Before his shopping spree, Hall owned 31 phones. Then he bought 74

more phones. What is the ratio of phones purchased to resulting total

number of phones?

the only critical number of g(y) is -1/4.

To find the critical numbers of the function g(y) = y - 2y^2 - 2y + 4, we need to find its derivative and set it equal to zero.

g'(y) = 1 - 4y - 2

Setting g'(y) = 0, we get:

1 - 4y - 2 = 0

-4y - 1 = 0

y = -1/4

what is number?

A number is a mathematical object used to represent a quantity or value. Numbers can be classified into different types based on their properties and the set of numbers they belong to. Some common types of numbers include:

Natural numbers: These are the counting numbers, such as 1, 2, 3, and so on.

Whole numbers: These are the natural numbers plus zero, such as 0, 1, 2, 3, and so on.

Integers: These are the whole numbers plus their negative counterparts, such as -3, -2, -1, 0, 1, 2, 3, and so on.

Rational numbers: These are numbers that can be expressed as a ratio of two integers, such as 1/2, 0.75, or -3/4.

Irrational numbers: These are numbers that cannot be expressed as a ratio of two integers, such as pi (3.14159...) or the square root of 2 (1.41421...).

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Answer:

Step-by-step explanation:

trapezoid's S1 = 20m

                  S2 = 18m

distance between the sides, i.e. height of the trapezoid, h = 25m

1.

area of the garden = area of a trapezoid =

(S1 + S2) / 2 * h

2.

area of a garden is asked which is in the shape of a trapezoid so we have to calculate the area of a trapezoid.

3.

the given facts are the length of two sides as well as the distance between the sides which will be considered as the height.

4.

formula to find the area of a trapezoid, = (a+b) / 2 * h

where a, b are the two sides and h is the height

5.

number sentence = (20 + 18) / 2 * 25

                             = 38 / 2 * 25

                             = 19 * 25

6.

answer is 475 m²

The factory overhead efficiency variance for May is $480 unfavorable.

What is overhead efficiency variance ?

The overhead efficiency variance measures the difference between the actual hours worked and the standard hours allowed, multiplied by the standard overhead rate.

Step 1: Budgeted overhead at 90% capacity:

Budgeted overhead = 6,120 DLHs * $3.00 per DLH = $18,360

Step 2: Budgeted overhead at 70% capacity:

Budgeted overhead = $15,640

Step 3: Standard hours at 70% capacity:

Standard hours = 6,120 DLHs / 90% * 70% = 4,760 DLHs

Step 4: Variable overhead rate:

Variable overhead rate = ($18,360 - $15,640) / (6,120 DLHs - 4,760 DLHs) = $2.00 per DLH

Step 5: Variable overhead efficiency variance:

Variable overhead efficiency variance = (4,760 DLHs - 5,000 DLHs) * $2.00 = $480 unfavorable

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Step-by-step explanation:

First, you need to find the difference 3201-2750=451, it has increased by 451, then divide the difference by the original number, which is 2750 because thats what she started off with (3201 would be the new number)

Increase% = Increase ÷ Original Number ×100

451÷2750×100=16.4%

The percent of Maria’s savings increase from 2018 to 2019 will be 16.4%.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

The amount of money that Maria had in a savings account at the beginning of 2018 was $2,750.

And, At the beginning of 2019, the same savings account now had $3,201 in it.

Now,

The increased amount = $3,201 - $2,750

                                   = $451

So, The percent of Maria’s savings increase from 2018 to 2019 is,

⇒ Increased percent = 451/2750 × 100

                                = 16.4%

Thus, The percent of Maria’s savings increase from 2018 to 2019 = 16.4%.

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After 5 months the total cost at each health club be the same.

Given that, club A offers membership for a fee of $40 plus a monthly fee of $25.

Let the number of months be x.

Membership fee of club A = 40+25x ------(i)

Club B offers a membership fee of $15 plus a monthly fee of $30.

Membership fee of club B = 15+30x

The total cost at each health club be the same

40+25x = 15+30x

30x-25x=40-15

5x=25

x=25/5

x=5

Therefore, after 5 months the total cost at each health club be the same.

