understanding data, but they differ from inexplicable random components which include variations not explained by trend, cyclical, or seasonal patterns.
Explanation:
In the context of data patterns in a time series, a one-time variation that is explainable is usually referred to as an outlier. An outlier can be a potential key to understanding the data or it may be due to some abnormality or error. In a time series, data is analyzed over time to determine components such as the trend, cyclical, seasonal, and random components.
Trend component displays the long-term progression of the series, the cyclical component deals with fluctuations occurring at non-fixed intervals, the seasonal component reflects regular variations within a specific period, like quarters within a year, and the random component comprises those elements that cannot be attributed to the trend, cyclical, or seasonal patterns.
It's essential to distinguish outliers from the random components, which are, by definition, inexplicable variations. However, if an outlier can be explained by a particular event or change, it's not part of the random component but a distinct deviation from the expected pattern.
PLZ HELP THIS IS TIMED!!!!
Which formula can be used to describe the sequence? Negative two-thirds, −4, −24, −144,... f(x) = 6(negative two-thirds) Superscript x minus 1 f(x) = −6(Two-thirds) Superscript x minus 1 f(x) = Negative two-thirds(6)x − 1 f(x) = Two-thirds(−6)x − 1
Answer:
For the sequence is [tex]-\frac{2}{3}[/tex] ,-4 ,-24 ,-144 ,...
Hence the formula [tex]f(x)=-\frac{2}{3}(6)^{x-1}[/tex] for x=1,2,3,... represents the given geometric sequence
Step-by-step explanation:
Given sequence is [tex]-\frac{2}{3}[/tex] ,-4 ,-24 ,-144 ,...
To find the formula to describe the given sequence :
Let [tex]a_1=\frac{-2}{3}[/tex] ,[tex]a_2=-4[/tex] ,[tex]a_3=-24[/tex],...
First find the common ratio
[tex]r=\frac{a_2}{a_1}[/tex] here [tex]a_1=\frac{-2}{3}[/tex] and,[tex]a_2=-4[/tex]
[tex]=\frac{-4}{\frac{-2}{3}}[/tex]
[tex]=\frac{4\times 3}{2}[/tex]
[tex]=\frac{12}{2}[/tex]
[tex]r=6[/tex]
[tex]r=\frac{a_3}{a_2}[/tex] here [tex]a_2=-4[/tex] and [tex]a_3=-24[/tex]
[tex]=\frac{-24}{-4}[/tex]
[tex]=6[/tex]
[tex]r=6[/tex]
Therefore the common ratio is 6
Therefore the given sequence is geometric sequence
The nth term of the geometric sequence is
[tex]a_n=a_1r^{n-1}[/tex]
The formula which describes the given geometric sequence is
[tex]f(x)=a_1r^{x-1}[/tex] for x=1,2,3,...
[tex]=\frac{-2}{3}6^{x-1}[/tex] for x=1,2,3,...
Now verify that [tex]f(x)=a_1r^{x-1}[/tex] for x=1,2,3,... represents the given geometric sequence or not
put x=1 and the value of [tex]a_1[/tex] in [tex]f(x)=a_1r^{x-1}[/tex] for x=1,2,3,...
we get [tex]f(1)=-\frac{2}{3}(6)^{1-1}[/tex]
[tex]=-\frac{2}{3}(6)^0[/tex]
[tex]=-\frac{2}{3}[/tex]
Therefore [tex]f(1)=-\frac{2}{3}[/tex]
put x=2 we get [tex]f(2)=-\frac{2}{3}(6)^{2-1}[/tex]
[tex]=-\frac{2}{3}(6)^1[/tex]
[tex]=-\frac{12}{3}[/tex]
Therefore [tex]f(2)=-4[/tex]
put x=3 we get [tex]f(3)=-\frac{2}{3}(6)^{3-1}[/tex]
[tex]=-\frac{2}{3}(6)^2[/tex]
[tex]=-\frac{2(36)}{3}[/tex]
Therefore [tex]f(3)=-24[/tex]
Therefore the sequence is f(1),f(2),f(3),...
