1) The ages of trees in a forest are normally distributed with a mean of 25 years and a standard deviation of 5 years. Using the empirical rule, approximately what percent of the trees are between 20 and 30 years old?
2)Pizza delivery times at Pizza Time are normally distributed with a mean time of 27 minutes and a standard deviation of 3 minutes. Using the empirical rule, approximately what percent of pizzas are delivered between 24 and 30 minutes?

An exponential function may be given by:

f(x) = A(1+r)^x

A is the initial amount and r is a decimal representing the growth rate.

We can see that 1+r = 1.2, and we solve for r:

1 + r = 1.2

r = 0.2

The growth rate is 0.2, or 20%

Choice B

The rate of growth of Mason's daily sales is 20%.

The rate of growth of Mason's daily sales can be found by determining the percentage increase in the sales from one day to the next. To find this, we can compare the sales on two consecutive days and calculate the ratio of the second day's sales to the first day's sales. Let's consider the sales on the first day (x) and the sales on the second day (x+1).

Given the sales model f(x) = 50(1.2)^x, we can substitute x and x+1 into the equation to get the sales on the first and second day, respectively. The ratio of the second day's sales to the first day's sales is:

f(x+1) / f(x) = (50(1.2)^(x+1)) / (50(1.2)^x) = 1.2.

So, the rate of growth is 1.2, which represents a 20% increase in sales from one day to the next.

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Answer:

In general you can choose the vertices at any arbitrary points but for easier computations and calculations we can choose 1 vertex at origin with co-ordinates [tex](0,0)[/tex] and it's adjacent vertex either on x-axis with co-ordinates [tex](x,0)[/tex] or on y-axis with ordinates [tex](0,y)[/tex]

Thus the coordinates of vertices become

First lets change the fractions so they have common denominators:

3/5 = 6/10

The bank was 1/10, after adding the pennies it was 6/10

6/10 - 1/10 = 5/10 = 1/2

This means 400 pennies filled 1/2 the piggy bank.

There are 2 halves (1/2) to a whole ( full piggy bank).

The piggy bank can hold 400 x 2 = 800 pennies.

Answer:

  $1.45

Step-by-step explanation:

To answer the question, we would like to have an equation that has the cost of a game as its only variable. That is, we would like to eliminate the cost of a ride from the system of equations we must write.

Let g and r represents the costs of a game and a ride, respectively. Then the expenses of the two carnival-goers can be described by ...

  5g +6r = 11.75

  7g +8r = 16.15

We note that the ratio of coefficients in the variable (r) that we want to eliminate is 3:4. So we can subtract 4 times the first equation from 3 times the second to eliminate that variable.

  3(7g +8r) -4(5g +6r) = 3(16.15) -4(11.75)

  g = 1.45 . . . . . . simplify

The cost to play one game was $1.45.

Answer:

$1.45

Step-by-step explanation:

Answer:

420 ways

Step-by-step explanation:

According to the given statement:

We want to divide the 10 dogs into three groups, one with 3 dogs, one with 5 dogs, and one with 2 dogs. How many ways can we form the groups such that fluffy is in the 3-dog group and nipper is in the 5-dog group.

In this way we have 8 dogs left.

2 spaces left in 3 dogs group

4 spaces left in 5 dogs group

and 2 spaces in 2 dogs group

Therefore:

= 8!/2!4!2!

= 8*7*6*5*4*3*2*1/2*4*3*2*2

= 8*7*6*5/2*2

= 1680/4

=420

It means there are 420 ways to from the groups....

Answer:

The right answer us "is always" as its all angles are 60 degree.

Answer:

-4

Step-by-step explanation:

[√2(cos(3π/4) + i sin(3π/4))]⁴

(√2)⁴ (cos(3π/4) + i sin(3π/4))⁴

4 (cos(3π/4) + i sin(3π/4))⁴

Using De Moivre's Theorem:

4 (cos(4 × 3π/4) + i sin(4 × 3π/4))

4 (cos(3π) + i sin(3π))

3π on the unit circle is the same as π:

4 (cos(π) + i sin(π))

4 (-1 + i (0))

-4

Answer:

-17

Step-by-step explanation:

Plug in -2 as your x value for the g(x) equation and simplify.

[tex]g(-2)=\sqrt{-2+6} \\g(-2)=\sqrt{4} \\g(-2)=2[/tex]

Next, plug in your g(x) value (2) to the f(x) equation for x and simplify.

