Mr.Mole left his burrow and started digging his way down at a constant rate

A) exponential is the right answer.

Step-by-step explanation:

The formula used for increase after same number of time is:

[tex]A_t = A_0(1+r)^t\\Here\\A_0\ is\ the\ initial amount\\r\ is\ the\ rate\\and\\t\ is\ time[/tex]

We are given

A_0 = 35000

r = 3%

[tex]A_t = 35000(1+0.03)^t\\A_t = 35000(1.03)^t[/tex]

The function is an exponential function is the value of t can be put equal to 1,2,3,4..... which will increase the final output exponentially

Hence,

A) exponential is the right answer.

Keywords: Functions, Exponential function

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The sum of three consecutive odd integers is 76 less then seven times the middle number. The three integers are 17, 19 and 21 respeectively

Since each consecutive odd integer is separated by a difference of  2

Let "n" be the first integer

n + 2 be the second integer

n + 4 be the third integer

Given that the sum of three consecutive odd integers is 76 less then seven times the middle number

Which means,

The sum of ( n, n + 2, n + 4) is equal to 76 less than seven times the middle number ( 7(n + 2))

That is,

n + n + 2 + n + 4 = 7(n + 2) - 76

3n + 6 = 7n + 14 - 76

4n = 68

n = 17

So we get:

First integer = n = 17

Second integer = n + 2 = 17 + 2 = 19

Third integer = n + 4 = 17 + 4 = 21

Thus the three consecutive odd integers are 17, 19 and 21 respeectively

Answer:

20 years apart.

Step-by-step explanation:

Daughter is 10 years old, and mother is 3 times older. This makes mother 30 years old.  There is a 20 year difference between them.

Ten years later, the daughter is 20 years old. Since the mother is 20 years older, she is now 40, which is 2 times older than the daughter.

Answer:

y = (2/5) x + (11/5)

Step-by-step explanation:

recall that the slope-intercept form of a linear equation takes the general form:

y = mx + b

In this case, we simply have to use algebra rules to rearrange the given equation such that it looks like the one above:

-5y = 2x + 11   (divide both sides by -5)

y = -(2/5) x - (11/5)     (answer)

Answer:

The variables are 'p' and 'c'.

The inequality is: [tex]10p+4c\geq100[/tex]

The graph is plotted below.

Three possible solutions are: (0, 25), (10, 0) and (5, 20)

Step-by-step explanation:

Let the number of pizzas sold be 'p' and number of cookies sold be 'c'.

Given:

Price per pizza = $10

Price per cookie = $4

Minimum amount to be earned = $100

Price for 'p' pizzas sold = [tex]10p[/tex]

Price for 'c' cookies sold = [tex]4c[/tex]

As per question:

[tex]10p+4c\geq100[/tex]

Also, number of pizzas and cookies can't be negative. So,

[tex]p\geq0,c\geq0[/tex]

Plotting the above inequalities on a graph using DESMOS.

The region that is common to all the above inequalities is the solution region and is shown in the graph below.

The solution region also includes all the points on the line.

So, the three possible combinations of solutions can be any 3 points in the solution region. One such combination is:

(0, 25), (10, 0) and (5, 20)

Answer:

48 million

Step-by-step explanation:

Since 48,000,000 has TWO non-zero numbers, not one, it can't be the

answer.

The largest digit in the given number is the ten-millions digit, so

you want to round to the nearest ten million, rather than the nearest

million.

47,859,600 rounds to 50,000,000, to one significant digit.

Normally, we would say "round to one significant digit," but you

probably have not seen that term. Your question means the same th

To estimate 394/24, round 394 to 400 and 24 to 20, to get an estimated quotient of 20 after dividing the rounded figures.

To estimate 394/24 by rounding each number to have only one nonzero digit, we round 394 to 400 and 24 to 20. Now, let's divide the rounded figures:

This gives us an estimated result. To round to the nearest whole number, we start with our original rounded figures since both have 0 decimal places. Therefore, our final estimate after rounding is 20.

When performing mathematical operations like this, it's important to use the rounding rules properly. For division and multiplication, we round the final answer to the number of significant figures that matches the number with the least significant figures used in the calculation.

Answer:

h = 1.41

c = 3.46

Step-by-step explanation:

See the triangles diagram attached.

For the first triangle, Base = h, Hypotenuse = 2 and the angle between base and hypotenuse is 45°.

