Tools Question 2 Nicolas makes toys at a toy shop. The graph represents the relationship between the number of toys (1) that Nicolas makes and the number of hours Toy Making 50 45 40 35 30 Number of Toys 25 20 15 10 2 6 10 Number of Hours Which of the following equations represents a toy-making rate, in toys per hour, that is HALF that of Nicolas's toy-making rate?

Tools Question 2 Nicolas Makes Toys At A Toy Shop. The Graph Represents The Relationship Between The
Tools Question 2 Nicolas Makes Toys At A Toy Shop. The Graph Represents The Relationship Between The

Answers

Answer 1

The equation of a proportional relationship between two variables x and y with a constant of proportionality k, is:

[tex]y=kx[/tex]

If y represents the number of toys and x represents the number of hours, substitute the corresponding values of x and y to find the constant of proportionality k. Use, for instance, the fact that Nicholas made 40 toys in 10 hours:

[tex]40=k\cdot10[/tex]

Divide both sides of the equation by 10:

[tex]k=4[/tex]

Since Nicholas's toy-making rate is 4 toys per hour, half that rate would be 2 toys per hour. Then, out equation would become:

[tex]y=2x[/tex]

Using the letter "t" for toys instead of y and "h" for hours instead of x, then:

[tex]t=2h[/tex]


Related Questions

The number of hours it takes for ice to melt varies inversely with the air temperature. A block of ice melts in 2.5 hours whenthe temperature is 54 degrees.How long would it take for the same block of ice to melt if the temperature was 45 degrees?

Answers

Let t be the time in hours it takes a block of ice to melt at T degrees.

Since both variables have an inverse relation, we can say that:

[tex]t=\alpha\cdot\frac{1}{T}[/tex]

Where alpha is a constant value.

Since we know that a block of ice melts in 2.5 hours when the temperature is 54 degrees, we can plug in such data and find alpha as following:

[tex]\begin{gathered} 2.5=\alpha\cdot\frac{1}{54}\rightarrow2.5\cdot54=\alpha \\ \Rightarrow\alpha=135 \end{gathered}[/tex]

Therefore, our expression would be:

[tex]t=\frac{135}{T}[/tex]

For T = 45,

[tex]\begin{gathered} t=\frac{135}{45} \\ \\ \Rightarrow t=3 \end{gathered}[/tex]

We can conclude that it would take 3 hours for the block of ice to melt.

Suppose 72% of students chose to study French their freshman year, and that meant that there were 378 such students. How many students chose not to take French their freshman year?

Answers

As per the given percentage, there are 147 students are not take French their freshman year.

Students:

The students are the person formally engaged in learning, especially one enrolled in a school or college.

Given,

Suppose 72% of students chose to study French their freshman year, and that meant that there were 378 such students.

Here we need to find the number of students who are not take French as their freshman year.

Let x be the total number of students in the freshman year.

So according to the given question, we know that,

72% of x = 378

Therefore, we have to find the value of x, so we have to move the others,

Then we get,

x = 378/72%

x = 378 x 100/72

x = 525

So, the total number of students are 525.

Then the students who are not taken French is,

=> 525 - 378 = 147

Therefore, the students who are not taken French is 147.

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Question 10The table below shows the amount of water that is in a bathtub that is being filled.Minutes1234Gallons ofWater12172227Which of the following functions could model the amount of gallons of water, f(x), that the bathtub will contain after x minutes of being filled?Аf(x) = 5x + 7Bf(x) = 5x + 12сf(x) = 7x + 5Df%) = 12x + 5No

Answers

[tex]\begin{gathered} x=\text{ number of minutes} \\ f(x)=\text{amount of gallons of water the bathtub will contain} \\ \text{The function that fit the table is } \\ f(x)=5x+7 \end{gathered}[/tex]

5 tons of rocks cost $7,000.00. What is the price per pound ??

Answers

Answer: Per rock or pound?

it says on top that the image is not drawn to scale.

