Based on the diagram, which is a true statement?

- If a student plays in the band, then he/she is an honor student.
- If a student is an honor student, then he/she plays in the band.
- If a student is not an honor student, then he/she cannot play in the band.
- If a student is an honor student, then he/she may also be a band member.

The money spent on lottery tickets is 15.6% of the money spent to buy food.

The given parameters are:

Food = $122

Lottery = $19

The proportion of the lottery tickets is:

Proportion = Lottery/Food * 100%

This gives

Proportion = 19/122* 100%

Evaluate

Proportion = 15.6%

Hence, the money spent on lottery tickets is 15.6% of the money spent to buy food.

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Answer:

  about 33.3%

Step-by-step explanation:

The fraction of space not occupied will be the same as the unoccupied fraction of a cylinder of the same height and diameter as a sphere.

The volume of a cylinder of diameter d and height d will be ...

  V = πr²h = π(d/2)²(d) = (π/4)d³

The volume of a sphere of diameter d is ...

  V = 4/3πr³ = 4/3π(d/2)³ = (π/6)d³

The fraction of space that is occupied is ...

  occupied space = (sphere volume)/(cylinder volume)

  occupied space = ((π/6)d³) / ((π/4)d³) = 4/6 = 2/3

The fraction of unoccupied space is ...

  unoccupied fraction = 1 -2/3 = 1/3

  unoccupied fraction ≈ 33.3%

Answer:

Putangina okay

Step-by-step explanation:

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Answer:

Number 4

Standard form - Not sure if right

y = − 0.2734375x^2 − 1.09375x +11.40625

Factored form - Not sure if right

y= 0.0390625 (−7x^2 −28x+292)

Number 5

Either form of the equation other than standard form

Vertex form : y = −(x +3)^2 + 25

Vertex of the parabola

(-3,25)

X and Y intercepts

x-intercept(s): (2,0) ,(−8,0)

y-intercept(s): (0,16)

Answer:

Proof below

Step-by-step explanation:

If [tex]p[/tex] is prime such that [tex]p \neq2[/tex] and [tex]p \neq 3[/tex], then [tex]p[/tex] divided by 6 has remainder of 1 or 5.

Case 1: p/6 has remainder 0, 2, or 4.

Then there exists some natural number [tex]n[/tex] such that either [tex]p=6n[/tex], [tex]p=6n+2[/tex], or [tex]p=6n+4[/tex].  However,

By definition of divisibility, [tex]p[/tex] is divisible by 2.  Since [tex]p \neq2[/tex], [tex]p[/tex] cannot be prime.  This contradiction implies [tex]p[/tex] cannot have a remainder of 0, 2, or 4 when divided by 6.

Case 2: p/6 has remainder 3.

Then there exists some natural number [tex]n[/tex] such that [tex]p=6n+3[/tex].  However, if [tex]p=6n+3[/tex], then [tex]p=3*(2n+1)[/tex], so [tex]p[/tex] is divisible by 3.  Since [tex]p \neq 3[/tex], [tex]p[/tex] is not prime.  This contradiction implies [tex]p[/tex] cannot have a remainder of 3 when divided by 6.

Therefore, if [tex]p[/tex] is a prime number such that  [tex]p \neq2[/tex] and [tex]p \neq 3[/tex], then when divided by 6, [tex]p[/tex] must have a remainder of 1 or 5.

Check p=2

Consider [tex]p=2[/tex].  Then [tex]q=2+70=72[/tex].  However, [tex]72=2*36[/tex], so [tex]q[/tex] is not prime.  Hence, [tex]p \neq2[/tex].

Check p=3

Consider [tex]p=3[/tex].  Then [tex]q=3+70=73[/tex], and [tex]r=73+70=143[/tex].  However, [tex]143=11*13[/tex], so [tex]r[/tex] is not prime.  Hence, [tex]p \neq 3[/tex].

So, thus far, we've proven that if there is a prime trio with a common difference of 70, that [tex]p \neq2[/tex] and [tex]p \neq 3[/tex].

Proof of the rest of primes by contradiction

By way of contradiction, assume that there does exist some prime trio [tex]\{ p,q,r \}[/tex] such that [tex]q-p=r-q=70[/tex], and [tex]p \neq2[/tex] and [tex]p \neq 3[/tex].

