Question 4
Is this a function? Explain, why or why not!
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Answer:

9.652 kg

Step-by-step explanation:

144 kg 780 g = 144.78 kg

if there are 15 packets in the box then:

144.78 ÷ 15 = x

x = 9.652 kg

Therefore the weight of each bag is 9.652 kg

Answer:

Step-by-step explanation:

[tex]P(t)=400cos(30t-180)+1100[/tex]

a.  What was the population of arctic foxes in Yukon in 1992?

t' represents the number of years since 1992. So plugging in 0 gives the population in 1992.

[tex]P(0)=400cos(30*0-180)+1100[/tex]

Subtract 180 from 0.

[tex]P(0)=400cos(-180)+1100[/tex]

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.

[tex]P(0)=400(-cos(0))+1100[/tex]

The exact value of cos (0) is 1.

[tex]P(0)=400(-1*1)+1100[/tex]

[tex]P(0)=400*-1+1100[/tex]

Multiply 400 by −1. Then add −400 and 1100.

[tex]P(0)=700[/tex]

D. What will be the population of arctic foxes in 2030?

[tex]P(38)=400cos(30(38)-180)+1100[/tex]

[tex]P(38)=900[/tex]

Answer: Sale tax rate is 5%

Step-by-step explanation:

Take $53 divided by $1060, then time 100% = 5%

The probability that their average score is between 200 and 250 is 42.49%.

The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a given data point deviates from the mean. In essence, standard deviation represents the degree

Given:

Mean = 240

and standard deviation = 27

So, P( 200 < x < 250) =  P( (x- [tex]\mu[/tex])/ [tex]\sigma[/tex] < x <  x- [tex]\mu[/tex])/ [tex]\sigma[/tex])

                                    = P (200- 240 / 27  < x < 250- 240 /27)

                                    = P( -1.481 < x < 0.370)

                                    = 0.42499

Hence, the probability that their average score is between 200 and 250 is 42.49%.

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Answer:

q = -9

Step-by-step explanation:

(3, -15), (4, -21)

(-21 + 15)/(4 - 3) = -6/1 = -6

y + 15 = -6(x - 3)

y + 15 = -6x + 18

y = -6x + 3

q = -6(2) + 3 = -12 + 3 = -9

An expression that represents the number of bracelet Leslie designs is

Information from the question include

Her most recent order included a total of 7 bracelets

It takes 14 stones to make one bracelet

let s represent stone

It takes 14 stones to make one bracelet means that one bracelet = 14 s

hence if 1 bracelet is 14 stones then 7 bracelet will be

1 bracelet = 14 s

7 bracelet = ?

cross multiplying

1 * ? = 7 * 14

? = 98 stones

the equation is written as

s/14 = 7 ; s = 98 stones

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The side of each square in terms of y is y/16.

What is a perimeter?

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges.

Here, we have

The figure is made up of 10 identical squares. The perimeter is y cm.

The number of outer sides is 16

Let the side be x

then

16x = y

x = y/16

Hence,  the side of each square in terms of y is y/16.

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0.3108 is the probability that a single tire randomly selected from the population will have a lifetime between 46,800 and 49,200 miles

Probability is a mathematical discipline that concerns with numerical figures of how probable an occurrence is to occur or how probably a statement is to be true. A number between 0 and 1 is the probability of an occurrence, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

X ~ N ( µ = 48000 , σ = 3000 )

As we know, P ( 46800 < X < 49200 )

Standardizing the  value, we get -

Z = ( X - µ ) / σ

Z = ( 46800 - 48000 ) / 3000

Z = -0.4

Z = ( 49200 - 48000 ) / 3000

Z = 0.4

Also,

P ( -0.4 < Z < 0.4 )

P ( 46800 < X < 49200 ) =  P ( Z < 0.4 ) - P ( Z < -0.4 )

P ( 46800 < X < 49200 )  = 0.6554 - 0.3446  (Probability calculated from Z table)

P ( 46800 < X < 49200 )  = 0.3108

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Answer: C

Step-by-step explanation:

Distributive property 2. combine like terms 3. subtraction proerty of equality 4 division of equality.

Answer:

y = -2/5 x + 4

Step-by-step explanation:

slope = (0-4)/(10-0)

-4/10

-2/5

y intercept = 4

y = -2/5 x + 4

Answer:

152°

Step-by-step explanation:

Circle Theorem vocabulary

Secant: a straight line that intersects a circle at two points.

Arc: the curve between two points on the circumference of a circle

Intercepted arc: the curve between the two points where two chords or line segments (that meet at one point on the other side of the circle) intercept the circumference of a circle.