[tex]f(2)=-7(2)-3\\f(2)=-14-3\\f(2)=-17[/tex]

Answer:

Step-by-step explanation:

The way you have written the first question may be what is confusing you. It should be written as

bn = 3*b_(n-1) + 2

So b2 =

b2 =3*b_(2 -1) + 2

b2 = 3*b1 + 2

b2 = 3*5 + 2

b2 = 15 + 2

b2 = 17

===========

b3 = 3b_(n _1) + 2

b_2 = 17 (from the step above)

b3 = 3*17 + 2

b3 = 51 + 2

b3 = 53

==========

b_4 = 3*b_3 + 2

b_4 = 3*53 + 2

b_4 = 159 + 2

b_4 = 161

Do you see how this works? You take the previous term, multiply by 3 and add 2 to get the current term. This one builds up rather quickly.

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Next Question

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tn = a + (n - 1)*d

t6 = a + (6 - 1)*d

t4 = a + 5d

4 = a + 5d    

t10 = a + 9d

Subtract t4 [4 = a + 3d ] from t10 written bellow

- 4 = a +  9d

4  = a + 5d

- 8 = 4d              Divide by 4

-8/4 = 4d/4

-2 = d

t6 = a + 5d

4 = a + 5*(-2)

4 = a - 10               Add 10 to both sides.

4 + 10 = a - 10 + 10

14 = a

tn = 14 + (n - 1)*d

Answer: d

Please don't use red. It is really hard to read.

Answer:

blank 1 = 24

blank2= 30

Step-by-step explanation:

Given:

2(4x+3)(3x+5)

=2(12x^2+20x+9x+15)

=2(12^2+29x+15)

=24x^2+58x+30

Hence blank 1= 24 and blank2= 30 !

Answer:

47.88 in^2 of paper.

Step-by-step explanation:

The amount of paper needed for the base = 4.2^2 = 17.64 in^2.

There are 4 triangular faces.

The area of each triangular face = 1/2* base * height

= 1/2 * 4.2 * 3.6

=  7.56 in^2

That is a total of 4 * 7.56 = 30.24 in^2.

So the total amount of paper need to cover the entire pyramid

= 17,64 + 30.24

= 47.88 in^2.

Answer:

a=b

greater than

Step-by-step explanation:

Answer:

volumes of the cones are equal when (a=b)

If a > b, then the cross-sectional area of cone a is (GREATER THAN) is  the cross-sectional area of cone B at every level parallel to their respective bases.

Step-by-step explanation:

Answer:

x = 11.79

? = 6.25

Step-by-step explanation:

Using the law of sines

[tex]\frac{10}{sin58}[/tex] = [tex]\frac{x}{sin90}[/tex]

x = sin 90° x [tex]\frac{10}{sin58}[/tex] = 11.79

by Pythagorean theorem,

?² + 10² = x²

? = √  (x²- 10²)

? = √  (11.79²- 10²) = 6.25

Answer:

(4/3, 4  5/9) and (-32, -53)

Step-by-step explanation:

When a curve is given as a set of parametric equations, as this one is, then the slope of the tangent line to the curve is

              dy/dt

dy/dx = ------------

               dx/dt

which here is

              dy/dt        8 - 20t

dy/dx = ----------- = --------------

               dx/dt         12t^2

If the slope at a certain point on this curve is 1, then we conclude that:

8 - 20t = 12t^2, or

12t^2 + 20t - 8 = 0, or

3t^2 + 5t - 2 = 0

We have to solve this equation for the parameter, t:

Here a = 3, b = 5 and c = -2, and so the discriminant is

b^2 - 4ac = 25 - 4(3)(-2), or 49, and the square root of that is 7.

Thus, the roots are:

     -5 ± 7

t =  --------- = 1/3 and t = -2

        2(3)

Evaluate x and y twice, once each for each t value.

Case 1:  t = 1/3

x = 4(1/3) and y = 3 + 8(1/3) - 10(1/3)^2, or

x = 4/3 and y = 3 + 8/3 - 10/9:  (4/3, 4  5/9)

Case 2:  t = -2

x = 4(-2)^3 and y = 3 + 8(-2) - 10(-2)^2, or y = 3 - 16 - 40, or y = -53.

This gives us the point (-32, -53)

To find the points where the tangent line has a slope of 1 on the given curve, we derive expressions for dx/dt and dy/dt, set dy/dx equal to 1, and solve for t.