Therefore the sequence is [tex]-\frac{2}{3}[/tex] ,-4 ,-24 ,-144 ,...
Hence the formula [tex]f(x)=a_1r^{x-1}[/tex] for x=1,2,3,... represents the given geometric sequence is verified
Therefore the formula [tex]f(x)=-\frac{2}{3}(6)^{x-1}[/tex] for x=1,2,3,... represents the given geometric sequence
Answer:
a
Step-by-step explanation:
Help plz if you know this then plz answer back! How do you solve (x to the power of -1) (x to the power of -5) The lesson is multiplying and dividing expressions with exponents.
Answer:
(x⁻¹)(x⁻⁵) = x⁻⁶
Step-by-step explanation:
When multiplying number with the same base, you add up their exponent.
(x⁻¹)(x⁻⁵) =
= x⁽⁻¹⁾ ⁺ ⁽⁻⁵⁾
= x⁻⁶
you can also write x⁻⁶ as 1/x⁶. The negative sign in the exponent just flip the numerator and denominator with each others.
Answer:
The answer to your question is x⁻⁶ or 1/x⁶
Step-by-step explanation:
Multiplying exponents
-To multiply exponents they must have the same base and the result will be the base and the exponents will add.
Ex
(a³)(a²)
base = a
exponents = 3 and 2
result a³ ⁺ ² = a⁵
In your question
(x⁻¹)(x⁻⁵) = x⁻¹⁻⁵ = x⁻⁶ = 1/x⁻⁶
In AABC, 2B= 2C, and m_A= 349. Find mzo
A. 56°
B. 730
c. 112°
1460
Answer:
i think it' =-8abc(a+b-c)
Step-by-step explanation:
FIND THE INVERSE OF -5 + 7i
Answer:
Additive inverses for complex numbers are just like they are for real numbers: they mean the number you'd add to get back to 0. Just like real numbers, this means that you change the signs. Thus, the additive inverse of -4+7i is 4-7i
hope it helps
Step-by-step explanation:
Maytag wants to administer a satisfaction survey to its current customers. Using their customer database, the company randomly selects 6060 customers and asks them about their level of satisfaction with the company. What type of sampling is used?
a. Simple random
b. Cluster
c. Systematic
d. Stratified
e. Convenience
Answer:
Correct answer is (a). Simple random sampling
Step-by-step explanation:
Simple random sampling (SRS) is a statistical techniques used in choosing subset of members of the population randomly without given special priority to anyone to be chosen. It gives every members of the population equal chance.
By randomly selecting 6060 customers from the customer's database, Maytag has employed Simple Random Sampling method of survey.
These two ways of setting up a String yield identical results: a) String string = new String("123.45"); b) String string = "" + 123.45; Group of answer choices True False
Answer:
Step-by-step explanation:
Simplify.
4n + 12 + 7n
16n + 7
23n
11n + 12
4n + 19
Which of the following is the image of the point for the given rotation, r (120°) (F)?
Answer:
B
Step-by-step explanation:
360/6
6 is number of sides
You get 60
Rotate twice to reach 120
Moving F Counter clockwise twice is where B was
The image of point F after the rotation of 120°, r(120°), will be point B.
Which point will represent the given rotation of F?
So, we need to rotate point F a total angle of 120°.
As you can see, in the image we have 6 sections, and equally distributed in these 6 sections we will have an angle of 360° (a complete rotation). So each section has an angle of:
360°/6 = 60°.
Then a rotation of 120° (two times 60°) will rotate the point F two sections counterclockwise. Then the image of the point after the rotation will be point B.
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Trista had 95 correct out of 100 problems on her math test. The ratio of correct answers to total problems is . Written in fraction form, this is . Written as a percent, Trista got of the problems correct.
Answer:
Fractional form = [tex]\frac{95}{100}=\frac{19}{20}[/tex]
Percent form = 95%
Trisha got 95% of her problems correct.