Answers

D; Both statements are correct

Here, we want to check the correct statement

Basically from the diagram, it is confirmed that what we have is a 30-60-90 triangle

Now, for a 30-60-90 degrees triangle, the side lengths are in a particular ratio

From the diagram, MO faces the right angle and thus, it is the longest side and the hypotenuse

Now, let us take a look at the ratio of the sides in both submissions

For a 30-60-90 degrees triangle, the ratio of the sides is;

[tex]1\colon\sqrt[]{3}\text{ :2}[/tex]

Hence, one side must be twice the length of the other

From Kellie's statement we can see MO is twice NO

From Eddie's statement, we can also see that MO is twice NO

Lastly, we can also see in both that dividing MN by NO yields the root of 3 in both statemets which confirms the existence of the theoretical ratio

So the conclusion here is that;

Both students are correct

on a map where each unit represents one kilometer two marinas are located at p(4,2) and q(8,12). if a boat travels in a straight line from one marina to the other how far does the boat travel. Answer choices: 14 kilometers 2sqrt296 kilometer 2sqrt5 kilometers

Answers

Solution:

Given the points below

[tex]p\left(4,2\right)and\text{ }q\left(8,12\right)[/tex]

To find the distance between two points, the formula is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Where point p represents coordinates 1 and point q represents coordinates 2

Substitute the coordinates into the formula above

[tex]\begin{gathered} d=\sqrt{(8-4)^2+(12-2)^2} \\ d=\sqrt{4^2+10^2} \\ d=\sqrt{16+100} \\ d=\sqrt{116} \\ d=\sqrt{4\times29} \\ d=2\sqrt{29}\text{ units} \end{gathered}[/tex]

Since, 1 unit represents 1 kilometer on the map,

Hence, the answer is

[tex]2\sqrt{29}\text{ km}[/tex]

In the distribution shown, state the mean and the standard deviation. Hint: The vertical lines are 1 standard deviation apart.

Answers

We are given a distribution graph.

The mean of the distribution is the center that is 125.

[tex]\operatorname{mean}=\mu=125[/tex]

The standard deviation is given by

[tex]std=\sigma=153-125=28[/tex]

Therefore, the mean of the distribution is 125 and the standard deviation is 28.

How many times larger is 8.1 than 2.7

Answers

8.1 is 5.4 more times larger than 2.7

Four of the twelve members of the panel were late for
the meeting. What fraction of the members were on
time?

Answers

Answer:

2/3

Step-by-step explanation:

If 4 were late, then 8 were on time.

8/12  Divide the top and bottom by 4

2/3

Solve tan(x){tan(%) - 1) = 0 O A. x = 5 + 27T7,X = 3 37 + 27 O B. x = -2779,x=37 + X +277, X = +27 2. C. X = +19,X = = tnx +277 O D. X = n,X = x FT 4

Answers

Given the trigonometry equation below,

[tex]\tan (x)(\tan (x)-1)=0[/tex]

Solving each part separately

[tex]\begin{gathered} \tan \mleft(x\mright)=0\quad \mathrm{or}\quad \tan \mleft(x\mright)-1=0 \\ x=\tan ^{-1}0\text{ or tan(x)=1} \\ x=\pm n\pi\text{ }or\text{ }x=tan^{-1}1 \\ x=\pm n\pi\text{ or x=45} \\ x=\pm n\pi\text{ or x=}\frac{\pi}{45}\pm n\pi \end{gathered}[/tex]

Therefore,

[tex]x=\pm n\pi,\text{ x=}\frac{\pi}{45}\pm n\pi[/tex]

Hence, Option D is the correct answer.

2. A membership to the theme park is $48 per year. Marcos cancelled his membership early and is only required to pay for 0.25 of a year. How much will he need to pay?

Answers

Marcos needs to pay $12 for 0.25 of a year due to cancelling the membership

Membership cost to the theme park per year = $48

Payment required to be made by Marcos = 0.25 of a year

When we divide a whole into smaller parts, we get decimals. Then, there are two parts to a decimal number: a whole number part and a fractional part. The whole component of a decimal number has the same decimal place value system as the complete number. However, as we proceed to the right following the decimal point, we obtain the fractional portion of the decimal number.

Converting the decimal into a fraction we get:

=0.25

= 25/100

= 1/4 of a year

So, Marcos needs to pay the membership fees for only 1/4 of a year

According to which we get: 48*1/4 = $12

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To rent a certain meeting room, a college charges a reservation fee of $46 and an additional fee of $6.70 per hour. The math club wants to spend less than$106.30 on renting the meeting room.What are the possible amounts of time for which they could rent the meeting room?Use t for the number of hours the meeting room is rented, and solve your inequality for t.