Therefore, [tex]\cos 45 = \frac{\textrm {Base}}{\textrm {Hypotenuse}} = \frac{h}{2}[/tex]

⇒ [tex]h = 2 \cos 45 = \frac{2}{\sqrt{2} } = \sqrt{2} = 1.414 = 1.41[/tex] (Answer)

{Rounded to the nearest tenth}

Again in the second triangle, Perpendicular = c, Hypotenuse = 4 and the angle between base and hypotenuse is 60°.

Therefore, [tex]\sin 60 = \frac{\textrm {Perpendicular}}{\textrm {Hypotenuse}} = \frac{c}{4}[/tex]

⇒ [tex]c = 4 \sin 60 = \frac{4 \times \sqrt{3} }{2} = 2\sqrt{3} = 3.46[/tex] (Answer)

{Rounded to the nearest tenth}

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange - 8x - 6y - 4 = 0 by adding 8x + 4 to both sides

- 6y = 8x + 4 ( divide all terms by - 6 )

y = - [tex]\frac{4}{3}[/tex] x - [tex]\frac{2}{3}[/tex] ← in slope- intercept form

with slope m = - [tex]\frac{4}{3}[/tex] and y- intercept c = - [tex]\frac{2}{3}[/tex]

To find the x- intercept let y = 0 in the equation and solve for x

- 8x - 0 - 4 = 0 ( add 4 to both sides )

- 8x = 4 ( divide both sides by - 8 )

x = - [tex]\frac{1}{2}[/tex] ← x- intercept

The algebraic expression represents the phrase "the quotient of negative eight and the sum of a number and three" is [tex]\frac{-8}{n+3}[/tex] or [tex]-8 \div n+3[/tex]

Given statement is "the quotient of negative eight and the sum of a number and three"

To write the algebraic expression, follow these steps:

Let "n" be the number

The expression "negative eight" is equivalent to -8

Now look at the statement "the sum of a number and three"

"The sum of a number and three" is equivalent to n + 3

Now put all the statements together:

Quotient means you are dividing. So use division

"The quotient of negative eight and the sum of a number and three" = [tex]\frac{-8}{n+3}[/tex] or [tex]-8 \div n+3[/tex]

Answer: Choice D,  -5x^3 + 8

A binomial consists of two terms being added or subtracted. The two terms are -5x^3 and 8. The term -5x^3 has a leading coefficient -5 and exponent 3. The largest exponent determines the degree of the polynomial. The 8 is constant as there are no variables attached or multiplying with it.

Answer:

C) 15n=10

Step-by-step explanation:

Because 15(2/3)=5*2=10.

Answer:

n = 12 + 19

Step-by-step explanation:

Flip the equation around like this: 12 + 19 = n

Then you are going to add: 12 + 19 = 31

So, n = 31

Hope this helps

-Amelia

Answer:

13.5

Step-by-step explanation:

2/3=9/x

2x=9*3

2x=27

x=27÷2

x=13.5

Final answer:

There are 13.5 cups of vegetables in the soup.

Explanation:

If the ratio of chicken to vegetables in a soup is 2:3, and there are 9 cups of chicken, we can find the number of cups of vegetables by setting up a proportion. According to the ratio, for every 2 cups of chicken, there are 3 cups of vegetables. Since we have 9 cups of chicken, we want to know how many cups of vegetables correspond to this amount.

Write the ratio of chicken to vegetables as a fraction: 2/3.

Set up a proportion where 2 cups of chicken is to 3 cups of vegetables as 9 cups of chicken is to x cups of vegetables.

2/3 = 9/x

Cross multiply to solve for x: 2x = 9 × 3

2x = 27

Divide both sides by 2 to solve for x: x = 27/2

x = 13.5

Therefore, there are 13.5 cups of vegetables in the soup.

[tex]\bf \textit{zeros at } \begin{cases} x = -3\implies &x+3=0\\ x = -1\implies &x+1=0\\ x = 4\implies &x-4=0 \end{cases}\qquad \implies (x+3)(x+1)(x-4)=\stackrel{y}{0} \\\\\\ (x^2+4x+3)(x-4)=0\implies x^3~~\begin{matrix}+ 4x^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~+3x~~\begin{matrix} -4x^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~-16x-12=0 \\\\\\ x^3-13x-12=0[/tex]

we know that f(-2) = 24, namely when x = -2, y = 24, let's see if that's true

[tex]\bf x^3-13x-12=y\implies \stackrel{x = -2}{(-2)^3-13(-2)-12}=y \\\\\\ -8+26-22=y \implies 6=y[/tex]

darn!! no dice.... hmmmm wait a second.... 4 * 6 = 24, if we could just use a common factor of 4 on the function, that common factor times 6 will give us 24, let's check.

