Bighorn sheep are beautiful wild animals found throughout the western United States. Data for this problem are based on information taken from The Desert Bighorn, edited by Monson and Sumner 9University of Arizona Press). Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information:
x 1 2 3 4 5
y 14 18.9 14.4 19.6 20.0
∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275
(a) Draw a scatter diagram.
(b) Find the equation of the least-squares line, and plot the line on the scatter diagram of part (a).
(c) Find the correlation coefficient r. Find the coefficient of determination . What percentage of variation in y is explained by the variation in x and the least squares model?

A(t) = 100t^2 + 500t + 625

3,025 square pixels

Answer:

A(t) equals 100t²+ 500t + 625.

The area of the square image after 3 seconds is 3,025 square pixels.

Answer:

Step-by-step explanation:

Given  1 caplet = 325 mg of medication, to calculate the number of caplet 975mg of medication will contain, we will follow the steps below;

Let  1 caplet = 325 mg of medication

x caplet = 975 mg of medication

Cross multiply

325 * x = 1 * 975

325x = 975

Divide both sides by 325

325x/325 = 975/325

x = 3

Hence 3 caplets contains 975 mg of medication.

Answer: see below

Step-by-step explanation:

The standard form of an exponential equation is: y = a(b)ˣ    where

Growth:

Exponential growth is where the final value (y) is greater than the initial value (a).

An example would be the spreading of a rumor:  

You tell 1 person (a = 1) who then tells 2 people each minute (b = 2).  How many people will they have spread the rumor to after 5 minutes (x = 5)?

y = 1(2)⁵

  = 32

Decay:

Exponential decay is where the final value (y) is less than the initial value (a).

An example would be the decrease of bacteria in a person:

A person has 100 bacteria (a = 1) who takes a pill that is supposed to cut in half the number of bacteria each hour (b = 1/2).  How many bacteria will the person have after 2 hours (x = 2)?

[tex]y=100\bigg(\dfrac{1}{2}\bigg)^2\\\\\\.\quad =100\bigg(\dfrac{1}{4}\bigg)\\\\\\.\quad = 25[/tex]

Answer:

1256 i think

Step-by-step explanation:

Answer:

Approximately 38.56 kilometers

Step-by-step explanation:

So, from the picture, we want to find x.

To do this, we can use the Law of Cosines. We simply need to find the angle between the two sides and then plug them into the Law of Cosines. First, the Law of Cosines is:

[tex]c^2=a^2+b^2-2ab\cos(C)\\[/tex]

The c in this equation is our x, and the C is the angle we need to find.

From the picture, you can see that angle C is the sum of the red and blue angles.

From a bearing of 190 degrees, we can determine that the red angle measures 10 degrees. Then by alternate interior angles, the other red angle must also measure 10 degrees.

From a bearing of 318 degrees, the remaining 48 degrees is outside the triangle. However, we have a complementary angle, so we can find the angle inside the triangle by subtracting in into 90. Therefore, the blue angle inside is 90-48=42 degrees.

Therefore, angle C is 42+10 which equals 52 degrees. Now we can plug this into our formula:

[tex]x^2=a^2+b^2-2ab\cos(C)\\\\x^2=(18.9)^2+(47.2)^2-2(18.9)(47.2)\cos(52)\\x=\sqrt{(18.9)^2+(47.2)^2-2(18.9)(47.2)\cos(52)}\\\text{Use a Calculator}\\x\approx38.5566 \text{ km}[/tex]

Answer:

A. The interquartile range (IQR) for brand A, $10, is less than the IQR for brand B, $25.

Step-by-step explanation:

The most appropriate measure that can be used to compare the SPREAD of the data of the 2 brands plotted on a box plot, is the Interquartile range (IQR).

Interquartile range is the difference between Q3 and Q1.

Q3 is the value which lies at the end of the rectangular box, while the Q1 lies at the beginning of the box.

From the box plot given,

IQR for brand A = 80 - 70 = $10

IQR for brand B = 50 - 25 = $25

Therefore, the correct option is "A. The interquartile range (IQR) for brand A, $10, is less than the IQR for brand B, $25."

Answer:

A

Step-by-step explanation:

This is the graph of y = x^2. It is a parabola that opens upward and has its vertex at the origin. Applying various transformations to the parent function will allow us to produce any parabolic graph we want. In effect, the parent function is like the most basic building block.

