A school principal ordered 1,000 pencils .He gave equal number to each of 7 teachers until he had given out as many as possible . How many pencils were left?

ANSWER

Explicit formula:

[tex]a_n= 8n - 23[/tex]

Recursive

[tex]a_{n}= a_{n - 1} + 8,a_1=-15[/tex]

EXPLANATION

The first term of the sequence is

[tex]a_1=-15[/tex]

The common difference is

[tex]d = - 7 - - 15[/tex]

[tex]d = 8[/tex]

The nth term is given by the formula,

[tex]a_n=a_1 + d(n - 1)[/tex]

[tex]a_n= - 15+ 8(n - 1)[/tex]

[tex]a_n= - 15+ 8n -8[/tex]

The explicit formula is;

[tex]a_n= 8n - 23[/tex]

The recursive definition is

[tex]a_{n}= a_{n - 1} + 8,a_1=-15[/tex]

Final answer:

To find the two numbers whose sum is 16 and difference is 20, we set up two equations from the given conditions and solve them simultaneously, yielding the numbers 18 and -2.

Explanation:

The student has asked about solving a system of equations where the sum of two numbers is 16 and their difference is 20. We can set up two equations based on the given information:

x + y = 16 (Equation 1, where x and y are the two numbers)

x - y = 20 (Equation 2, because the difference between the two numbers is 20)

To find the two numbers, we can solve this system of equations by adding both equations to eliminate the 'y' variable:

2x = 36

Dividing both sides by 2 gives us x = 18. We then substitute x back into Equation 1 to find y:

18 + y = 16 => y = 16 - 18 => y = -2

Therefore, the two numbers are 18 and -2.

This would be D cause these are 30,60, 90 angles. 30 (X) 60(X square root of 3 and 90 2x).

Answer:

C

Step-by-step explanation:

Using the sine ratio on the right triangle on the right side

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{8}[/tex]

Multiply both sides by 8 × sin30° = y

⇒ y = 8 × [tex]\frac{1}{2}[/tex] = 4 → C

he is still looking for seven more flowers

Answer:

The answer is n, greater than or less than 13.

Answer:

Option C. [tex]65[/tex]

Step-by-step explanation:

we know that

The discriminant of a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]D=b^{2}-4ac[/tex]

in this problem we have

[tex]2x^{2} +3x-7[/tex]  

so

[tex]a=2\\b=3\\c=-7[/tex]

substitute

[tex]D=3^{2}-4(2)*(-7)[/tex]

[tex]D=9+56[/tex]

[tex]D=65[/tex]

The discriminant of the giving polynomial is 65. The correct option is C. 65

From the question, we are to determine the discriminant of the given polynomial

The given polynomial is

2x²+3x-7

This is a quadratic function

The discriminant of a quadratic function is simply the value in the square root of the quadratic formula

That is,

Discriminant, D = b² - 4ac

In the given quadratic function, 2x²+3x-7

a = 2, b = 3 and c = -7

∴ D = 3² -4(2)(-7)

D = 9 +56

D = 65

Hence, the discriminant of the giving polynomial is 65. The correct option is C. 65

Learn more on Discriminant of a quadratic function here: https://brainly.com/question/7961542

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Answer:

Centimeter

Step-by-step explanation:

Erasers are pretty small so I would say it was about 5 cm.

Answer:

−115.940465

Step-by-step explanation:

Simplified = −115.940465

Answer:

-4/3.

Step-by-step explanation:

Using the change of base formula  convert to  log 3:

logb x = loga x / loga b

log(1/27) 81 = log3 81 / log3 1/27

log3 81  = 4 ( because 3^4 = 81) and log3 1/27 = -3 (because 3^-3 = 1/27)

So  log(1/27) 81 = 4/-3 = -4/3.

Length:width

6 inches: 1 inch

30 inches: 5 inches

Since the ratio for length is multiplied by 5, you would do the same for width.

Answer: The temperature would be -2 degrees at midnight.

Step-by-step explanation:

If you take 8 and minus 10 then you get -2!

Answer:

-2

Step-by-step explanation:

hope it will help youu!!!

Answer: option d.

Step-by-step explanation:

You have the following formul given in the problem:

[tex]p=1-e^{-mt}[/tex]

You know that:

The number of  customers serviced in an hour by the technical support representative is 6 costumbers, therefore:

[tex]m=6[/tex]

As the problem asked for the probability that  a costumber will be on hold less than 30 minutes, we know that:

[tex]t=0.5[/tex]

Substitute the values above into the formula.