Then, by the Lemma proven earlier, when [tex]p[/tex] is divided by 6, it must have a remainder of 1 or 5.

Case 1: p/6 has remainder 5

Assume that [tex]p[/tex] has remainder 5 when divided by 6.  Then, there exists some natural number [tex]n[/tex], such that [tex]p=6n+5[/tex].  

[tex]q=p+70\\q=(6n+5)+70\\q=6n+75\\q=3*(2n+25)[/tex]

Since [tex]n[/tex] was a natural number, and the natural numbers are closed over multiplication and addition (meaning, multiplying and adding more natural numbers results in another natural number), then [tex]q[/tex] is divisible by 3.

Since [tex]p[/tex] is prime, [tex]0 < p[/tex], which implies [tex]0+70 < p+70[/tex]

Since [tex]q=p+70[/tex], [tex]70 < q[/tex], so [tex]q[/tex] cannot equal 3.  Since [tex]q[/tex] is divisible by 3, but [tex]q \neq 3[/tex], [tex]q[/tex] is not prime, which is a contradiction to the existence of this prime trio.

Therefore, either [tex]p[/tex] cannot have a remainder of 5 when divided by 6, or the prime trio does not exist.

Case 2: p/6 has remainder 1

Assume that [tex]p[/tex] has remainder 1 when divided by 6.  Then, there exists some natural number [tex]n[/tex], such that [tex]p=6n+1[/tex].  

[tex]q=p+70\\q=(6n+1)+70\\r=q+70\\r=((6n+1)+70)+70\\r=6n+141\\r=3*(2n+47)[/tex]

Since [tex]n[/tex] was a natural number, and the natural numbers are closed over multiplication and addition (meaning, multiplying and adding more natural numbers results in another natural number), [tex]r[/tex] is divisible by 3.

Since [tex]q[/tex] is prime, [tex]0 < q[/tex], implying [tex]0 +70 < q+70[/tex].

Since [tex]r=q+70[/tex], then [tex]70 < r[/tex].  Therefore, [tex]r\neq 3[/tex].

Since [tex]r[/tex] is divisible by 3, but [tex]r\neq 3[/tex], [tex]r[/tex] is not prime, which is a contradiction to the existence of this prime trio (with a common difference of 70).  Therefore, either [tex]p[/tex] cannot have a remainder of 1 when divided by 6, or the prime trio does not exist.

Since [tex]p[/tex] was prime, by our lemma [tex]p[/tex] must have either a remainder of 1 or 5.  Since both remainder possibilities resulted in a contradiction, our contradiction assumption is false, so there cannot exist a prime trio such that their common difference is 70.

Answer:

[tex]\pm i\sqrt{2}\text{ and } \pm i[/tex]

Step-by-step explanation:

[tex]\text{let u = } x^2[/tex] so then [tex]u^2=x^4[/tex].

This gives you the equation: [tex]u^2+3u+2=0[/tex].

Now factor the equation by looking for factors of 2 that add up to 3, which is just 2 and 1. Use these to rewrite the equation: [tex](u+2)(u+1)[/tex]. So now just set each factor equal to 0:

[tex]u+2=0\\u=-2[/tex]

Now substitute x^2 back in as u

[tex]x^2=-2[/tex]

Take the square root of both sides

[tex]x=\pm \sqrt{-2}[/tex]

Separate the radical into sqrt(-1) * sqrt(2)

[tex]x=\pm \sqrt{-1}*\sqrt{2}[/tex]

Rewrite using i

[tex]x=\pm i\sqrt{2}[/tex]

Now set the other factor equal to 0

[tex]u+1=0\\u=-1[/tex]

substitute x^2 back in as u

[tex]x^2=-1[/tex]

Take the square root of both sides

[tex]x=\pm\sqrt{-1}[/tex]

rewrite using i

[tex]x=\pm i[/tex]

The NPV is positive, therefore, this order can be placed.