Angles of Intersecting Secants Theorem

If two secant segments are drawn to the circle from one exterior point, the measure of the angle formed by the two lines is half of the (positive) difference of the measures of the intercepted arcs.

[tex]\implies m \angle PRD=\dfrac{1}{2}\left(m\overset{\frown}{PD}-m\overset{\frown}{QS} \right)[/tex]

From inspection of the given diagram:

Substitute these into the formula and solve for x:

[tex]\implies 50^{\circ}=\dfrac{1}{2}\left((12x+8)-(4x+4)\right)^{\circ}[/tex]

[tex]\implies 50^{\circ}=\dfrac{1}{2}\left(8x+4\right)^{\circ}[/tex]

[tex]\implies 100^{\circ}=(8x+4)^{\circ}[/tex]

[tex]\implies 96^{\circ}=8x^{\circ}[/tex]

[tex]\implies x=12[/tex]

Substitute the found value of x into the expression for arc PD:

[tex]\implies m\overset{\frown}{PD}=(12x+8)^{\circ}[/tex]

[tex]\implies m\overset{\frown}{PD}=(12 \cdot 12+8)^{\circ}[/tex]

[tex]\implies m\overset{\frown}{PD}=(144+8)^{\circ}[/tex]

[tex]\implies m\overset{\frown}{PD}=152^{\circ}[/tex]

Therefore, the measure of arc PD is 152°.

Answer:

[tex]y=\frac{1}{5}x+\frac{6}{5}[/tex]

Step-by-step explanation:

Parallel lines have the same slope, so the slope of line [tex]d[/tex] is [tex]1/5[/tex].

So, the equation of line [tex]d[/tex] is:

[tex]y-1=\frac{1}{5}(x+1) \\ \\ y-1=\frac{1}{5}x+\frac{1}{5} \\ \\ y=\frac{1}{5}x+\frac{6}{5}[/tex]

Answer: 1/2

Step-by-step explanation:

Let N be any number and M be the additive inverse of N

N + M = 0 = M + N

that additive inverse of N is - N

x + ( - 1/2 ) = 0

x - 1/2 = 0

x = 1/2

the additive inverse of -1/2 is 1/2

One way to solve 2(a - 1.1) = 5.8 is divide both sides by 2 and then add 1.1 on both sides to find a = 4.

To solve 5/2 b - 2 3/4= 7 1/4, add 2 3/4 on both sides, and then multiply both sides by 2/5 to find b = 4.4

In the equation a and b divide the same value.

What is an equation?

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Given equation is

2(a - 1.1) = 5.8

divide both sides by 2

a - 1.1 = 5.8/2

a - 1.1 = 2.9

Add 1.1 on both sides:

a - 1.1 + 1.1 = 2.9 + 1.1

a = 4.

Another equation is

5/2 b - 2 3/4= 7 1/4

add 2 3/4 on both sides:

5/2 b= 7 1/4 + 2 3/4

Convert the mixed fraction to improper fraction:

5/2 b  = 29/4 + 15/4

5/2 b  = 44/4

Multiply both sides by 2/5:

b = (44/4) × (2/5)

b = 11× (2/5)

b = 22/5

b = 4.4

Both number 4 a and 4.4 is divisible by 4.

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By evaluating the linear equation, we will see that Mr. Dyson will buy 20 packs of nickel strings.

We know that the linear equation:

6x + 4.5*y = 90

Represents the given situation, where the variable x is the number of bronze strings and y is the number of nickel strings.

We want to find the number of packs of nickel strings that he will buy if he does not buy any bronze strings, so we need to evaluate in x = 0.

We will get:

6*0 + 4.5*y = 90

4.5*y = 90

y = 90/4.5 = 20

He will buy 20 packs of nickel strings.

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Answer:

Step-by-step explanation:

u got it right the first time it is D

The interpretations of the equations are

From the question, we have the following parameters that can be used in our computation:

The function `P` gives the number of people, in millions,

Years = t

The function P(17) = 2320

Recall that, we have

P(t) = the number of people, in millions,

This means that the year is

Year = 2000 + 17

Year = 2017

So, the interpretation is there are 2320 million people in 2017

The function P(-10) = 0

So, we have

Year = t + 2000

Substitute the known values in the above equation, so, we have the following representation

Year = -10 + 2000

Evaluate

Year = 1990

So, the interpretation is there are 0 million people in 1990

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Complete question

The function gives the number of people , in millions. who own smarphone t years alter the year 2000

What does each equaton tell us about smartphone ownership?