Step-by-step explanation:
Given:
Total number of questions (N) = 100
Number of correct questions (C) = 95
Therefore, the ratio of the correct answers to the total number of problems is given by dividing the the number of correct questions by the total number of questions. This is given as:
Ratio expressed as a fraction = [tex]\frac{C}{N}=\frac{95}{100}=\frac{95\div 5}{100\div 5}=\frac{19}{20}(Simplest\ form)[/tex]
Now in order to express this ratio in percentage form, we need to multiply the given ratio by 100. This gives,
Ratio expressed as a percent = [tex]\frac{C}{N}\times 100=\frac{95}{100}\times 100=95\%[/tex]
Therefore, Trisha got 95% of her problems correct.
Answer:
1: the first one
2:the third one
3:the third one
Step-by-step explanation:
The ratio of the weight of an object on Mars to its weight on Earth is 9 to 25. If a person weighs 120 pounds on Earth, how much would the person weigh on Mars?
Answer:
Wm = 43.2 pounds
Step-by-step explanation:
If the ratio of the weight of an object on Mars to its weight on Earth is 9 to 25, this means that what on Mars weighs 9 units on earth weighs 25 units, therefore:
Data
ratio = 9/25
Weight on Mars (Wm) = ?
Weight on Earth (We) = 120 pound
Wm = (9/25)*120 pound = 43.2 pounds
TRY IT! Simplity
x(x + 5)
2x2 - 50
The perimeter of square JKLM is 48 units. Square J K L M is shown. The length of J K is x + 3. What is the value of x? 6 9 12 15
Answer:
x = 9
Step-by-step explanation:
if the perimeter os square JKLM is 48
each side has 48/4
so each side has 12
now if JK is x + 3 = 12
we only need to solve that
x + 3 = 12
x = 12 -3
x = 9
Answer:
B. 9
Step-by-step explanation:
There are 100 bags each with 100 coins, but only one of these bags has gold coins in it. The gold coin has weight of 1.01 grams and the other coins has weight of 1 gram. We are given a digital scale, but we can only use it once. How can we identify the bag of gold coins?
Answer:
So, with one measurement, we can determine the bag of gold coins.
Step-by-step explanation:
We will number the bags with numbers from 1 to 100. Then we will take one coin from the first bag, from the second we will take 2 coins, from the third we will take 3 coins. We will continue the process to the last bag, from which we will take all 100 coins. Then we'll put it all on a digital scale.
Depending on how many numbers in the decimal notation we mean what the bag of gold coins is. For example, if the decimal number is .02, we will conclude that 2 is a bag of gold coins. For example, if the decimal number is .33, we would conclude that 33 is a bag of gold coins. If there are no decimal numbers, we conclude that the gold bag is the last bag on the digital scale, because 100 · 1.01 = 101.
So, with one measurement, we can determine the bag of gold coins.
Divide the following polynomials. Then place the answer in the proper location on the grid. Write your answer in order of descending powers of x. Do not include parentheses in your answer.6x3 + 11x2 - 4x -4 / 3x - 2
Answer:
The Final answer will be [tex]2x^2+5x+2[/tex] with remainder 0.
Step-by-step explanation:
We have attached the division for your reference.
Given:
Dividend = [tex]6x^3 + 11x^2 - 4x -4[/tex]
Divisor= [tex]3x - 2[/tex]
Explaining the division we get;
Step 1: First when we divide the Dividend [tex]6x^3 + 11x^2 - 4x -4[/tex] with divisor [tex]3x - 2[/tex] we will first multiply [tex]2x^2[/tex] with the divisor then we get the Quotient as [tex]2x^2[/tex] and Remainder as [tex]15x^2-4x-4[/tex]
Step 2: Now the Dividend is [tex]15x^2-4x-4[/tex] and Divisor is [tex]3x - 2[/tex] we will now multiply [tex]5x[/tex] with the divisor then we get the Quotient as [tex]2x^2+5x[/tex] and Remainder as [tex]6x-4[/tex]
Step 3: Now the Dividend is [tex]6x-4[/tex] and Divisor is [tex]3x - 2[/tex] we will now multiply 2 with the divisor then we get the Quotient as [tex]2x^2+5x+2[/tex] and Remainder as 0.