The calculation of probability of default will be:

= 1 / 200 = 0.005

We use NPV formula to find out whether the order should be filled or not

NPV = -Variable cost per unit +[(1-π)(price of equipment/1+percentage of return)]

= -$1.6 million +[(1-0.005)($1.725m/1.018)]

= -$1.6m + $1.6860

= 0.0860 million

As NPV is positive this order can be placed.

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Answer:

d i did the thing

Step-by-step explanation:

The amount of money a farmer can make by selling the milk produced by the cow in the month of April is $90

From the equation given, we have that

$3 = I gallon

Let's take it that the farmer sells one gallon by per day

We know that the month of April has 30 days

So if he makes $3 in 1 day

He would make x in 30 days

Collect like terms

$30 × 30 days = amount

Multiply through

Amount = $90

Thus, the amount of money a farmer can make by selling the milk produced by the cow in the month of April is $90

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The values of m and n from the given equation are 1/4 and -2

Given the polynomial function below

f(x) = mx^4+2x^3-3x^2+nx-4

If the zeros are 2 and -2, hence;

0 = 16m+16-12+2n-4
0 = 16m-16+12-2n-4

_______________
16m+2n = 0
16m - 2n = 8

Subtract

2n+2n = -8
4n = -8

n = -2

Substitute for "m'

16m + 2(-2) = 0
16m = 4

m = 1/4

Hence the values of m and n from the given equation are 1/4 and -2

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a. The probability of winning the prize by the resident who purchased 10 tickets is 1% (10/1,000).

b. The expected profit (winnings - cost) for the resident who purchased 10 raffle tickets is $1,900 ($2,000 - $100).

c. The amount raised by the fire department after paying out the $2,000 prize (ignoring other raffle costs) is $8,000 ($10,000 - $2,000).

A raffle is a gambling competition or lottery organized to raise money for a purpose.

A raffle involves the sale of tickets which are drawn randomly to select some winners.

Price of a raffle ticket = $10

Prize = $2,000

Cost of purchasing 10 tickets = $100 ($10 x 10)

Number of raffle tickets sold = 1,000

Total revenue realized = $10,000 ($10 x 1,000)

Thus, if a resident purchases 10 tickets, the chance of winning the raffle is 1%.

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Answer:

Move all the points on the graph two points to the right

Step-by-step explanation:

f(x-2) is just a translation to the right by 2. The whole formula is typically y = a f(b(x + c)) + d. In this case, the C value is the one being changed and that indicates a translation left or right. -2 indicates 2 to the right.

Answer:

The Slope: 0

The y-intercept: (0,0_

x y

0 0

1 0 (there is supposed to be a line between the x and y that goes down all the way down the numbers but i cannot type that)

Step-by-step explanation:

Answer:

15.2 in

Step-by-step explanation:

The surface area of a sphere is given by the formula below:

Surface area of sphere= 4πr², where r is the radius

Given that the surface area is 2903.33 in²,

2903.33= 4πr²

Divide both sides by 4π:

[tex] {r}^{2} = \frac{2903.33}{4\pi} [/tex]

Square root both sides:

[tex]r = \sqrt{ \frac{2903.33}{4\pi} } [/tex]

r= 15.2 in (3 s.f.)

For a similar question on surface area of sphere, do check out the following!

the simplified value of the exponential expression is 1/9

Answer:

[tex]\huge\boxed{\sf \$ \ 1.47}[/tex]

Step-by-step explanation:

6 oranges = $0.49

Multiply 3 to both sides

6×3 oranges = $0.49 × 3

18 oranges = $1.47

[tex]\rule[226]{225}{2}[/tex]

Answer:

n>2      (see below)

Step-by-step explanation:

Triangle side rule says    n+2   + 5   must be greater than 9

    n+2   +5  > 9

    n > 2      

      (but it must be less than 12   o/w   5 + 9 will not be greater than n+2)  

Answer:

Step-by-step explanation:

1250x0.05x1.5=93.75

93.75 is the interest

1343.75 is the total ammount.

Answer:

p = 7.3

Step-by-step explanation:

Equation: p - 2.5 = 4.8

add 2.5 to both sides:

P - 2.5 + 2.5 = 4.8 + 2.5

simplify

P = 7.3

hope that helps! :)

Answer:

= -x+6

Step-by-step explanation:

we can simply substitute (x-4) in x place because when we say function of x , we are basically saying when we substitute a given value in the place of x we will find a given y.so for example if we have a question f(4), we can simply plug 4 to -x +2 so we will find y or f(x) = -2.

so the answer for the above question will be f(x)= -x +6.