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"Your question is incomplete, probably the complete question/missing part is:"

You are choosing between two health clubs. Club A offers membership for a fee of $40 plus a monthly fee of $25. Club B offers a membership fee of $15 plus a monthly fee of $30.

Using variables of your choice, set-up an equation for each club’s membership cost. Make sure your variables are defined clearly.

After how many months will the total cost at each health club be the same?

To show that w is in the subspace of R4 spanned by V1, V2, and V3, we need to find constants c1, c2, and c3 such that:

w = c1V1 + c2V2 + c3V3

We can write this as a matrix equation:

| 1 -4 -9 -4 | | c1 | | -2 |

| 6 3 5 1 | x | c2 | = | -1 |

| 2 4 11 -8 | | c3 | | -1 |

| -15 7 22 -14 | | -2 |

We can solve this system of equations using row reduction:

| 1 -4 -9 -4 | | c1 | | -2 |

| 6 3 5 1 | x | c2 | = | -1 |

| 2 4 11 -8 | | c3 | | -1 |

| -15 7 22 -14 | | -2 |

R2 = R2 - 6R1

R3 = R3 - 2R1

R4 = R4 + 15R1

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 12 29 -16 | | c3 | | 3 |

| 0 -23 67 -59 | | -32 |

R4 = R4 + 23R2

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 12 29 -16 | | c3 | | 3 |

| 0 0 174 -294 | | 225 |

R3 = R3 - (12/27)R2

R4 = (1/174)R4

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 0 -1 22/3 | | c3 | | -13/3 |

| 0 0 1 -98/87 | | 25/58 |

R1 = R1 + 4R3

R2 = R2 - 59R3

R4 = R4 + (98/87)R3

| 1 0 -13 -10/3 | | c1 | | 21/29 |

| 0 27 0 -2119/87 | x | c2 | = | 2238/87 |

| 0 0 1 -98/87 | | c3 | | 25/58 |

| 0 0 0 1390/2391 | | 1009/2391 |

R1 = R1 + (13/1390)R4

R2 = (1/27)R2

R3 = R3 + (98/1390)R4

| 1

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Answer:

A=45

B=110

Step-by-step explanation:

Interior angles of a triangle add up to 180.

So, do 180-25=155.

Then, 155-65=90.

90 divided by 2 is 45.

x=45 so B is 45+65, which is 110.

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. It is calculated based on the number of favorable outcomes divided by the total number of possible outcomes.

To solve this problem, we will use the formula for probability of independent events:

P(A and B and C) = P(A) x P(B|A) x P(C|A and B)

where P(A) is the probability of the first event, P(B|A) is the probability of the second event given that the first event has occurred, and P(C|A and B) is the probability of the third event given that the first two events have occurred.

a.) Probability of drawing three red balls in succession:

P(RRR) = (24/81) x (23/80) x (22/79) = 0.027 or 2.7%

b.) Probability of drawing three green balls in succession:

P(GGG) = (27/81) x (26/80) x (25/79) = 0.061 or 6.1%

c.) Probability of drawing three blue balls in succession:

P(BBB) = (30/81) x (29/80) x (28/79) = 0.080 or 8.0%

Therefore, the probability of drawing all three balls of the same color without replacement from the box are:
a.) 2.7%
b.) 6.1%
c.) 8.0%

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Answer:

I can see the pdf

Step-by-step explanation:

Answer:

Yes, they do because both of the morning graphs had a better range in grades than the afternoon students.

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

y = 3x - 5

Compare with y = mx + b

b is the y-intercept. Here b = -5, so I would place a dot on the point (0, -5) since that is the y-intercept.

m is the slope.

m = rise/run

m = 3, so starting at (0, -5), go up 3 units and 1 unit right. Place a dot there. Connect the dots and extend the line in both directions past the dots. Then put arrowheads at the ends of the segment to show it represents a line.

f(-2) = 4
f(-1) = 1
f(0) = 7
f(1) = 8
f(2) = 9

The given function is a piecewise defined function, which means it is defined differently for different values of x.