Then, you obtain:

[tex]p=1-e^{-(6)(0.5)}=0.95[/tex] or 95%

Answer:

10 quarts

Step-by-step explanation:

There are 4 quarts to a gallon, and she bought 2 1/2 gallons, or 2.5 gallons, so she bought 4(2.5) = 10 quarts

Answer:

70

Step-by-step explanation:

50+20 = 70

ANSWER

70

EXPLANATION

We want to increase 50 by 40%

Method 1

New amount =50+40% of 50

[tex] = 50 + \frac{40}{100} \times 50[/tex]

[tex] = 50 + \frac{40}{2} [/tex]

[tex] = 50 + 20[/tex]

[tex] = 70[/tex]

Method 2.

50 corresponds to 100%.

New amount corresponds to (100+40=140)%

This implies that, New amount

[tex] = 140\% \times 50[/tex]

[tex] = \frac{140}{100} \times 50[/tex]

[tex] = \frac{140}{2} [/tex]

[tex] = 70[/tex]

Answer:

2

Step-by-step explanation:

3(2x + 4)=?

6x + 12

6x/6=x

12/6=2

x=2

Answer:

a:  1003 < µ < 1023

b:  See attached photo for answers

c:  see below

d and e:  See second attached photo

f:  See below

Step-by-step explanation:

a.  to find a confidence interval, first find the error with the formula,

E = Z(σ/√n)  where Z is the value of the z-score that relates to the confidence level, σ is the standard deviation of the population (or of the sample if the population standard deviation isn't given), and n is the sample size

For this problem, E = 1.96(108/√453) = 9.95 = 10

Now add and subtract that value form the sample average...

x - E < µ < x + E      becomes    1013 - 10 < µ 1013 + 10

simplifies to 1003 < µ < 1023

b.  See attached photo for hypothesis test results...

c.  H0:  µ = 1013  

    Ha:  µ > 1013 (claim)

They want to test if it's greater than their first attempt,  so this claim becomes the alternate hypothesis.  We're testing against their first attempt, that's why µ = 1013, not 1000

d and e.  See second attached photo for hypothesis test results...

f.  There is enough evidence to support the claim that the students second attempt was an improvement from their first attempt.  They happened to take a 2 hour tutoring course between tests.  This doesn't prove that the tutoring was effective thought.  It very well might have been effective, but also, the students taking the test again means they've already seen the test and know what to expect, which could have also boosted their scores.  

Answer:

[tex]\large\boxed{Q4.\ C.\ \text{Infinitely Many Solutions}}\\\boxed{Q5.\ D.\ \text{No Solution}}[/tex]

Step-by-step explanation:

[tex]Q4.\\\\\left\{\begin{array}{ccc}-4y+4=x&(1)\\2x+8y=8&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\2(-4y+4)+8y=8\qquad\text{divide both sides by 2}\\-4y+4+4y=4\qquad\text{combine like terms}\\4=4\qquad\bold{TRUE}\\\\\text{Infinitely Many Solutions}[/tex]

[tex]Q5.\\\\\left\{\begin{array}{ccc}6x+2=y&(1)\\3y-18x=12&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\3(6x+2)-18x=12\qquad\text{divide both sides by 3}\\6x+2-6x=4\qquad\text{combine like terms}\\2=4\qquad\bold{FALSE}\\\\\text{No Solution}[/tex]

Answer:

26

Step-by-step explanation:

Let his age = x

Equation

x - 12 = 14            

Solution

Add 12 to both sides.

x - 12 +12 = 14 + 12

x = 26

He is currently 26 years old.

Final answer:

The best first step to simplify the equation -2(x+3)=-10 is to distribute the -2 to the terms inside the parentheses and simplify. Then, solve for x by isolating the variable.

Explanation:

The best first step to simplify the equation -2(x+3)=-10 is to distribute the -2 to the terms inside the parentheses. This can be done by multiplying -2 with each term inside the parentheses.

So, -2(x+3) becomes -2x-6. The equation now becomes -2x - 6 = -10.

Now, we can proceed with solving the equation by isolating the variable x.

We can begin by adding 6 to both sides of the equation to get -2x = -4.

Finally, we divide both sides of the equation by -2 to solve for x.

So, x = 2.

The correct answer is option c. [tex]\frac{-2}{\ 2}(x+3) = \frac{-10}{\ 2}[/tex]

When solving the equation -2(x+3)=-10, the best first step is to divide both sides by 2. This simplifies the equation by making it easier to solve.

Here are the steps:

By dividing first, you simplify the algebraic manipulation and make solving the equation straightforward.

