Let "x" represent the number of hours that John works and "y" represent John's earnings after working x hours.
b) John receives $25/hour → this value represents the change in John's earnings for every unit increase of x, which is, the constant proportionality (k) of the relationship.
a) If x and y have a direct relationship, you can express it as follows:
[tex]y=25x[/tex]A car drove 300 miles in four hours. How fast was the car traveling in miles per hour?
Given that,
A car drove 300 miles in four hours.
We can simply put it in this way.
In 4 hours, a total distance covered by the car = 300 miles
In 1 hour, a total distance covered by the car = 300/4 miles = 75 miles.
Hence, the car was traveling at a speed of 75 miles per hour.
How do you decide which rational number operations to use to solve problems
One can decide which rational number operations to use to solve problems based on the context of the information.
What is a rational number?Studying rational numbers is significant because they illustrate how the world is so complex that we will never be able to comprehend it.
A rational number is defined as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively. Every integer and 3/7, for example, are rational numbers.
A rational number is defined as the quotient of the fraction p/q of two integers, a numerator p and a non-zero denominator q. Every integer is a rational number since q might be equal to 1.
In this case, the operation include addition, subtraction, division, etc. This will be based on the context.
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Find the equation of the line though the point (-3, -2) and perpendicular to the line y = 2/3x-2.Write your answer in the form y=mx+b.
For this question we know that we have a point (-3,-2) and we want to find an equation perpendicular to the line
y=2/3x-2.
Since both lines are perpendicular we need to satisfy this:
[tex]m_1\cdot m_2=-1[/tex]With m1= 2/3. If we solve for m2 we got:
[tex]m_2=\frac{-1}{m_1}=\frac{-1}{\frac{2}{3}}=-\frac{3}{2}[/tex]And then we can find the intercept for the new line using the point given with x=-3 and y=-2 and we got this:
[tex]-2=-\frac{3}{2}(-3)+b[/tex]And solving for b we got:
[tex]b=-\frac{9}{2}-2=-\frac{13}{2}[/tex]And then our final answer would be:
[tex]y=-\frac{3}{2}x-\frac{13}{2}[/tex]What is the value of an edge length of the larger prism in centimeterMecand vou answer and now in the bubbles on your answer document. Be sure to use thecorect place value
Ok, we have here two similar prisms, which means that the length of every sides of one prism is proportional to the correspondent side of the other prism.
From this, we have the following relation: (7/2.8) = (x/11.2)
Multiplying both sides by 11.2, we got: x = (11.2*7)/2.8 = 28 cm.
The graph shows the relationship between pounds of grapes, g, and their cost, c.
A graph on a coordinate plane shows cost of grapes on the horizontal axis (c), numbered 2 to 6, and pounds of grapes on the vertical axis (g), numbered 1 to 4. Solid circles are at points (0, 0), (2, 1), (4, 2), (6, 3), and are connected by a solid line.
Use the graph to complete the statements.
For every dollar you spend, you can get
0.5
pounds of grapes.
For each pound of grapes, you would need $
.
For every dollar you spend, you can get 0.5 pounds of grapes.
For each pound of grapes, you would need $2.
How to interpret the graph?From the coordinates of this graph, we can reasonably infer and logically deduce that it models a straight line, shows a proportional relationship and can be represented by using a linear function.
Mathematically, a proportional relationship can be represented by the following equation:
g = kc
Where:
k is the constant of proportionality.g represent the pounds of grapes.c represent the cost of grapes in dollar.Next, we would determine the constant of proportionality (k) for the data points shown on this graph as follows:
k = g/c
k = 1/2 or 0.5
Therefore, the linear equation is given by g = 0.5c.
For the amount of dollar needed at g = 1, we have:
g = 0.5c
c = g/0.5
c = 1/0.5
c = $2.
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Audrey was attempting to draw a picture that would be the cover of the upcoming movie, Up 2. Thepicture would be of the house being carried by balloons again. She started her drawing with theballoons, which she wanted to make all the same size.She drew a circle for the balloon and found the radius, which was 9cm. How big around will all ofAudrey's balloon drawings be?——Please help me.