To evaluate the function at the indicated values, we need to substitute the given values of x into the corresponding parts of the function.

Given function:
f(x) = { x^2               if x < 0
               { x + 7          if x ≥ 0

To evaluate f(-2), we substitute -2 into the first part of the function (x < 0):
f(-2) = (-2)^2
     = 4

To evaluate f(-1), we substitute -1 into the first part of the function (x < 0):
f(-1) = (-1)^2
     = 1

To evaluate f(0), we substitute 0 into the second part of the function (x ≥ 0):
f(0) = 0 + 7
    = 7

To evaluate f(1), we substitute 1 into the second part of the function (x ≥ 0):
f(1) = 1 + 7
    = 8

To evaluate f(2), we substitute 2 into the second part of the function (x ≥ 0):
f(2) = 2 + 7
    = 9

Therefore, we have:
f(-2) = 4
f(-1) = 1
f(0) = 7
f(1) = 8
f(2) = 9

Each value is obtained by substituting the given value of x into the appropriate part of the piecewise defined function.

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Answer:

y = -3x+7

Step-by-step explanation:

i hope this helps :)

There are 24 permutations of the letters in the word 'PODS' if all the letters are used without repetition.

To find the number of permutations of the letters in the word 'PODS' without repetition, we need to find the number of ways we can arrange the four letters.

We can use the formula for permutations of n objects taken r at a time, which is nPr = n! / (n-r)!, where n is the total number of objects and r is the number of objects we are taking.

In this case, n = 4 (since there are four letters in the word 'PODS') and r = 4 (since we are using all four letters). Substituting these values into the formula gives:

4P4 = 4! / (4-4)! = 4! / 0! = 24 / 1 = 24

Therefore, there are 24 permutations of the letters in the word.

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We know that \(sin^-1(beta) + cos^-1(a) = pi/2\) (using the identity \(sin^-1(x) + cos^-1(x) = pi/2\))

So, \(sin^-^1(beta) = pi/2 - cos^-^1(a)\)

Substituting the given value, we get:

\(pi/2 - cos^-^1(a) = pi/2 - cos^-^1(a)\)

This is true for any value of a and β. Therefore, we cannot determine the value of β from the given equation.

Answer:

0

Step-by-step explanation:

If you replace y with 0 (which you do since you are given y = 0 and you are trying to find x from the (_,0) point), you get \(2x = 5x\). The only way for x to satisfy this is x = 0.

(x+1) & (x-5) are the factors of given equation.

The given Equation is,

x3- \(3x^{3}\) - 9

Here, If we substitute x =5, in the given equation, then we find

     (5)3 - 3(5)3 - 9*5 -5 = 0

x-5 is factor of given equation to find another factor dividing given equation by x-5

    we will get =(x2+2x+1) after dividing the equation by x - 5

Hence x3- \(3x^{3}\) - 9 =(x2+2x+1) (x-5)

                            =(x+2)2 (x-5)

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For a binomial random variable with = 10 and = 0.4 P(X = 4) is ≈ 0.2508, P(X ≥ 4) is ≈ 0.6513, P(X > 4) ≈ 0.4756, P(X ≤ 4) ≈ 0.3487, E(X) = np = 10 * 0.4 = 4 and σ(X) is ≈ 1.55

Given,

X is a binomial random variable with n = 10 and p = 0.4.

a) P(X = 4) can be calculated using the probability mass function of the binomial distribution:

P(X = 4) = (10 choose 4) * 0.4^4 * 0.6^6 ≈ 0.2508

b) P(X ≥ 4) can be calculated using the cumulative distribution function of the binomial distribution:

P(X ≥ 4) = 1 - P(X < 4) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3)

Using the probability mass function, we get:

P(X ≥ 4) ≈ 0.6513

c) P(X > 4) can be calculated as:

P(X > 4) = P(X ≥ 5) = 1 - P(X < 5) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3) - P(X = 4)

Using the probability mass function, we get:

P(X > 4) ≈ 0.4756

d) P(X ≤ 4) can be calculated using the cumulative distribution function of the binomial distribution

P(X ≤ 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

Using the probability mass function, we get:

P(X ≤ 4) ≈ 0.3487

e) The expected value of a binomial random variable is given by np, so:

E(X) = np = 10 * 0.4 = 4

f) The standard deviation of a binomial random variable is given by √(np(1-p)), so:

σ(X) = √(np(1-p)) = √(10 * 0.4 * 0.6) ≈ 1.55

For a binomial random variable with = 10 and = 0.4 P(X = 4) is ≈ 0.2508, P(X ≥ 4) is ≈ 0.6513, P(X > 4) ≈ 0.4756, P(X ≤ 4) ≈ 0.3487, E(X) = np = 10 * 0.4 = 4 and σ(X) is ≈ 1.55

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The height of the poll is 40/3 and 13.3ft.

Let us assume that the Height of an object is h.

Let us assume that the shadow of an object is y.

(As the shadow is always proportional to height .)

Thus y∝h

y = kh

As given

when a person 5 ft. tall has a shadow of 6 ft.

h = 5 ft and y = 6 ft

Put in y = kh

6 = 5k

\(k=\frac{6}{5}\)

As given

A telephone pole has a shadow of 16 ft.  

Let us assume that the height of the pole is x.

h = x and y = 16 ft

16 = hk       compare the value of k

\(k=\frac{16}{x} \\\\\frac{6}{5} =\frac{16}{x} \\\\x=\frac{16*5}{6} \\\\x=\frac{80}{6} \\\\x=\frac{40}{3} ft\)

0r

x=13.3ft

Therefore, The height of the poll is 13.3ft

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Answer:

40/3

Step-by-step explanation:

-0.6X=-8

X=-8/-06

X=40/3

9514 1404 393

Answer:

  D.  90

Step-by-step explanation:

The radius VG is the same as the radius VO. That radius is ...

  VG = VA +AG = 24 +27 = 51

Then the Pythagorean theorem tells you ...

  VO^2 = VA^2 +AO^2

  AO = √(VO^2 -VA^2)

  AO = √(51^2 -24^2) = √2025 = 45

The desired length is ...

  TO = 2·AO = 2·45

  TO = 90

Answer:

Step-by-step explanation:

trfhvugfhgr6uf475ugf7t,f6ydrb 7857 f5r  dtd67e7 r6ft7 v 7t  fvt t7 6r r6 7ry  t7 fu7 r6 7tgfv7t ug fy f c  y uygfg  gdv cbj c v  fv

The actual distance between the basketball court and the pool is 37.5 feet

Distance refers to the amount of space between two objects or points. It is a measure of how far apart two things are from each other.

The scale of the model is 3 inches = 5 feet. This means that every 3 inches on the model represents 5 feet in actual size. We are given that the distance between the basketball court and the pool on the model is 22.5 inches. To find the actual distance between these areas, we need to use the scale.

We can start by setting up a proportion using the scale. We know that 3 inches on the model represents 5 feet in actual size. Therefore, we can say that:

3 inches / 5 feet = 22.5 inches / x

We are trying to solve for x, which represents the actual distance between the basketball court and the pool. To solve for x, we can cross-multiply and simplify the equation:

3 inches x x = 5 feet x 22.5 inches

3x = 112.5

x = 37.5 feet

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Complete Question:

The scale of the model of a recreational facility is 3 inches = 5 feet. If the basketball court is 22.5 inches from the pool in the model, what is the actual distance between the basketball court and the pool?

A new homeowner must choose between two financing options while buying a $2,590 living room set.

Part A: The price of Offer 1 as a whole is $5,251.14.

Part B: The entire price of offer 2 is $5,304.32.

Part C: The superior financing option for the prospective homeowner is Offer 1.

Part A: To calculate the total cost of offer 1, we can use the formula for compound interest:

A = \(P (1 + r/n)^{(nt)}\)

where A represents the total amount paid, P represents the principal (amount borrowed), r represents the annual interest rate, n represents the number of times the interest is compounded annually, and t is the length of time in years.

Plugging in the values for offer 1, we get:

A = \(2590 (1 + 0.249/12)^{(12*3)}\)

= \(2590 (1.02075)^{36}\)

= 2590 (2.026)

= $5,251.14

Therefore, the total cost of offer 1 is $5,251.14.