Hence The Final answer will be [tex]2x^2+5x+2[/tex] with remainder 0.
How many days are there in one month? It is measured in the
A. thousands
B. tens
O ooo
c. ones
D. hundreds
Tens is the correct answer
A motorcyclist heading east through a small Iowa town accelerates after he passes a signpost at x=0 marking the city limits. His acceleration is constant (4.0 m/s2). At time t =0 he is 5 m east of the signpost and has a velocity of 15 m/s. (a) find his position and velocity at time t=2 sec. (b) where is the motor cyclist when his velocity is 25 m/s?
Answer:
a) 43 m b) 55 m
Step-by-step explanation:
a) From question at t = 0, initial velocity [tex]V_{o}[/tex] = 15 m/s
Using equation of motion, [tex]S = V_{o}t + \frac{1}{2} at^{2}[/tex] ; at t = 2 secs , a = 4 m/[tex]s^{2}[/tex]
S = (15 x 2) + (0.5 X 4 x [tex]2^{2}[/tex])
S = 30 + 8 = 38 m , Therefroe;
car is (38 + 5)m from the sign post
car is 43 m from the sign post at t = 2 secs
b) Also from equation of motion, [tex]V^{2} = V_{o} ^{2} + 2aS[/tex]
[tex]25^{2} = 15^{2}[/tex] + (2 x 4 x S)
625 - 225 = 8S
S = 50 m
Car is (50 + 5) m from the sign post
Car is 55 m from the sign post at V = 25 m/s
At t=2s, the motorcyclist is at position 29m east of the signpost with a velocity of 23m/s. When his velocity is 25m/s, he is at a position 38.75m east of the signpost.
Explanation:Given that the motorcyclist starts 5 m east of the signpost with an initial velocity of 15 m/s and a constant acceleration of 4.0 m/s2, we can use the equation of motion to find his position and velocity at any given time.
(a) At t=2s, the motorcyclist's position (x) and velocity (v) can be determined using the following two equations respectively:
Position (x) = x0 + v0*t + 0.5*a*t2 = 5 m + 15 m/s*2s + 0.5*4.0 m/s2* (2s)2 = 29 mVelocity (v) = v0 + a*t = 15 m/s + 4.0 m/s2*2s = 23 m/s
(b) When the velocity is 25 m/s, the time can be calculated using the equation v = v0 + a*t. By setting v=25m/s, v0=15m/s, and a=4.0m/s2, we get t = (25m/s-15m/s) / 4.0m/s2 = 2.5s. Substituting this time into the position equation gives x = 5m + 15m/s*2.5s + 0.5*4.0m/s2*(2.5s)2, which results in the motorcyclist being at position 38.75 m.
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To celebrate its grand opening a store is giving customers gift certificates which customer is the first to get two gift certificates every 8th gets a $50 gift certificate and every 6th person gets a $10 gift certificate
Answer:
The 24th Customer is the first to get two gift certificates.
Since, 2 x 2 x 2 x 2 x 3 = 24
The first customer to receive two gift certificates is the customer at the 24th position in the sequence of customers.
The LCM of 8 and 6 is 24. This means that the first customer to receive two gift certificates will be the one who appears at the 24th position in the sequence.
To calculate the position of this customer, we can consider the multiples of 24:
24, 48, 72, and so on.
The 24th customer is the first to receive two gift certificates, as they satisfy both the every-8th and every-6th customer criteria.
The Greatest Common Factor (GCF) and the Least Common Multiple (LCM) are fundamental concepts in number theory. The GCF of two or more numbers is the largest positive integer that divides all the given numbers without leaving a remainder. On the other hand, the LCM of two or more numbers is the smallest positive multiple that is divisible by all the given numbers.