Answers

As given by the question

There are given that the college charges a reservation fee of $46.

Now,

According to the question, the inequality is:

[tex]46+6.70t<106.30[/tex]

Then,

To solve the above inequality, collect the constant terms on the right side

So,

[tex]\begin{gathered} 46+6.70t<106.30 \\ 6.70t<106.30-46 \\ 6.70t<60.3 \\ t<\frac{60.3}{6.70} \\ t<9 \end{gathered}[/tex]

Hence, the room could be rented for up to 9 hours less than the stated amount.

Find sinθ, tanθ, and secθ, where θ is the angle shown in the figure. Give exact values, not decimal approximations.sinθ=tanθ=secθ=

Answers

[tex]undefined[/tex]

1) We have here a right triangle, so we can use the Pythagorean Theorem to find the adjacent leg. Note that the hypotenuse is leg opposite to the right angle. In this case, a=4.

a²=b²+c²

4²=b²+3²

16=b²+9

16-9=b²

b=√7

2) Let's find the trigonometric functions. The first one is the sine (θ), which relates the opposite side and the hypotenuse:

[tex]\sin (\theta)\text{ =}\frac{3}{4}[/tex]

2.2)Moving on, we can deal with the tangent of theta, relating the opposite side over the adjacent, for this one we have to rationalize it:

[tex]\begin{gathered} \tan (\theta)\text{ =}\frac{3}{\sqrt[]{7}} \\ \tan (\theta)=\frac{3\sqrt[]{7}}{7} \end{gathered}[/tex]

Finally, let's find the reciprocal function of the cosine function by setting this as the reciprocal of the cosine, and then calculating it:

[tex]\begin{gathered} \sec \text{ (}\theta)=\frac{1}{\cos(\theta)}\Rightarrow\sec (\theta)=\frac{1}{\frac{\sqrt[]{7}}{4}}\Rightarrow\sec (\theta)\text{ =}\frac{4}{\sqrt[]{7}} \\ \sec (\theta)\text{ =}\frac{4\sqrt[]{7}}{7} \end{gathered}[/tex]

PLS HELP WILL MARK YOU BRAINLIEST!!

Point B is the midpoint of AC. AB=2x and AC=3x+20.
What is the value of x?
x=-20
x=20
x=4
x=6

Answers

Answer:

X=4

Step-by-step explanation:

i got the answer on a different app

Answer: The correct answer is 20 or -20

Step-by-step explanation:

its between 20 and -20 since i selected x=6 and x=4 and they were both wrong lol

Write the inequality shown by the shaded region in the graph with the boundary line y = -3x +5

Answers

Inequality is an inequality comparison of numbers or expressions.

Given inequality:

y < -3x+5, y < x+2, y < -1

Graph the above inequality using Geogebra's online graphing calculator.

Answer:

...................... Hoffe er u

Choose the equation that represents a line that passes through points (−3, 2) and (2, 1)

5x + y = −13
5x − y = 17
x − 5y = −13
x + 5y = 7

Answers

The equation that represents a line that passes through points (−3, 2) and (2, 1) is x + 5y = 7.

How to find the equation of a line?

The equation of the line passes through the points  (−3, 2) and (2, 1).  The equation of the line can be represented as follows;

y = mx + b

where

m = slopeb = y-intercept

Therefore, let's find the slope using  (−3, 2) and (2, 1)

m = slope =  1 - 2 / 2 + 3

m = - 1 / 5

Therefore,

slope = - 1 / 5

Let's find the y-intercept of the line using (2, 1)

y = - 1 / 5 x + b

1 = - 1 / 5 (2) + b

b = 1 + 2 / 5

b =  5 + 2/ 5

b = 7 / 5

Therefore, the equation of the line can be represented as follows:

y = - 1 / 5 x + 7 / 5

5y = -x + 7

5y + x = 7

x + 5y = 7

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What is the exact decimal equivalent of 7/12​

Answers

Answer:


0.58333333333

Rajan climbed to a height of 15 ft from the bottom of a climbing wall. He then climbed up an additional 10 ft.

What must he do to return to the bottom of the climbing wall?

In the first blank, say whether Rajan must climb up or down. In the second blank, state the number of feet Rajan must travel up or down.