Part B: Using the same formula, we can calculate the total cost of offer 2:

A = \(2590 (1 + 0.229/12)^{(12*4)}\)

= \(2590 (1.01908)^{48}\)

= 2590 (2.048)

= $5,304.32

Therefore, the total cost of offer 2 is $5,304.32.

Part C: Comparing the two offers, we can see that offer 1 has a higher interest rate but a shorter time period, while offer 2 has a lower interest rate but a longer time period. To determine which offer is better, we can calculate the total amount of interest paid for each offer.

For offer 1, the total interest paid is:

$5,251.14 - $2,590 = $2,661.14

For offer 2, the total interest paid is:

$5,304.32 - $2,590 = $2,714.32

Therefore, offer 1 has a lower total amount of interest paid and is the better financing offer for the new homeowner.

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Answer:

72j + 63

Step-by-step explanation:

The defect rate for your product has historically been about 1.50% For a sample size of 200, the upper and lower 3​-sigma  The upper control limit (UCL) is approximately 0.0450.

The upper control limit (UCL) for a 3-sigma control chart is given by:

\(\[UCL\) = defect rate + 3 * sqrt((defect rate * (1 - defect rate)) / sample size)

Substituting the values, where the defect rate is 1.50% (0.015) and the sample size is 200, we get:

\(\[UCL = 0.015 + 3 \times \sqrt{\frac{0.015 \times (1 - 0.015)}{200}}\]\)

Calculating this expression, we find:

\(\[UCL \approx 0.0450\]\)

Therefore, the upper control limit (UCL) is approximately 0.0450.

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Answer:

Step-by-step explanation:

Area is

Area is

Circumference = πd, where d = diameter

we know the wheel has a diameter of 27 inches, so the total circumference is 27π, and that's the arc length of one revolution.

there are 5280 feet in 1 mile and 12 inches in 1 foot.

so in 40 miles there are 40(5280)(12) inches.

and we also know that there are 60 minutes in 1 hour.

\(\cfrac{40~miles}{hour}\implies \cfrac{~~ \frac{40(5280)(12)~in}{27\pi ~\frac{in}{rev}}~~}{60~minutes}~~\approx ~~\cfrac{29878.688~rev}{60~minutes}~~ \approx ~~497.978~\frac{rev}{minute}\)

Vertical angles are pairs of angles that are located on opposite sides of a line and are equal in measure, the value of k is 9.

Vertical angles are pairs of angles that are located on opposite sides of a line and are equal in measure. They are formed when two lines intersect, and they are always congruent, or equal in measure.

That if one angle measures 130°, the measure of its vertical angle must also be 130°.

If the other angle has a measure of (8k + 58)°, and it is a vertical angle to the angle that measures 130°, then it must also have a measure of 130°.

We can set up the equation 130 = 8k + 58 and solve for k to find the value of k.

Subtracting 58 from both sides gives us 72 = 8k. Dividing both sides by 8 gives us k = 9.

Therefore, the value of k is 9.

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Answer:

Step-by-step explanation:

Using the formula for calculating heat energy H = mcΔT

m = mass of the aluminum (in g/kg)

c = specific heat capacity of aluminum

ΔT = change in temperature = T - Ti (in °C)

T is the final temperature

Ti is the initial temperature

Given m = 100.0g,  c = 0.931096J/g °C, Ti = 20°C, H = 1100J T = ?

Substituting the given values into the formula;

1100 = 100*0.931096 (T - 20)

1100 = 93.1096T - 1862.192

93.1096 T = 1100+1862.192

93.1096 T  = 2962.192

T = 2962.192/93.1096

T = 31.81°C

The final temperature of the metal is 31.81°C

Answer:

31.81c

Step-by-step explanation:

1100 = 100*0.931096 (T - 20)

1100 = 93.1096T - 1862.192

93.1096 T = 1100+1862.192

93.1096 T  = 2962.192

T = 2962.192/93.1096

T = 31.81°C

INSTANCE.

In my opinion a red mustang is an instance of the car class.

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