Answer: [tex]4x^2-21x-2[/tex] .

Step-by-step explanation:

Given: The difference of two trinomials is [tex]x^2 -10x + 2[/tex]. If one of the trinomials is [tex]3x^2 - 11x - 4[/tex].

Then, the other trinomial will be ([tex]3x^2 - 11x - 4[/tex] ) + ([tex]x^2 -10x + 2[/tex])

[tex]=3x^2-11x-4+x^2-10x+2\\\\=3x^2+x^2-11x-10x-4+2\\\\=4x^2-21x-2[/tex]

Hence, the other trinomial could be : [tex]4x^2-21x-2[/tex] .

Answer:

The simplified form is 2 (c - 7).

Step-by-step explanation:

The expression to be solved is:

[tex]f (c)=\frac{2}{5} (10c -35)[/tex]

Simplify the expression as follows:

[tex]f (c)=\frac{2}{5} (10c -35)[/tex]

       [tex]=[\frac{2}{5}\times 10c]-[\frac{2}{5}\times 35]\\\\=[2\times 2c]-[2\times 7]\\\\=4c-14\\\\=2(c-7)[/tex]

Thus, the simplified form is 2 (c - 7).

Answer:

Step-by-step explanation:

5(y–3.8)=4.7(y–4)

Expand the terms in the bracket

That's

5y - 19 = 4.7y - 18.8

Group like terms

5y - 4.7y = 19 - 18.8

0.3y = 0.2

Divide both sides by 0.3

We have the final answer as

Hope this helps you

Answer:

40

Step-by-step explanation:

In the question only lies the answer:

"and a total of forty students plan to participate in cross country."

Answer:

2

Step-by-step explanation:

2

Answer:

Below

Step-by-step explanation:

First triangle)

This triangle is a right one so we will apply the pythagorian theorem.

● 25 is the hypotenus

● 25^2 = b^2 + 24^2

■■■■■■■■■■■■■■■■■■■■■■■■■■

Seconde triangle)

Again it's a right triangle

x is the hypotenus.

● x^2 = 12^2 +5^2

● 12^2 = x^2-5^2

■■■■■■■■■■■■■■■■■■■■■■■■■■

This is a right triangle

AC is the hypotenus.

● AC^2 = BC^2 + BA^2

Notice that: BC = BE+EC and BA=BD+DA

● AC^2 = (BE+EC)^2 + (BD+DA)^2

Answer:  2) b = 7       3) x = [tex]\sqrt{119}[/tex]

Step-by-step explanation:

Use Pythagorean Theorem: (leg₁)² + (leg₂)² = hypotenuse²

2) b² + 24² = 25²

   b² + 576 = 625

            b² = 49

         [tex]\sqrt{b^2}=\sqrt{49}[/tex]

            b = 7

3) 5² + x² = 12²

   25 + x² = 144

            x² = 119

        [tex]\sqrt{x^2}=\sqrt{119}[/tex]

           [tex]x=\sqrt{119}[/tex]

Answer:

Answer:

x = 58

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angles

90  = 32+x

Subtract 32 from each side

90-32 = x

58 =x

Answer:

I'm confused by this. What do they mean by prove?

Step-by-step explanation:

Answer: 3

Step-by-step explanation:

first, we know that:

1 + 2 + 3 + 4 +5 +6 = 21

Now, which two numbers we should take out in order to have 15?

we can remove the 2 and the 4, or the 1 and the 5.

so here we have two possibilities, 2 and 4 are opposite, or 1 and 5 are opposite (they are located in opposite faces of the die)

in the other arrange, we have that removing two numbers we should get 12.

in order to reach 12, we should remove two numbers that add 9 together.

those can be 4 and 5, or 6 and 3.

Now, notice that in the first restriction we have that:

Or 2 and 4 are opposite,

or 1 and 5 are opposite.

So 4 and 5 can never be opposite, so we should have that 6 and 3 are opposite.

Then we can affirm that the value that appears in the face opposite to the 6, is the 3.

0riginal break even point:

285000/ 60/35 = $166,250

New break even point = new fixed costs / ( selling price - variable cost/ selling price)

New break even point = 285,000 + 15,900. / ( 60-( 35-4.50)/60

300,900 / 60-30.50/60 = $612,000

The new break even point increases.