[tex]\bf 4(x^3-13x-12)=y\implies \stackrel{x = -2}{4[~~(-2)^3-13(-2)-12~~]}=y \\\\\\ 4[~~-8+26-22~~]=y\implies 4[6]=y\implies 24=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill 4x^3-52x-48=y~\hfill[/tex]

Answer:

Sally had 917 bottles of water \she plans on buying 67 more bottles of water so in all she will have 984 bottles of water.

Step-by-step explanation:

Answer:

6/8, 9/12, and 12/15

Step-by-step explanation:

3/4 + 3/4 = 6/8

6/8 + 3/4 = 9/12

9/12 + 3/4 = 12/15

Answer:

no becase the x value 2 has two y values 5 and 7. for it to be a function each x value can only have 1 y value

Step-by-step explanation:

Answer:

no it is not

Step-by-step explanation:

Answer:

The graph is possible for [tex]b^2-4ac=4[/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]

If D=0 the quadratic equation has only one real solution

If D>0 the quadratic equation has two real solutions

If D<0 the quadratic equation has no real solution (complex solutions)

In this problem , looking at the graph, the quadratic equation has two real solutions (the solutions are the x-intercepts)

so

[tex]b^2-4ac > 0[/tex]

therefore

The graph is possible for [tex]b^2-4ac=4[/tex]

Answer:

b^2 – 4ac = 4

Answer:

4.5 sq. units.

Step-by-step explanation:

The given curve is [tex]y = (3x)^{\frac{1}{2} }[/tex]

⇒ [tex]y^{2} = 3x[/tex] ...... (1)

This curve passes through (0,0) point.

Now, the straight line is y = 3x - 6 ....... (2)

Now, solving (1) and (2) we get,

[tex]y^{2} - y - 6 = 0[/tex]

⇒ (y - 3)(y + 2) = 0

⇒ y = 3 or y = -2

We will consider y = 3.

Now, y = 3x - 6 has zero at x = 2.

Therefor, the required are = [tex]\int\limits^3_0 {(3x)^{\frac{1}{2} } } \, dx - \int\limits^3_2 {(3x - 6)} \, dx[/tex]

= [tex]\sqrt{3} [{\frac{x^{\frac{3}{2} } }{\frac{3}{2} } }]^{3} _{0} - [\frac{3x^{2} }{2} - 6x ]^{3} _{2}[/tex]

= [tex][\frac{\sqrt{3}\times 2 \times 3^{\frac{3}{2} }  }{3}] - [13.5 - 18 - 6 + 12][/tex]

= 6 - 1.5

= 4.5 sq. units. (Answer)

The width of the rectangles is 4.

Step-by-step explanation:

Given that two rectangles have same width. So, let be the two rectangles [tex]R_{1}[/tex] and [tex]R_{2}[/tex] and width of rectangle is ‘x’. So, according to question, we have  

Length of one rectangle , [tex]R_{1}[/tex] = x + 1

Length of other rectangle, [tex]R_{2}[/tex] = x + 2

But we also know that,

                  [tex]\text { Area of rectangle } = \text { Length } \times \text { width }[/tex]

So,  then the area for one rectangle,

                [tex]\text { Area of rectangle } R_{1} = x \times(x+1)[/tex]

Similarly,

                [tex]\text { Area of rectangle } R_{2} = x \times(x+2)[/tex]

So, according to question,

                [tex]\text {Area of rectangle } R_{2} = 4 \times \text { Area of rectangle } R_{1}[/tex]

                [tex]x \times(x+2) = 4+x \times(x+1)[/tex]

Now, by solving the above equation, we get

                [tex]x^{2}+2 x = 4+x^{2}+x[/tex]

                [tex]x = 4[/tex]

So, from the above equation, we found that width of the rectangle is 4.

Answer: For number one it's decreasing

Step-by-step explanation:

Answer:

Step-by-step explanation:

points that lie on an axis do not lie in any quadrant.  

So point A lies in the  positive x-axis

The origin (0,0) does't lie on any quadrant.