The complete question is:
When solving equation which is the best first step to begin to simplify the equation -2(x+3)=-10

a. [tex](-2)(-2)(x+3) = -10(-2)[/tex]

b. [tex]\frac{-1}{\ 2}(-2)(x+3) = (-10)\frac{-1}{\ 2}[/tex]

c. [tex]\frac{-2}{\ 2}(x+3) = \frac{-10}{\ 2}[/tex]

d. [tex]\frac{-2}{-10}(x+3) = \frac{-10}{-10}[/tex]

Answer:

[tex]m<1=26.4\°[/tex]

[tex]m<2=153.6\°[/tex]

Step-by-step explanation:

we know that

If m<1 and m<2 form a linear pair

then

[tex]m<1+m<2=180\°[/tex] -----> by supplementary angles

substitute the values and solve for x

[tex](2x+20)+48x=180\°[/tex]

[tex]50x=180\°-20\°[/tex]

[tex]50x=160\°[/tex]

[tex]x=3.2\°[/tex]

Find the measure of each angle

[tex]m<1=(2x+20)=2(3.2\°)+20\°=26.4\°[/tex]

[tex]m<2=48x=48(3.2\°)=153.6\°[/tex]

Answer:

SLOPE = -5

Step-by-step explanation:

Because that's what x is.

Answer:

The second option.

3x + 6 = 21.

Step-by-step explanation:

3x + 6 = 21.

If x = 5, plug it in.

3 · 5 + 6 = 21

15 + 6 = 21

Hope this helps,

Davinia.

Answer:

Second Option

Step-by-step explanation:

Answer:

999

 530

+469

----------

 999

Answer:

1/15

Step-by-step explanation:

You have a 1/3 chance of being an elf.

You have a 1/5 change of having the magic tool.

1/3 × 1/5 = 1×1/3×5 = 1/15

Answer:

it is 1/15

Step-by-step explanation:

48 students in group 2

43 students in group 1

So in total there are 91 students

7 students play the trump

And 20 play the trombone

Therefore it is known that 27 students play those two instruments in total

Because of this, Subtract 27 from 91 to get the num of students who doesn't play those instruments.

Answer:

[tex]\large\boxed{Q\#1.\ A)\ \dfrac{8}{3}x+6}\\\boxed{Q\#2.\ A)\ \dfrac{1}{3}(p+45)}[/tex]

Step-by-step explanation:

[tex]Q\#1:\\\\\dfrac{2}{3}(4x+9)\qquad\text{use the distributive property}\\\\=\left(\dfrac{2}{3}\right)(4x)+\left(\dfrac{2}{3}\right)(9)=\dfrac{8}{3}x+(2)(3)=\dfrac{8}{3}x+6\\\\Q\#2:\\\\\dfrac{1}{3}p+15=\dfrac{1}{3}p+\dfrac{1}{3}\cdot(3)(15)=\dfrac{1}{3}p+\dfrac{1}{3}\cdot45=\dfrac{1}{3}(p+45)[/tex]

Answer:

  3.9

Step-by-step explanation:

A calculator is useful for this.

Answer:

[tex]\large\boxed{P=(16+36x)\ ft}[/tex]

Step-by-step explanation:

The formula of an area of a rectangle:

[tex]A=bh[/tex]

b - base

h - height

We have A = 144x ft² and h = 8. Substitute and solve for b:

[tex]144x=8b[/tex]              divide both sides by 8

[tex]b=18x\ ft[/tex]

The formula of a perimeter of a rectangle:

[tex]P=2b+2h[/tex]

Substitute:

[tex]P=2(18x)+2(8)=36x+16[/tex]

Answer:

  [tex]r=\dfrac{I}{Pt}[/tex]

Step-by-step explanation:

Solve this the way you do any "solve for" problem. Locate the variable of interest and identify what has been done to it. Undo that.

Here, the variable of interest is "r". It has been multiplied by Pt. We undo that multiplication by dividing by that product:

  [tex]I=Prt\\\\\dfrac{I}{Pt}=\dfrac{Prt}{Pt}\\\\\dfrac{I}{Pt}=r \quad\text{simplify}[/tex]

Answer:

Linear

Step-by-step explanation:

Hello

Is linear

Best regards

Answer:

Linear

Step-by-step explanation:

Linear function : if the value increases with the constant value per period,

It can written as y = a + bx

Where, a = initial value, b = constant value per period,

Exponential function :  if the value increases with the constant rate per period,

It can be written as,

[tex]y=ab^x[/tex]

Where, a = initial value, b = growth factor per period.

∵ Every year 39 million cars cross the Golden Gate Bridge in San Francisco.

Then after x years, the number of cars ( in million )

f(x) = 39x

⇒ f(x) = 0 + 39x

By the above explanation,

Hence, the function that represents the number of cars that have crossed the Golden Gate Bridge is linear.