Rajan must climb_____ft to return to the bottom of the climbing wall.

Answers

Rajan must climb down 25 ft to return to the bottom of the climbing wall

Height climbed from the bottom of the wall = 15ft

Height: The measurement of an object's height from the base to the top is known as height. It is sometimes referred to as altitude in geometry. The vertical distance between the lowest and highest point is measured. In coordinate geometry, it is often the measurement along the y-axis of an object.

Additional height climbed = 10ft

Total height climbed = 25ft

He should climb down the distance, as climbing up will further move him away from the bottom of the wall

Distance to climb down to the bottom of the wall = 25ft

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can you help me factor the expression x^2+4x-21

Answers

To factor this expression we need to find two numbers which sum is 4 and the product is -21.

Now, 21 has only 2 factors (besides 1 and 21), 7 and 3, se we need to write them in a way such that they sum 4, so

[tex]x^2+4x-21=(x+7)(x-3)[/tex]

we see that 7-3=4 and 7(-3)=-21, so the factorization is correct.

Jolie is redesigning a water bottle to fit better in her cup holder. The diameter will have to be no larger 2.5 in. The water bottle is straight up and down. What would the height of the bottle be if she wants it to have a 99.34 in3 volume. (Round to nearest whole number)

Answers

Answer:

20in

Explanations:

The water bottle in question is known to be cylindrical in shape. The formula for calculating the volume of a cylinder is expressed as:

[tex]V=\pi r^2h[/tex]

where;

r is the radius

h is the height

Given the following parameters

diameter = 2.5in

radius = 2.5/2 = 1.25in

volume = 99.34 in^3

Required

Height of the water bottle

Substitute the given parameters intothe formula

[tex]\begin{gathered} 99.34=3.14(1.25)^2\times h \\ 99.36=4.90625h \\ h=\frac{99.36}{4.90625} \\ h=20.25\approx20in \end{gathered}[/tex]

The height of the water bottle will be 20in

I just need to know how to work it out for future problems. (Business Calc)
Find the price elasticity of the demand function as a function of p.
1. q=D(p)=600-3p
A)E(p)= p/p-200
B)E(p)= p/600-3p
C)E(p)= p/200-p
D)E(p)= p(200-p)

Answers

The price elasticity of the demand function as a function of p is C. E(p)= p/200-p

How to illustrate the information?

It should be noted that the price elasticity of demand simply means the ratio of the percentage change in quantity demanded to the percentage change in price.

In this case, the function is given as:

q = D(p) = 600-3p

Differentiate with respect to p

D'(p) = 3

The elasticity of demand will be:

= (P / 600 - 3p) × (-3)

= P / (200 - P)

In conclusion, the correct option is C.

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(Solve the problem down below & simplify the answer. Round to the nearest hundredth as needed.)

Answers

From the given information, we know that the decreasing function values is

[tex]V(t)=3600(3^{-0.15t})[/tex]

and we need to find the time t when V(t) is equal to $1200. Then by substituting this values into the function, we have

[tex]1200=3600(3^{-0.15t})[/tex]

By dividing both sides by 3600, we get

[tex]3^{-0.15t}=\frac{1200}{3600}=\frac{1}{3}[/tex]

So we have the equations

[tex]3^{-0.15t}=\frac{1}{3}[/tex]

From the exponents properties, we know that

[tex]3^{-0.15t}=\frac{1}{3^{0.15t}}[/tex]

so we have

[tex]\frac{1}{3^{0.15t}}=\frac{1}{3}[/tex]

or equivalently,

[tex]3^{0.15t}=3[/tex]

This means that

[tex]0.15t=1[/tex]

Then, by dividing both sides by 0.15, we obtain

[tex]t=\frac{1}{0.15}=6.6666[/tex]

So, by rounding to the nearest hundreadth, the answer is 6.67 years

Can you please help me solve this questions. I want a clear explanation thank you.

Answers

Given:

[tex]\begin{gathered} \text{Mean}=\mu=21.4 \\ \text{Standard deviation=}\sigma=5.0 \\ \text{Smple size=n=66} \end{gathered}[/tex]

The z-score for 90 percent is 1.64.