Origin is the point that lies on both x-axis and y-axis

There are 120 professors at the university

Step-by-step explanation:

At one really small university:

We need to find how many professors are at the university

Assume that the number of people the university is 100%

∵ 53% of the people in the university are undergraduates

∵ 37% of the people in the university are graduates

∵ There are 100% people in the university

- To find the rest subtract the sum of the undergraduates and

   graduates from 100%

∵ The rest = 100% - (53% + 37%)

∴ The rest = 100% - 90%

∴ The rest = 10%

∴ The rest is 10% from 1200 people in the university

∵ The rest are going for their doctorate

∴ The rest is the number of the professors in the university

∵ The rest is 10% from 1200 people in the university

∴ The number of professors = 10% × 1200

∵ 10% = 10 ÷ 100 = 0.1

∴ The number of professors = 0.1 × 1200

∴ The number of professors = 120

There are 120 professors at the university

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Answer:

89

Step-by-step explanation:

2^3=2*2*2=8

3^4=3*3*3*3=9*9=81

8+81=89

The equation of a parabola that opens up and has the following x intercepts (-3,0) and (4,0) is [tex]y=x^{2}-x-12[/tex]

We have to find the equation of a parabola that opens up and has the following x intercepts (-3, 0) and (4, 0)

x-intercepts of the parabola are (−3, 0) and (4, 0)

So, we can form an equation:

Also x = 4

x – 4 = 0

x – 4 = 0 is another factor of quadratic equation.

The quadratic function is:

[tex]\begin{array}{l}{y=(x+3)(x-4)} \\\\ {y=x^{2}-4 x+3 x-12} \\\\ {y=x^{2}-x-12}\end{array}[/tex]

Hence, the equation of the parabola is  [tex]y=x^{2}-x-12[/tex]

To find the equation of a parabola with x-intercepts at (-3,0) and (4,0), we can use the factored form of a quadratic equation. By plugging in the values of the roots and simplifying, we can determine that the equation of the parabola is y = x^2 - x - 12.

To find the equation of a parabola that opens up and has x-intercepts at (-3,0) and (4,0), we can start by recognizing that the x-intercepts are the points where the parabola intersects the x-axis. This means that the parabola has roots of -3 and 4. To find the equation, we can use the factored form of a quadratic equation: (x - root1)(x - root2) = 0. Plugging in the values of the roots, we get (x - (-3))(x - 4) = 0. Simplifying this, we have (x + 3)(x - 4) = 0. Expanding this, we have x^2 - x - 12 = 0. Therefore, the equation of the parabola is y = x^2 - x - 12.

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Answer:

The longest bolt that can be acceptable is [tex](12+0.2)=12.2\ mm[/tex]

Step-by-step explanation:

To find the acceptable measure of the bolt we have to add and subtract the clearance limit.

a.For longest measure of the bolt we will perform addition.

And for shortest measure of the bolt we will go with subtraction.

So the longest acceptable measure of the bolt [tex]=12\ mm +0.2\ mm = 12.2\ mm[/tex]

Hope there question b is missing.

b.

The shortest measure of the bolt  [tex]=12\ mm -0.2\ mm = 11.8\ mm[/tex]

The acceptable measure of the bolt are:

For longest it is [tex]12.2\ mm[/tex] and for shortest it is [tex]11.8\ mm[/tex]

Answer:

Thomas still has 1 3/5 suitcases available for his own belongings.

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Number of souvenirs bought by Thomas = 6

Space that each souvenir takes of Thomas suitcase = 1/15

Number of Thomas suitcases = 2

2.  How much room is left for his own belongings in his suitcases?

Let's find out how much space the souvenirs take:

Number of souvenirs * Space that each souvenir takes

6 * 1/15 = 6/15 = 2/5 (Dividing by 3 the numerator and the denominator)

The souvenirs take 2/5 of one suitcase.

Now, we can calculate the room that is left for Thomas' belongings.

2 Suitcases - 2/5 for the souvenirs

2 - 2/5 = 10/5 - 2/5 = 8/5 = 1 3/5

Thomas still has 1 3/5 suitcases available for his own belongings.

Note: Same answer to question 14040097, answered by me.

Answer:

26.

Step-by-step explanation:

15% of 29.90 is 3.90

26+3.90= 29.90

The price of Mr Johnson's lunch bill before the 15% tip paid is $26.

Percentage can be described as a fraction of an amount expressed as a number out of hundred.

In order to determine the price before the tip, divide the lunch bill by the percentage tip.

Price before the tip = lunch bill / ( 1 + percentage tip)

29.90 / 1/15 = $26

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Answer:

29 feet

2.6 seconds

Step-by-step explanation:

h(t) is a downwards parabola, so the maximum is at the vertex.

t = -b / (2a)

t = -40 / (2×-16)

t = 1.25

h(1.25) = -16(1.25)² + 40(1.25) + 4

h(1.25) = 29

When the ball lands, h(t) = 0.

0 = -16t² + 40t + 4

0 = 4t² − 10t − 1

t = [ -(-10) ± √((-10)² − 4(4)(-1)) ] / 2(4)

t = (10 ± √116) / 8

t = (5 ± √29) / 4

t is positive, so:

t = (5 + √29) / 4

t ≈ 2.6