Answer:

-2 ≤ x ≤10

Step-by-step explanation:

Notice that x can never be less than -2  and can never exceed.

-2 and 10 are all inclusive  thus the last answer is not correct as it tries to leave them out

Answer:

31465

Step-by-step explanation:

n!/((n-r)! r!)

= 31!/(31-4)! 4!

= 31!/ 27! 4!

= 31465

Answer:

Step 2

Step-by-step explanation:

In step 1, Gary had the right idea of multiplying both sides by 4 to eliminate the denominator, but in step 2, Gary makes a mistake since e should equal 10 not 8. 2.5 * 4 = 10 not 8

Answer:

B) Step 2

Step-by-step explanation:

Gary's mistake occurs in Step 2. He was right to multiply both sides of the equation by 4 to find e, but his error is in the multiplication of 2.5*4. 2.5*4 = 10, not 8.

The augmented matrix of the system of equations is [tex]\left[\begin{array}{ccc}-2&2&-1\\-3&-1&1\\-1&3&-2\end{array}\right] \left[\begin{array}{c}13&7\\0\end{array}\right][/tex]

The system of equations is given as:

-2x + 2y - z = 13

-3x - y + z = 7

-x + 3y - 2z = 0

Remove the variables x, y and z

-2      2    -1  13

-3    -1        1    7

-1     3      -2     0

Express as matrix

[tex]\left[\begin{array}{ccc}-2&2&-1\\-3&-1&1\\-1&3&-2\end{array}\right] \left[\begin{array}{c}13&7\\0\end{array}\right][/tex]

Hence, the augmented matrix of the system of equations is [tex]\left[\begin{array}{ccc}-2&2&-1\\-3&-1&1\\-1&3&-2\end{array}\right] \left[\begin{array}{c}13&7\\0\end{array}\right][/tex]

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Complete question

Write the augmented matrix of the system of equations given below. (10 points)

-2x + 2y - z = 13

-3x - y + z = 7

-x + 3y - 2z = 0

Answer:

that's all I could do. hope it helps.

good day.

It would take approximately 11 years for this population to reach 7300.

Based on the information provided, the future size of the population can be modelled by using an exponential function:

F = Pe^rt

Substituting the given parameters into the formula, we have;

7300 = 5000e^{0.035 × t}

7300/5000 = e^{0.035t}

1.46 = e^{0.035t}

Taking the ln of both sides, we have:

ln(1.46) = ln(e^{0.035t})

0.378 = 0.035t

t = 0.378/0.035

Time, t = 10.8 ≈ 11 years.

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Answer:

$11,000

Step-by-step explanation:

Let amount invested for 12% yield be p . Amount for 4% yield is therefore (18000-p)

Interest for 12%: 12% of p=0.12p

Interest for 4%: 4% of (18000-p)=0.04(18000-p)=720-0.04p

Total interest:

=0.12p + (720-0.04p)

=0.12p-0.04p+720

=0.08p+720

But we already know the total interest is 1280

Therefore: 0.08p+720=1280

0.08p=1280-720

0.08p=560

p=560÷0.08

p=7000

Therefore at 4% the person invested:

(18000-p)

18000-7000

$11,000

The logarithmic form of √x = y is ㏒ₓy = 1/2

We have, logarithmic form as;

Given √x = y

Convert the square root to power of 1/2 as that is what it represents, we get

x^1/2 = y

Then compare with the universal logarithmic form, we have

㏒ₓy = 1/2

Thus, the logarithmic form of √x = y is ㏒ₓy = 1/2

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Answer: B and D

Step-by-step explanation:

A is not, it's an arithmetic sequence where each term is +5 greater than the previous

B is because each term is 1/2 the previous term (common ratio of 1/2) thus making it a geometric sequence

C is not, it's the Fibonnaci sequence which is neither an arithmetic or geometric sequence

D is because each term is 1/3 the previous term (common ratio of 1/3) thus making it a geometric sequence