To find the 90 percent confidence interval,

[tex]\begin{gathered} \mu+(\frac{\sigma}{\sqrt[]{n}}\times1.64)=21.4+(\frac{5}{\sqrt[]{66}}\times1.64) \\ =21.4+1.0094 \\ =22.4094\ldots\ldots(\text{ upper limit)} \\ \text{And} \\ \mu-(\frac{\sigma}{\sqrt[]{n}}\times1.64)=21.4-(\frac{5}{\sqrt[]{66}}\times1.64) \\ =21.4-1.0094 \\ =20.3906\ldots\ldots\ldots(\text{lower limit)} \end{gathered}[/tex]

Answer: The 90 % confidence interval is ( 20.3906 , 22.4094 )

convert these measurements to centimeters : (a)73.1 cm and (b) 0,0012km​

Answers

Answer:

(a) 73.1 cm (b) 120 cm

Step-by-step explanation:

Step-by-step explanation:

Part (a)

73.1 cm                 [It remains the same as it is already given in cms]

Part (b)  

To convert 0.0012km to cm we multiply x 100000

=> 0.0012 x 100000

=> 120 cm

Find X.

Cirucumscribed angles

Answers

Answer:

x = 64

Step-by-step explanation:

to find x add make an equation to solve for x. the equation is 90+90+44+2x+8=360. after solving for x, x will equal 64.

All eleven letters from the word MATHEMATICS are written on individual slips of paper and placed in a hat. If you reach into the hat and randomly choose one slip of paper, what are the odds against the paper having a vowel written on it?

Answers

Let:

A = Get a paper having a vowel written on it

N = Total number of letters = 11

a = Number of vowels = 4

so:

[tex]\begin{gathered} P(A)=\frac{a}{N} \\ P(A)=\frac{4}{11} \\ P(A)\approx0.36 \end{gathered}[/tex]

Answer:

36%

(3ax - n) ÷ 5
Solve for X.

Answers

Answer:

x = 10/a; restrictions a ± 0

Answer:

[tex]x = \cfrac{n+5}{3a}[/tex]

=============================

Given expression

[tex](3ax - n) : 5 = 1[/tex]

Solve it for x in steps below:

[tex]3ax - n = 5[/tex][tex]3ax = n + 5[/tex][tex]x = \cfrac{n+5}{3a}[/tex]

I dont know how to answer this pls help

Answers

The hedgehog's total change in weight is -2.5 ounces.

What is the total change in weight?

A relationship is proportional if the ratio of the variables is constant. The variables can either increase or decrease at a constant rate. A proportional relationship can be modelled with a linear equation.

Ratio = change in weight / days of hibernation

-0.18 / 9 = -0.02

-0.56 / 28 = -0.02

-1.44 / 76 = -0.02

-1.96 / 98 = -0.02

Weight when the day of hibernation is 125 = number of days x ratio

125 x -0.02 = -2.5

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A person tosses a coin 14 times. In how many ways can he get 10 heads?

Answers

probability 50% for each side
14 times 14 =196 divided by 2 = 98
10 times 10 = 100 divided by 2 = 50
He can get 10 heads 50 different ways

which number is the closest approximation to the value of 3/94?

Answers

Answer:

[tex] \frac{1}{3} [/tex]

Step-by-step explanation:

[tex] \frac{3}{94} = 0.31 \\ \\ \frac{1}{3} = 0.33[/tex]