Audrey drew a circle for the balloon, this circle has a radius of 9 cm.
To know how big the baloon is you have to determine its circumference.
To calculate the circumference of a circle you have to multiply its diameter by number pi:
[tex]C=d\pi[/tex]The formula is C=dπ
The diameter is twice the circle so the diameter of the baloon is:
[tex]\begin{gathered} d=2r \\ d=2\cdot9 \\ d=18\operatorname{cm} \end{gathered}[/tex]The calculation for the diameter is:
d=2r
d=2*9
d=18cm
So the circumference of a circle with diameter 18cm is:
[tex]\begin{gathered} C=18\pi \\ C\cong56.548\operatorname{cm} \end{gathered}[/tex]For this balloon:
C=18π
C≅56.548xm
Which number is irrational? A. 0.656656665... B. 0.78 C. 2.35 D. 꼭
can be expressed as a fraction:
[tex]\frac{39}{50}[/tex]Therefore, it is a rational number
[tex]2.35[/tex]Can be expressed as a fraction:
[tex]\frac{47}{20}[/tex]Therefore, it is a rational number
However:
[tex]0.656656665[/tex]can't be expressed as a fraction, therefore, it is an irrational number
Add these fractions using fraction bars after choosing a common denominator Use the fraction bar inactivate to find the difference
The fractions you have to add are 1/3 and -5/6
[tex]\frac{1}{3}+(-\frac{5}{6})[/tex]The denominators are "3" and "6"
The common denominator between both numbers is 6.
6*1=6
3*2=6
Multiply 1/3 by factor 2 so that both fractions will have the same denominator
[tex]\frac{1}{3}\cdot2=\frac{1\cdot2}{3\cdot2}=\frac{2}{6}[/tex]Now you can add both fractions
[tex]\frac{2}{6}+(-\frac{5}{6})=\frac{2}{6}-\frac{5}{6}=\frac{2-5}{6}=-\frac{3}{6}[/tex]The result is not in its most reduced form, to siplify the fraction divide both the numerator and denominator by 3
[tex]-\frac{3}{6}\div3=-\frac{1}{2}[/tex]The result is -1/2, in the number line:
what kind of triangle congruence would i put for the last reason?
Looking at the diagram, The last statement means that trangle PQS is congruent to triangle RSQ. This means that
line PQ is equal to line RS
line QS is equal to line SQ
angle Q is equal to angle S
Thus, the reason would be
Side Angle Side(SAS)
Two sides and one angle are equal or congruent
whats x+7, y equals and how do i find it?
The figure HGD was translated 7 units right; and then it was translated 9 units up. This can be shown as:
(x, y) → (x + 7, y + 9)
Answer = 9
You are researching the speed of sound waves in dry air
at 86°F. The linear function d = 0.217t represents the distances d (in miles) sound waves
travel in t seconds.
A. Represent the situation using a table and a graph.
B. Which of the three representations would you use to find how long it takes sound waves to travel 0.1 mile in dry air at 86°F? Explain.
By observing the pace at which this compressed region moves through the medium, we may determine the sound speed.The speed of sound is roughly 343 meters per second or 767 miles per hour in dry air at 20 degrees Celsius.
Calculate speed of sound wave?
The formula for the airborne sound speedThe equation for the speed of sound in air as a function of absolute temperature is given by the simplification of v=RTM:v=√γRTM=√γRTM(273K273K)=√(273K)γRM√T273K≈331m 2) Time required for 1620m to be traveled at that speed: t = d / v 0.217m / 0.1 m/s) = 2.17m/ s from the beginning of the sound wave.Since you were watching the lightning, you might have wanted to know the time.Then, using the speed of light, you can determine how long it was between the lights being generated o.217 meters distant from you and Light travels at a speed of3*108 m/s, hence t = 0.217m / (3*108 m/s) = 0.000669 s.