(a) P(17) = 2320

(b) P(-10) = 0

The time at which the lorry the time taken arrive at it destination is 12.20.

Given :

A lorry leave a factory on a journey of 195km at 08 45 , travelling at an average speed of 52 km/h.

here,

Distance = 195 km

Speed = 52 km/h

we know that ,

speed = distance / time

on cross muliplicating

speed * time = distance

time = distance / speed

substitute the values

time = 195 / 52

= 3.75 hours

destination time = 8.45 + 3.75

= 12.20

Therefore the time at which the lorry the time taken arrive at it destination is 12.20

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The probability that  is more likely between selecting a tube of blue or yellow paint, OR selecting a tube of green or red paint id; Both are equally lilkely.

We are given;

Number of blue tubes = 7

Number of red tubes = 4

Number of yellow tubes = 3

Number of green tubes = 6

Thus;

Total number of painted tubes = 7 + 4 + 3 + 6 = 20

Probability of selecting a blue tube = 7/20

Probability of selecting a red tube = 4/20

Probability of selecting a yellow tube = 3/20

Probability of selecting a green tube = 6/20

Thus;

P(selecting a tube of blue or yellow paint) = (7/20) + (3/20) = 10/20

P(selecting a tube of green or red paint) = (6/20) + (4/20) = 10/20

Thus, they are equally likely.

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Two figures are similar when they have some common properties. The value of PQ as required is 28 units.

Similar triangles are two or more which have a series of common properties. This may be in relations to the length of their sides or measure of their angles.

In the given triangle PQR,

ΔPQS ll ΔSTR

Given that PS = RS, and QT = RT.

Then we can say that;

[tex]\frac{RS}{ST}[/tex] = [tex]\frac{PQ}{PQ}[/tex]

But, PR = 2RS;

[tex]\frac{RS}{ST}[/tex] = [tex]\frac{2RS}{PQ}[/tex]

[tex]\frac{1}{ST}[/tex] = [tex]\frac{2}{PQ}[/tex]

2ST = PQ

2(-22 + 9x) = 9x - 8

-44 + 18x = 9x - 8

18x - 9x = -8 + 44

9x = 36

x = 4

So that,

PQ = 9x - 8

     = 9(4) - 8

PQ = 36 - 8

     = 28

Thus, the length of PQ is 28 units.

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forty-five times three equals one-hundred-thirty-five

45x3=135

The equivalent salary in Canadian dollars per hour of the driver is $28.13/hour.

To convert the annual salary of a truck driver in the US from US dollars to Canadian dollars, you can use the current exchange rate between the two currencies. The exchange rate fluctuates constantly, so you will need to use the most current rate.

Assuming the current exchange rate is 1 US dollar to 1.26 Canadian dollars, the annual salary of a truck driver in the US, $55,065, is equivalent to 71,040.90 Canadian dollars. If the truck driver works 70 hours per week and 52 weeks per year, their hourly wage in Canadian dollars would be $28.13.

Here's the calculation:

Annual salary in Canadian dollars = $55,065 * 1.26 = $71,040.90

Hourly wage in Canadian dollars = $71,040.90 / (70 hours/week * 52 weeks/year) = $28.13/hour

Keep in mind that this is just a rough estimate, as the exchange rate can change over time, and the actual wage may vary depending on the driver's experience, location, and other factors.

So, the equivalent salary in Canadian dollars per hour of the driver is $28.13/hour.

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A straight line = 180°. You have: 58° , 40°, and q so:

q = 180° - (58° + 40°)

q = 82°

Answer:

82

Step-by-step explanation:

180 i s the line length so

180-40=140

140-58=82

Answer: 131072

Step-by-step explanation:

Basically the sequence is just being multiplied by 4, like 2(4)=8 and 8 is the next number in the sequence or 32(4)=128 which then again is the next number in the sequence.

The reqiured two digit number is 54

Let, a two-digit number be n

the digit at tens place as x and the digit at unit place be y

The tens digit of a two-digit number exceeds the units digit by 1.

x = y + 1                      .............(1)

if the number is divided by the sum of its digits, the quotient is 6.

(10x + y)/(x + y) = 6

Substitute above value of x in this equation.

(10(y + 1) + y) = 6(y + 1 + y)

10y + 10 + y = 6(2y + 1)

11y + 10 = 12y + 6

y = 4

Substitute above value of y in equation (1),

x = 4 + 1  

x = 5

So, the number would be, 10x + y = 50 + 4

                                                      = 54

Therefore, the number is 54

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It is evident from the steps above that it is impossible to be have two numbers with the same LCM and HCF as 12 and 5, respectively.