In this scenario, the GCF and LCM were used to determine the customer who would receive two gift certificates. The GCF was not explicitly required to solve this particular problem, but it is a useful concept in various mathematical contexts.
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Complete Question:
To celebrate its grand opening, a store is giving -customers gift certificates. Which customer is the first to get two gift certificates? Every 8 th customer gets Every 6th customer gets a $10 gift certificate. 200 4-2 Find Greatest Common Factor and Least Common Multiple
The sum of six fifths 6 5 and six timessix times a number is equal to four fifths 4 5 subtracted from seven timesseven times the number. Find the number.
Answer :
The required number is 2.
Step-by-step explanation:
Given : The sum of six fifths and six times a number is equal to four fifths subtracted from seven times the number.
To find : The number ?
Solution :
Let the number be 'x'.
The sum of six fifths and six times a number i.e. [tex]\frac{6}{5}+6x[/tex]
Four fifths subtracted from seven times the number i.e. [tex]7x-\frac{4}{5}[/tex]
According to question,
[tex]\frac{6}{5}+6x=7x-\frac{4}{5}[/tex]
[tex]7x-6x=\frac{6}{5}+\frac{4}{5}[/tex]
[tex]x=\frac{10}{5}[/tex]
[tex]x=2[/tex]
The required number is 2.
If six cookies cost the same as 2 brownies, and four brownies cost the same as 10 cupcakes, how many cupcakes can Bob buy for the price of eighteen cookies?
Bob can buy 15 cupcakes for the price of 18 cookies.
Step-by-step explanation:
Assume the cost of a cookie is $x, the cost of a brownie is $y and the cost of a cupcake is $z.It is given that 6 cookies and 2 brownies cost the same, so 6x = 2y, take this as equation 1.It is also given that 4 brownies cost the same as 10 cupcakes, so 4y = 10z, take this as equation 2.If we divide equation 2 by 2 we get, 2y = 5z so that the y value is the same as equation 1 and we can equate equation 1 and 3.We get 6x = 2y = 5z, 6x = 5z, dividing both sides by 5, we get 1.2x = z.We need to calculate how many cupcakes Bob can buy for the price of 18 cookies, So we must find the z value when the x = 18.If we multiply 1.2 with 15 we get 18 so we the last equation is multiplied with 12 so that 18x = 15z. 18 cookies and 15 cupcakes cost the same.A student and a pet run straight towards each other at constant speed, starting with a separation of 30 m. They meet somewhere in between. Draw a picture at the beginning and another at the end, and establish a coordinate system. Give names to important quantities.
Answer:
View graph
Step-by-step explanation:
we have that at constant speed the student and the pet must travel equal distances in equal times, so they must be in the middle of the distance with the same travel time
As can be seen in graph 2 the distance of P = -15 m, and that of S = 15, the sign is due to the orientation, P goes to the left and S to the right
Kenneth measured a hotel and made a scale drawing the scale he used was 1 inch= 4 feet the actual length of a room in the hotel is 20 feel how long is the room in the drawing
Answer:
The length of the room in the drawing is 5 inches.
Step-by-step explanation:
Given:
Kenneth measured a hotel and made a scale drawing the scale he used was 1 inch= 4 feet.
The actual length of a room in the hotel is 20 feet.
Now, to find the length of the room in the drawing.
Let the length of the room in the drawing be [tex]x.[/tex]
The actual length of the room = 20 feet.
The scale used in drawing is 1 inch = 4 feet.
As, 1 inch is equivalent to 4 feet.
Thus, [tex]x[/tex] is equivalent to 20 feet.
Now, to get the length of the room in the drawing we use cross multiplication method:
[tex]\frac{1}{4} =\frac{x}{20}[/tex]
By cross multiplying we get:
[tex]20=4x[/tex]
Dividing both sides by 4 we get:
[tex]5=x[/tex]
[tex]x=5\ inches.[/tex]
Therefore, the length of the room in the drawing is 5 inches.