The answer is o.000669 s, as determined in step 2, even though this time is entirely negligible.
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Arc Length Formula:: Cx = degree measure of arcC-circumferenceDirections: Find each arc length. Round to the nearest hundredth.10. If EB = 15 cm, find the length of CD. 11. IF NR = 8 ft, find the length of NMP.DC12. IF VS = 12 m, find the length of UT.13. If JH = 21 in, fnd the length of KJG.12759DBS14. If FG = 27 yd, find the length of FED.15. If WS = 4.5 mm, find the length of TS.4780128317.62
Arc length formula:
[tex]\begin{gathered} \text{Arc length=}\frac{x}{360}\cdot C \\ \\ C=2\pi r \\ r=\text{radius} \end{gathered}[/tex]____________________________
10. r= 15cm
Angle CED is supplementary with angle BEC (add up to 180°)
[tex]\begin{gathered} m\angle\text{CED}+m\angle\text{BEC}=180 \\ \\ m\angle CED=180-m\angle BEC \\ m\angle CED=180-68 \\ m\angle CED=112 \end{gathered}[/tex]Then, arc CD is:
[tex]\begin{gathered} CD=\frac{112}{360}\cdot2\pi(15\operatorname{cm}) \\ \\ CD\approx29.32\operatorname{cm} \end{gathered}[/tex]___________________________________________________
11. r=8ft
The measure of central angle MRQ is equal to the measure of the given arc MQ (162°) and this angle and angle NRP are vertical angles (have the same measure) then, angle MRN and QRP (also vertical angles) need to add up 360° with the other angles, use it to find the measure of angle MRN:
[tex]\begin{gathered} m\angle NRP+m\angle NRP+m\angle MRN+m\angle QRP=360 \\ \\ 2m\angle NRP+2m\angle MRN=360 \\ 2(162)+2m\angle MRN=360 \\ 324+2m\angle MRN=360 \\ 2m\angle MRN=360-324 \\ m\angle MRN=\frac{36}{2} \\ \\ m\angle MRN=18 \end{gathered}[/tex]The angle for arc NMP is equal to the sum of angle MRP (180°) and angle MRN (18°).
Then, the length of arc NMP is:
[tex]\begin{gathered} \text{NMP}=\frac{180+18}{360}\cdot2\pi(8ft) \\ \\ \text{NMP}=27.65ft \end{gathered}[/tex]___________________________
Select the similarity transformation(s) that make ABCD similar to EFGH.
Answer:
D
F
Explanation:
We would compare the coordinates of the corresponding vertices of rectangles ABCD and EFGH. We would compare vertices A and E. From the information given,
A = (1, - 2)
E = (- 2, 4)
If we apply (x, y)---(- x, - y) to A, it becomes (- 1, - - 2) = (- 1, 2)
If we apply (x, y)---(2x, 2y) to (- 1, 2), it becomes (2 * - 1, 2 * 2) = (- 2, 4)
Thus, the correct similarity transformation(s) that make ABCD similar to EFGH are
D
F
Question 2 A recipe for homemade modeling clay requires 4 parts plain flour to 1 part cornstarch. Indicate whether each set of ingredients below is proportional to the recipe. Proportional Not Proportional 8 cups plain flour and 2 cups cornstarch 20 cups plain flour and 5 cups cornstarch 2 cups plain flour and 1 cup cornstarch Next Question Check Answer Privacy and Cookies | Terms of Use | Minimum Frequirements | Platform Status 2021 McGraw-HI Education. All Rights Reserved
The given ratio is 4 parts of plain flour to 1 part of cornstarch.
So, each recipe with the same ratio will be the answer.
As you can observe, the first choice is proportional because the plain flour is 4 times the cornstarch.
The second choice is proportional too because the plain flour is 4 times the cornstarch.
However, the last choice is not proportional because it has a ratio of double, which is not correct.