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What is the probability thata student who passed the test did not complete the homework?Passed the test Failed the testCompleted the homework112.2Did not complete the homework3N which statement most accurately describes one way that either Judeo-Christan principles or Greco-Roman principles have influenced modern democracy For what value of x will 3x + 4 = x - 6 be a true statement?A x = -5. x = -5/2C x = -1D x = - 1/2 The equation of Line 1 is y=-2x + 7. Line 2 passesthrough the points (2, 3) and (4, 4). Which statementis true about Line 1 and Line 2?Line 1 and Line 2 are perpendicularO Line 1 is longer than Line 2Line 1 has the same y-intercept as Line 2Line 1 and Line 2 are parallel question 23 which statement about fat replacers is false? a. fat-based fat replacers are heat stable and used in cake mixes. b. olestra is an artificial fat that delivers a small amount of energy. c. they provided the taste and texture of fats, but with fewer kcalories. d. olestra is fortified with vitamins a, d, e, and k. e. carbohydrate-based fat replacers are used as thickeners in soups. Which sentence in this excerpt from Mark Twain's "The 1,000,000 Bank-Note" is an example of satire?A. I was admitted by a gorgeous flunkey, and shown into a sumptuous room where a couple of elderly gentlemen were sitting.B. They had just finished their breakfast, and the sight of the remains of it almost overpowered me.C. I could hardly keep my wits together in the presence of that food, but as I was not asked to sample it, I had to bear my trouble as best I could.D. Now, something had been happening there a little before, which I did not know anything about until a good many days afterwards, but I will tell you about it now.E. Those two old brothers had been having a pretty hot argument a couple of days before, and had ended by agreeing to decide it by a bet, which is the English way of settling everything.F. For some reason or other only one of these had been used and canceled; the other still lay in the vaults of the Bank. a can of fruit contains 5 cups of fruit.The suggested serving size is cup.How many servings are in a can of fruit? Oral rehydration salts are used to __________.A.purify air that has been pollutedB.replenish moisture in the environment after natural disasters such as earthquakesC.purify water supplies to help minimize the risk of catching choleraD.help replenish fluids in the body after it suffers fluid loss from diseases such as choleraPlease select the best answer from the choices providedABCD There are 25 birds and 12 ducks. Compare the number of birds to the total number of animals. Write you answer three ways. Your answer Write the equation of the line with a slope of -3 that passes through (-5,20) What archetype does the Sergeant-Major BEST represent?A the tyrantthe tyrantB the mysterious strangerthe mysterious strangerC the best friendthe best friendD the championANWSER GETS BRAINLIEST What is the full meaning of COPOOL 2 Lots of touristswhales.3 I(just arrive) to see the(never be) much of aconservationist. How about you?4 My friendsSierra Leone for the last six months.6(work) for a charity in5 Volunteers(comb) the coastline everyday this week, picking up plastic bottles and otherrubbish.(use) a sat navyoubefore? I don't know how this works.7 She(always love) travelling alone. A segment that is both an altitude and a median of a triangle is a? The cross country team ran 1.772 hours yesterday and 1.49 hours today. Each member of the team ran 3.5 miles every hour. How many miles did each member run yesterday? Heads of Elysia cf. marginata sea slugs sometimes pull themselves free from their bodies. The heads just keep crawling around. Within a few hours, some heads start nibbling algae again. Within about 20 days, heads from young slugs can have regrown those missing body parts, including heart and all.Sayaka Mitoh and Yoichi Yusa are ecologists at Nara Women's University in Japan. They described the regrowth of cells and ultimately the sea slugs bodies March 8 in Current Biology.Mitoh first noticed the sea slugs' extreme regeneration by chance. It showed up in some Elysia slugs in his lab. "We were really surprised to see the head crawling," Yusa says.The head of a sea slug can take several hours to rip itself loose from its body. That's so slow that Mitoh and Yusa don't think the move helps slugs escape predators.Instead, a detachable body could give the sea slug a drastic, but effective, way of fighting parasites. Mitoh monitored 82 E. atroviridis slugs infested with copepods. Three of the slugs ditched their bodies along with a lot of those copepods. Two of the three managed to grow a new body. An additional 39 of the parasitized slugs let parts of their bodies slowly fall away. In contrast, 64 more sea slugs that had been collected at the same time had no pests. And none of them threw away its body. That supports the idea that parasites could drive slug heads to detach and crawl away from their bodies.What might help Elysia slug heads regrow a whole body is stealing, Yusa suggests. These animals can take the green sunlight-trapping energy factories called chloroplasts from algae. Very young slugs don't have any chloroplasts. "They need to pierce the cell walls of sea algae and sip the contents," he says. Once ingested, the chloroplasts remain alive inside the slugs for weeks to months.Biologists have debated what stealing chloroplasts does for the slugsUsing what you know about cellular differentiation and the description of sea slug regeneration explain what is happening at a cellular level:?A;Specialized cells undergo cellular differentiation to create stem cells that will grow and replace the old cellsB:Stem cells undergo cellular differentiation to create specialized cells to replace missing body parts like cardiac (heart) cells.C:Cellular differentiation is not necessary in order for the sea slugs to regrow its missing body parts.D:None of the above.