The given equation defines a parametric curve with x = 4t3 and y = 3 + 8t − 10t2. To find the points on this curve where the tangent line has a slope of 1, we'll first need to find expressions for dx/dt and dy/dt, which represent the rates of change of x and y with respect to the parameter t.

By differentiating x = 4t3 with respect to t, we find dx/dt = 12t2. Similarly, by differentiating y = 3 + 8t − 10t2 with respect to t, we find dy/dt = 8 - 20t.

The slope of the tangent line at a particular point on the curve corresponds to dy/dx, which we can find by dividing dy/dt by dx/dt, yielding (8 - 20t) / (12t2). We can set this equal to 1 (since we want a slope of 1) and solve for t to find the points on the curve where the tangent line has slope 1.

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Check the picture below.

so, the vertex at N, is noticeably not a right angle is an acute angle, so is less than 90°, so we don't need to check that one.

now, is the angle at L 90°?

well, if that's true LM and LN are perpendicular, and if they're indeed perpendicular, their slopes are negative reciprocal, meaning the slope of one is the same as the other but negative and upside down, well, let's check.

[tex]\bf L(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad M(\stackrel{x_2}{2}~,~\stackrel{y_2}{2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{2-0}{2-0}\implies \cfrac{2}{2}\implies 1 \\\\[-0.35em] ~\dotfill\\\\ L(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad N(\stackrel{x_2}{2}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-0}{2-0}\implies \cfrac{-1}{2}\implies -\cfrac{1}{2}[/tex]

[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope~of~LM}{1\implies \cfrac{1}{\underline{1}}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{\underline{1}}{1}}\qquad \stackrel{negative~reciprocal}{-\cfrac{\underline{1}}{1}\implies -1}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{slope of LM}}{1}\qquad \stackrel{\textit{negative reciprocal of LM}}{-1}\qquad \stackrel{\textit{slope of LN}}{-\cfrac{1}{2}}~\hfill -1\ne -\cfrac{1}{2}[/tex]

so that means Lydia put too much espresso on her last cup.

Answer:

A = 14 units ^2

Step-by-step explanation:

The area of a triangle is

A = 1/2 b h  where b is the base and h is the height

b = the length of EF  which is 7 units

h = D to the line EF which is 4 units

A = 1/2 (7*4)

A = 14 units ^2

Answer:

BD = 10

Step-by-step explanation:

Since AC is a tangent to the circle at B then ∠ABD = 90°

Using Pythagoras' identity in the right triangle ABD with hypotenuse AD

The square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

BD² + AB² = AD²

BD² + 24² = 26²

BD² + 576 = 676 ( subtract 576 from both sides )

BD² = 100 ( take the square root of both sides )

BD = [tex]\sqrt{100}[/tex] = 10

Answer:

The range in shelter A is 22, and the range in shelter B is 18.

Step-by-step explanation:

The range is the largest value minus the smallest value.

For shelter A, the range is 30 − 8 = 22.

For shelter B, the range is 28 − 10 = 18.

Answer:

The range in shelter A is 22, and the range in shelter B is 18.

Step-by-step explanation:

The box plots show the weights, in pounds, of the dogs in two different animal shelters. The range in shelter A is 22, and the range in shelter B is 18 correctly compares the ranges of the data.

There are 52,920 ways to select 5 appetizers, 4 main courses, and 5 desserts for the banquet.

To solve this problem, we can use the concept of combinations, as we're selecting items without considering the order.

For appetizers:

We need to choose 5 appetizers out of 6 available. This can be calculated using the combination formula: nCr = n! / [r! * (n-r)!], where n is the total number of items, and r is the number of items to be chosen.

So, for appetizers, it's [tex]6C_5 = 6! / [5! * (6-5)!] = 6 ways[/tex].

For main courses:

Similarly, we need to choose 4 main courses out of 7 available. So, it's

[tex]7C_4 = 7! / [4! * (7-4)!] = 35 ways[/tex].

For desserts:

We need to choose 5 desserts out of 10 available. So, it's

[tex]10C_5 = 10! / [5! * (10-5)!] = 252 ways[/tex].

To find the total number of ways:

We multiply the number of ways for each category since these choices are independent.

Total ways = (6 ways for appetizers) * (35 ways for main courses) * (252 ways for desserts) = 52920 ways.

Thus, there are 52,920 ways to select 5 appetizers, 4 main courses, and 5 desserts for the banquet.