24 miles is to 1 gallon of gas as 60 miles is to 2.5 gallons of gas Choose the correct letter
Since 24 miles is to 1 gallon of gas as 60 miles is to 2.5 gallons of gas
These are 2 equal ratios, then
They will be 2 equal fractions
[tex]\frac{24\text{ miles}}{1\text{ gallon}}=\frac{60\text{ miles}}{2.5\text{ gallons}}[/tex]The correct answer is D
Lloyd is standing near a telephone pole. When his head touches the support wire, he is 25 feet from where the wire meets the ground. Lloydis 5 ft tall. Hon tallis the pole?1-8f feetO A 20 ft.B. 15 ftC. 80 ft.D. 17 ft
We will use the pythagorean theorem to figure the answer out.
Applying the Pythagorean Theorem, we have (let unknown side be x):
[tex]\begin{gathered} 6^2+x^2=10^2 \\ 36+x^2=100 \\ x^2=100-36 \\ x^2=64 \\ x=\sqrt[]{64} \\ x=8 \end{gathered}[/tex]Answer 8 feet (B)1 litre=1000cm³. About how many test tubes, each holding 24cm³ of water, can be filled from a
1 litre flask?
Answer: 125/3 or about 41.667
Note that you can't have 2/3 of a test tube, so the expected answer may be 42 test tubes.
Step-by-step explanation:
Write a simple algebra equation using the word problem
24x = 1000
x represents the number of test-tubes, each of which hold 24cm^3 of water.
divide both sides by 24
x = 125/3 or about 41.667
(Score for Question 1: ___ of 5 points)1. Wendy wants to find the width, AB, of a river. She walks along the edge of the river 300 ft and markspoint C. Then she walks 80 ft further and marks point D. She turns 90° and walks until her location,point A, and point C are collinear. She marks point E at this location, as shown.AriverAD 80 ft300 ftBE(a) Can Wendy conclude that AABC and AEDC are similar? Why or why not?(b) Suppose DE = 50 ft Calculate the width of the river, AB. Show all your work.Answer
We know that two triangles are similar if two pairs of corresponding angles are equal.
In this case, we have:
• Angles EDC and ABC are right angles. Then, these angles are equal.
,• Angles DCE and ACB are ,vertical angles,. In other words, they are opposite angles made by two intersecting lines. Vertical angles are ,congruent,, then these angles are equal.
AnswerSince the above condition is fulfilled, triangles ABC and EDC are similar.
Part b)When two triangles are similar, their corresponding sides are in the same ratio.
[tex]\frac{a}{e}=\frac{b}{d}=\frac{c}{c^{\prime}}[/tex]Then, we can write and solve the following equation:
[tex]\begin{gathered} \frac{300ft}{80ft}=\frac{c}{50ft} \\ 3.75=\frac{c}{50ft} \\ \text{ Multiply by 50ft from both sides} \\ 3.75*50ft=\frac{c}{50ft}*50ft \\ 187.5ft=c \end{gathered}[/tex]AnswerThe width of the river is 187.5 feet.
For the function f(x)5x – 2, what does the x represent?
The given function is
f(x) = 5x - 2
If we are given a function f(x), the x is called argument of the function.
You just have to pass argument x to get the value of f(x).
Rewrite the polynomial expression using the GCF: 4x^2+8x+24 ?What is the new polynomial expression
GCF of 4,8 and 24
is. = 4
Then new expression is
y = 4• (x^2 + 2x + 6)
Select the correct answer.
What is the approximate value of this logarithmic expression?
log5 18
The logarithms as a sum or difference of logarithms, using the power rule if necessary, to expand them.
The approximate value exists [tex]$\log _5 18 \approx 1.80$[/tex].
What is meant by logarithmic expression?An equation using the logarithm of an expression containing a variable is referred to as a logarithmic equation. Check to verify if you can write both sides of the equation as powers of the same number before attempting to solve an exponential equation.
Write logarithms as a sum or difference of logarithms, using the power rule if necessary, to expand them. Utilizing the quotient rule, product rule, and power rule in that order is frequently beneficial.