The given condition are-

Helen considers two numbers that fit the following criteria:

The steps to solve the condition are-

1. It is assumed that when Helen considers of two numbers, they have corresponding HCF and LCM values of 5 and 12.

2. A smallest common multiple shared by two numbers is referred to as the least common number.

LCM of 4 with 6 is 12, for instance.

3. The highest number which divides the two selected numbers, leaving a residue of 0, is referred to as the highest common factor.

HCF of 6 and 8 is 2, for instance.

4. Given that the LCM of Helen's two chosen numbers is 12, even multiples of 12 are indeed the two numbers' common multiples. In light of this, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, and so forth.

5. The only numbers that may be divided by 5 are 60 and 120. All other numbers have HCF values apart from 5. 60 and 120 have an HCF of 60, but not 5.

6. As a result, it is evident from the steps above that it is impossible to be have two numbers with the same LCM and HCF as 12 and 5, respectively.

Therefore, the aforementioned criteria cannot exist mathematically.

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By applying this theory, it is discovered that there is an 0.5 = 50% chance that the marble will land on a 00 or even slot.

A probability is calculated by dividing the entire number of possible outcomes by the desired outcomes.

In this issue:

The preferred likelihood is:

P = D/T

P = 19/38 = 0.5

Thus, the probability that the marble will land on a 00 or even slot is 50%, or 0.5.

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The complete question is-

When playing American​ roulette, the croupier​ (attendant) spins a marble that lands in one of the 38 slots in a revolving turntable. The slots are numbered 1 to​ 36, with two additional slots labeled 0 and 00 that are painted green. Consider the numbers 0 and 00 as neither even nor odd. Half the remaining slots are colored red and half are black. Assume a single spin of the roulette wheel is made. Find the probability of the marble landing on a 00 or even slot.

The required equation is y = -(x + 1)² + 9.

Parabola is a curve like shape, in which any point is equal distance from a fix point.

The standard equation of parabola,

y = a(x-h)² + k.

Here, h = horizontal coordinate of the vertex,

k = vertical coordinate of the vertex.

In the given graph, the vertical coordinate of the vertex k = 9,

The horizontal coordinate of the vertex h = -1.

And the focus of the parabola = -1,

The required equation,

y = -1(x - (-1))² + 9

y = -(x + 1)² + 9

The required equation of the given graph is y = -(x + 1)² + 9.

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Liquid detergent do I have left is 8/9.

What is detergent ?

When washing items like clothing or dishes, detergent is a chemical compound that is often in the form of a powder or liquid. Alternatives include washing liquid, soap powder, and cleaner. More detergent synonyms. More detergent synonyms.

I have 2/3 L (litre) of liquid detergent. I ued 3/4 of thi to wah my heet on the weekend.

[tex]\frac{\frac{2}{3}}{\frac{3}{4}}$$[/tex]

Apply the fraction rule: [tex]$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a \cdot d}{b \cdot c}$[/tex]

[tex]=\frac{2 \cdot 4}{3 \cdot 3}$$[/tex]

Multiply the numbers: 2-4=8

[tex]=\frac{8}{3 \cdot 3}$$[/tex]

Multiply the numbers: 3-3=9

[tex]=\frac{8}{9}$$[/tex]

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Therefore in this question the probability that he is innocent is 0.1743

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Here,

In this case, let G represent the state of guilt and H represent the state of innocence.

and Let K stand for the situation where the truth serum shows that someone is guilty.

We are aware that 90% of the guilty suspects receive just verdicts, i.e. P(K|G)=0.9.

Additionally, we know that innocent suspects are mistakenly identified 1% of the time, or P(K|H)=0.01.

When a suspect is chosen from a group of suspects, of whom 5% committed a crime, and the serum suggests that the suspect is guilty, we must determine the likelihood that the suspect is innocent.

We must therefore determine the probability P(H|K).

A group of people was chosen for the suspect, of which 5% were criminals.

so the probability that selected person is guilty is

P(G) = 0.05

Therefore, the probability that selected person is not guilty is

P(H) = 1 – P(G) = 1 – 0.05 = 0.95

Then,

Using Bayes' Theorem, we get

P(H|K) =[tex]\frac{P(H)P(K|H)}{P(H)P(K|H) + P(G)P(K|G)}[/tex]

=     [tex]\frac{0.95*0.01}{0.95*0.01 + 0.05*0.9}[/tex]  =0.1743

Therefore in this question the probability that he is innocent is 0.1743

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