Complete Question:

A catering service offers 6 appetizers, 7 main courses, and 10  desserts. A customer is to select 5 appetizers, 4 main courses, and 5 desserts for a banquet. In how many ways can this be done?

Answer:

x≤ 60 - (3÷1/15)

Step-by-step explanation:

Number of blankets to be made = 3

Darcie crochets 1/15 blanket per day

To crochet one carpet she needs = 15 days

To crochet three carpets she needs = 15*3 = 45 days

Number of days she had = 60 days

She can skip days = 60-45 = 15 days

Let x be the number of days to complete her work.

Thus the equation becomes x≤ 60 - (3÷1/15)

You can solve for x to determine the number of days, Darcie can skip crocheting, you will get the answer 15....

The answer explains how to set up and solve an inequality to determine the number of days Darcie can skip crocheting while still meeting her goal of donating blankets.

To determine the number of days Darcie can skip crocheting and still meet her goal, we need to set up an inequality based on the information given.

First, calculate the total number of blankets Darcie needs to crochet: 3 blankets.

Set up the inequality: 1/15 * (60 - x) ≥ 3, where x represents the number of days she can skip crocheting.

Solve the inequality: 60 - x ≥ 45, x ≤ 15.

Therefore, Darcie can skip crocheting for up to 15 days and still meet her goal of donating 3 blankets.

Answer:

5.2 Km/Min

Step-by-step explanation:

Speed/Rate= Distance/Time

Speed/Rate = 114.4/22

Speed/Rate = 5.2 KM/min

Answer:

5.3 km/min

Step-by-step explanation:

Distance = 114.4 kilometers

Time = 22 minutes

Rate = 114.4 km /22 min

Rate = 5.2 km/min

Answer:

yes

Step-by-step explanation:

this is right i think

The correct answer is line HJ .

1. **Line AB**: The slope of line AB is not the negative reciprocal of 1/2, so it is not perpendicular.

2. **Line CD**: The slope of line CD is not the negative reciprocal of 1/2, so it is not perpendicular.

3. **Line FG**: The slope of line FG is not the negative reciprocal of 1/2, so it is not perpendicular.

4. **Line HJ**: The slope of line HJ is the negative reciprocal of 1/2, which makes it perpendicular.

A line with a slope of **-3/5** can be represented by the equation:

[tex]\[ y = -\frac{3}{5}x + b \][/tex]

where \(b\) is the y-intercept. To find points on this line, we need to consider different values of \(x\) and calculate the corresponding \(y\).

Let's explore some potential points:

1. **Point A (x, y)**:

  - Assume \(x = 0\):

  [tex]\[ y = -\frac{3}{5} \cdot 0 + b = b \] - So, point A is \((0, b)\).[/tex]

2. **Point B (x, y)**:

  - Assume \(x = 5\):

  [tex]\[ y = -\frac{3}{5} \cdot 5 + b = -3 + b \] - So, point B is \((5, -3 + b)\).[/tex]

3. **Point C (x, y)**:

  - Assume \(x = 10\):

  [tex]\[ y = -\frac{3}{5} \cdot 10 + b = -6 + b \] - So, point C is \((10, -6 + b)\).[/tex]

These are just a few examples. You can find more points by choosing different values of \(x\). Remember that any point on the line will satisfy the equation [tex]\(y = -\frac{3}{5}x + b\).[/tex]

Now, let's explore the concept of parallel lines. Two lines are parallel if they have the **same slope**. If we have another line with a slope of 1/2, we can find points on that line as well.

The correct answer is F. Quantitative data are numerical in​ nature, while qualitative data are categorical in nature.

Explanation:

In research and all the different fields that apply to it, the word "data" refers to information, values or knowledge that can be used to understand a specific situation or phenomenon. Additionally, data can be of two different types quantitative and qualitative, these differ in their nature, the phenomenons they described and the way they should be analyzed. Indeed quantitative data refers mainly to numerical data or information about quantities such as statistics that are especially useful in mathematics, science and similar that focus on numbers. On the other hand, qualitative data refers to data based on categories or qualities and because of this qualitative data is used in humanistic research, although both types of data can be combined to study a phenomenon. Considering this, the key difference between both types of data is "Quantitative data are numerical in​ nature, while qualitative data are categorical in nature".