The change of base formula can be used.
[tex]$\log _5(18)=\frac{\log 18}{\log 5} \approx \frac{1.25527}{0.69897} \approx 1.7959$$[/tex]
simplifying the above equation, we get
[tex]$\log _5 18 \approx 1.80$[/tex]
Therefore, the correct answer is option B. 1.80.
The complete question is:
Select the correct answer.
What is the approximate value of this logarithmic expression? [tex]$\log _5 18$[/tex]
A. 1.28
B. 1.80
C. 0.56
D. 2.89
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PLEASE HURRY!!!!!
Here is a hanger diagram. With a hanger diagram, when the diagram is balanced, there is equal weight on each side. Write an equation to represent the hanger. (Do NOT put spaces in your answer.)
Answer:
x = 8
x = 3
x = 2
x = 1
x = 1
x = 2
x + x+ x+ x+ x+ 2 = 17
try any number
Tom Blasting invested $4,500 in an investment paying 10% compounded quarterly for 3 years. Find the interest
Given that Tom invested $4500 in an investment paying 10% compounded quarterly for 3 years.
We have to find the interest for the given time period.
We know that the formula of amount on a principal P, rate r per annum, time t years where interest is compounding quarterly is:
[tex]A=P(1+\frac{r}{4})^{4t}[/tex]Here, P = 4500, r = 0.1 and t = 3. So,
[tex]\begin{gathered} A=4500(1+\frac{0.1}{4})^{4(3)} \\ =4500(1+0.025)^{12} \\ =4500(1.025)^{12} \\ =4500(1.3448) \\ =6051.6 \end{gathered}[/tex]So, the amount we get is $6051.6.
Now, it is known that the interest is the difference between the amount and the principal. So,
[tex]\begin{gathered} \text{ interest}=\text{ amount-principal} \\ =6051.6-4500 \\ =1551.6 \end{gathered}[/tex]Thus, the interest is $1551.6.
Write the expression as a sum and/or difference of logarithms. Express powers as factors
We will have the following:
[tex]\begin{gathered} ln(x^3\sqrt{6-x})=ln(x^3)+ln(\sqrt{6-x}) \\ \\ =3ln(x)+\frac{1}{2}ln(6-x) \end{gathered}[/tex]A shellfish absorbed 40% of the heavy metals in the water in and just the concentration of heavy metals is 0.0002 mg/m³ .The shellfish ingests 4 L of water per hour. How many heavy metal does it absorb in 3 months? (Assume there are 30 days in a month there are 1000 L in one cubic meter)
Answer:
Step-by-step explanation:
simplify 425xy⁴/25xy²
We have the expression
[tex]\frac{425xy^4}{25xy^2}[/tex]We can already simplify x because it's both on the numerator and denominator
[tex]\frac{425y^4}{25y^2}[/tex]Now we can simplify 425/25 = 17
[tex]\frac{17y^4}{y^2}[/tex]Remember that
[tex]\frac{a^n}{a^m}=a^{n-m}[/tex]Then
[tex]17y^{4-2}=17y^2[/tex]The final result is
[tex]17y^2[/tex](A) A shipment of 10 cameras will likely have 6 defectives. If a person buys 2 cameras, what is the probability of getting 2 defectives?(B) What are the odds in favor of getting a defective camera?
To solve the exercise, you can use the formula of the binomial distribution:
[tex]\begin{gathered} P(x)=\binom{n}{x}p^x(1-p)^{n-x} \\ \text{ Where } \\ n\text{ is the number of trials (or the number being sampled)} \\ x\text{ is the number of successes desired} \\ p\text{ is the number of getting a success in one trial} \end{gathered}[/tex]So, in this case, we have:
[tex]\begin{gathered} n=10 \\ p=\frac{6}{10}=0.6 \end{gathered}[/tex]Because "success" is that there are defective cameras, 6 defective cameras out of 10 in total.