Answer:

it is F

Step-by-step explanation:

F. Quantitative data are numerical in​ nature, while qualitative data are categorical in nature.

Answer:

  2√3

Step-by-step explanation:

You recognize this as a 30°-60°-90° triangle, so you know the hypotenuse (R) is twice the length of the shortest side (√3).

The magnitude of R is 2√3.

_____

In case you haven't memorized the ratios for a 30°-60°-90° triangle, you can use trigonometry and the fact that ...

  Sin = Opposite/Hypotenuse

  sin(30°) = √3/R

  R = √3/sin(30°) = √3/(1/2) = 2√3

Of course, doing this on your calculator will give a numerical answer, which you may not want.

Answer: x=-3

Step-by-step explanation:

F(x)=9x^2-54x-19

F(x)=(x-57)(x+3)

X=57 X=-3

Answer:

A.) −2y + 10

Step-by-step explanation:

−x − 2y = −10

Add 2y to both sides.

-x = 2y - 10

Multiply both sides by -1.

x = -2y + 10

Let's solve the system using the substitution method. We'll start by isolating \( x \) in the second equation.
The second equation is given by:
\[ -x - 2y = -10 \]
To isolate \( x \), we'll follow these steps:
1. Add \( 2y \) to both sides of the equation, which gives us:
\[ -x = 2y - 10 \]
2. Now, we multiply both sides by \( -1 \) to solve for \( x \), which gives us:
\[ x = -1(-2y + 10) \]
\[ x = 2y - 10 \]
The expression that we would substitute into the first equation for \( x \) is \( 2y - 10 \).
Therefore, the correct answer is:
C.) \( 2y - 10 \)

Answer:

5

Step-by-step explanation:

Given

Original Measurement = 11*9 inches

Measurement after enlargement = 55 * 45 inches

In order to find the scale factor, we can choose one side of the figure or the whole area and find the ratio between the measurement before enlargement and after enlargement.

In case of a side the answer will be the scale factor while in case of finding scale factor using areas the answer will be the square of scale factor.

So,

[tex]Scale\ factor =s^2= \frac{55*45}{11*9} \\s^2 = \frac{2475}{99} \\s^2=25[/tex]

As we know that this is the square of scale factor.

Hence the scale factor will be:

[tex]\sqrt{s^2}=\sqrt{25}  \\s=5[/tex]

So, the scale factor is 5 ..

Answer:

[tex]\large\boxed{-2x^3y^2+9x^2y^3-3xy^4-6x^4y+y^5}[/tex]

Step-by-step explanation:

[tex](-2x^3y^2+4x^2y^3-3xy^4)-(6x^4y-5x^2y^3-y^5)\\\\=-2x^3y^2+4x^2y^3-3xy^4-6x^4y+5x^2y^3+y^5\qquad\text{combine like terms}\\\\=-2x^3y^2+\underline{4x^2y^3}-3xy^4-6x^4y+\underline{5x^2y^3}+y^5\\\\=-2x^3y^2+9x^2y^3-3xy^4-6x^4y+y^5[/tex]

Answer:

b ≈ 17

Step-by-step explanation:

Using trigonometric ratio, sine we can find side b.

sine x = opposite/hypotenuse

sin 45 = 12/b

b ≈ 17

Answer:

b = 12[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin45° = [tex]\frac{1}{\sqrt{2} }[/tex]

From the triangle

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{12}{b}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex]

Cross- multiply

b = 12[tex]\sqrt{2}[/tex]

[tex]\bf \textit{Sum and Difference Identities} \\\\ tan(\alpha + \beta) = \cfrac{tan(\alpha)+ tan(\beta)}{1- tan(\alpha)tan(\beta)} \qquad tan(\alpha - \beta) = \cfrac{tan(\alpha)- tan(\beta)}{1+ tan(\alpha)tan(\beta)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ tan(x-3\pi )=\cfrac{tan(x)-tan(3\pi )}{1+tan(x)tan(3\pi )} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf tan(3\pi )\implies \cfrac{sin(3\pi )}{cos(3\pi )}\implies \cfrac{0}{-1}\implies 0\qquad therefore \\\\[-0.35em] ~\dotfill\\\\ tan(3\pi )=\cfrac{tan(x)-tan(3\pi )}{1+tan(x)tan(3\pi )}\implies tan(x-3\pi )=\cfrac{tan(x)-0}{1+0} \\\\\\ tan(x-3\pi )=\cfrac{tan(x)}{1}\implies tan(x-3\pi )=tan(x)[/tex]