For part A, we have:
[tex]\begin{gathered} x=2 \\ P(x)=\binom{n}{x}p^x(1-p)^{n-x} \\ P(2)=\binom{10}{2}\cdot0.6^2\cdot(1-0.6)^{10-2} \\ P(2)=\binom{10}{2}\cdot0.6^2\cdot(0.4)^8 \\ P(2)=45\cdot0.36\cdot0.00065536 \\ P(2)=0.0106 \end{gathered}[/tex]Therefore, the probability of getting 2 defective cameras is 0.0106.
For part B, we have:
[tex]\begin{gathered} x=1 \\ P(x)=\binom{n}{x}p^x(1-p)^{n-x} \\ P(1)=\binom{10}{1}\cdot0.6^1\cdot(1-0.6)^{10-1} \\ P(1)=\binom{10}{1}\cdot0.6^1\cdot(0.4)^9 \\ P(1)=10\cdot0.6\cdot0.000262144 \\ P(1)=0.0016 \end{gathered}[/tex]Therefore, the probability of getting one defective camera is 0.0016.
A grocery store sales for $522,000 and a 25% down payment is made a 20 year mortgage at 7% is obtain compute and amortization schedule for the first three months round your answer to two Decimal place if necessary
The value of the mortgage (the real amount to be financed) is A = $391,500.
The annual interest rate is r = 7%. We must convert it to montly decimal rate:
r = 7 / 12 / 100 = 0.005833
Note: The decimals will be kept in our calculator. Only two decimal places will be shown in the results.
The monthly payment is R = $3,034.13 which includes interest and principal.
For the first month, the loan has not been paid upon, so the interest for this period is:
I = $391,500 * 0.005833 = $2,283.75
From the monthly payment, the portion that goes to pay the principal is:
$3,034.13 - $2,283.75 = $750.38
So the new balance of the loan is:
$391,500 - $750.38 = $390,749.62
Thus, for payment 1:
Interest - Payment on Principal - Balance of Loan
$2,283.75 - $750.38 - $390,749.62
Repeating the calcuations for the second payment:
The interest for this period is:
I = $390,749.62 * 0.005833 = $2,279.37
From the monthly payment, the portion that goes to pay the principal is:
$3,034.13 - $2,279.37 = $754.76
So the new balance of the loan is:
$390,749.62 - $754.76 = 389,994.86
The table is updated as follows:
Interest - Payment on Principal - Balance of Loan
$2,283.75 - $750.38 - $390,749.62
$2,279.37 - $754.76 - $389,994.86
For the third month:
The interest for this period is:
I = $389,994.86 * 0.005833 = $2,274.97
From the monthly payment, the portion that goes to pay the principal is:
$3,034.13 - $2,274.97 = $759.16
So the new balance of the loan is:
$389,994.86 - $759.16 = $389,235.70
The final updated table is:
Interest - Payment on Principal - Balance of Loan
$2,283.75 - $750.38 - $390,749.62
$2,279.37 - $754.76 - $389,994.86
$2,274.97 - $759.16 - $389,235.70
Sarah needs to lease out a music studio to record her new album. The studio chargesan initial studio-use fee plus an hourly fee for each hour in the studio. The fixed fee touse the studio is $150 and the total cost charged for 2 hours is $300. Write anequation for P, in terms of t, representing the amount of money Sarah would have topay to use the studio for t hours.
Fixed fee is 150
Total cost for 2 hours is 300
If the fixed fee is 150, and Sarah paid 300, then she paid 150 for the fixed fee and anohter 150 for the two hours, that means that each hour is 75
Then we can write the equation:
P = 75t + 150
Answer:
P = 75t + 150
Trying to figure out this for my home work assignment
Given:
Choosing a even number from the numbers between 1 and 10.
The sample space is
[tex]\mleft\lbrace2,3,4,5,6,7,8,9\mright\rbrace[/tex]Let A be the event of choosing a even number.
There are 4 out comes in the experiment.