Answer:

  x < -1

Step-by-step explanation:

Since the parabola opens upward, it is positive and decreasing where the left branch is above the x-axis: all points to the left of x=-1.

  all real values of x where x < -1

Answer:

9x³ + 27x²

Step-by-step explanation:

What the question is asking is to multiply f(x) and g(x) together:

Step 1: Write out expression

(fg)(x) = 3x²(3x + 9)

Step 2: Distribute

(fg)(x) = 9x³ + 27x²

Answer:

[tex]\huge\boxed{Option \ 3 : (fg)(x) = 9x^3+27x^2}[/tex]

Step-by-step explanation:

[tex]f(x) = 3x+9\\g(x) = 3x^2[/tex]

Multiplying both

[tex](fg)(x) = (3x+9)(3x^2)\\(fg)(x) = 9x^3+27x^2[/tex]

Answer:

5a³ - 40

Step-by-step:

The algebraic expression is:

5a³ - 40

Answer & Step-by-step explanation:

The ratio of square feet to gallons of paint:

[tex]1440:6[/tex]

This can also be written as:

[tex]\frac{1440}{6}[/tex]

This fraction can be simplified by dividing the numerator and denominator by 6:

[tex]\frac{1440}{6}=\frac{240}{1}[/tex]

So, the ratio of square feet to gallons of paint is:

1 gallon for every 240 ft².

:Done

Answer:

15x - y = - 126

Step-by-step explanation:

will make it simple and short

first we need to find the slope (m) first in order to get the equation

given: (-8,6) (-9,-9)

                     y2 - y1         -9  -  6

Slope = m = -----------  =  ------------------ =  15

                      -x2 - x1        -9  -  (-8)

so the equation of the line using point (-8,6) and slope 15 is y - 6 = 15( x + 8)

y - 6 = 15x + 120

using the form equation Ax + By = C,  15x - y = -120-6

therefore... 15x - y = - 126       is the answer

Answer:

Yes , it satisfies the hypothesis and  we can conclude that c = 1 is an element of [0,2]

c = 1 ∈ [0,2]

Step-by-step explanation:

Given that:

[tex]f(x) = 4x^2 -3x + 2, [0, 2][/tex]

which is read as the function of x = 4x² - 3x + 2 along the interval [0,2]

Differentiating the function with respect to x is;

f(x) = 8x - 3

Using the Mean value theorem to see if the function satisfies it, we have:

[tex]f'c = \dfrac{f(b)-f(a)}{b-a}[/tex]

[tex]8c -3 = \dfrac{f(2)-f(0)}{2-0}[/tex]

since the polynomial function is differentiated in [0,2]

[tex]8c -3 = \dfrac{(4(2)^2-3(2)+2)-(4(0)^2-3(0)+2)}{2-0}[/tex]

[tex]8c -3 = \dfrac{(4(4)-3(2)+2)-(4(0)-3(0)+2)}{2-0}[/tex]

[tex]8c -3 = \dfrac{(16-6+2)-(0-0+2)}{2-0}[/tex]

[tex]8c -3 = \dfrac{(12)-(2)}{2}[/tex]

[tex]8c -3 = \dfrac{10}{2}[/tex]

8c -3  = 5

8c = 5+3

8c = 8

c = 8/8

c = 1

Therefore, we can conclude that c = 1 is an element of [0,2]

c = 1 ∈ [0,2]

Answer:

Slope of the tangent line (m) = 1 / 2

Step-by-step explanation:

Given:

Point A = (4,2)

Origin point = (0,0)

Find:

Slope of the tangent line (m)

Computation:

Slope of the tangent line (m) = (y2-y1) / (x2-x1)

Slope of the tangent line (m) = (2-0) / (4-0)

Slope of the tangent line (m) = 2 / 4

Slope of the tangent line (m) = 1 / 2

Answer:

x = ±2

Step-by-step explanation:

log 7 (x^2 + 11) = log 7 15

We know that log a ( b) = log a(c)   means b =c

x^2 + 11 = 15

Subtract 11 from each side

x^2 = 15-11

x^2 =4

Take the square root of each side

sqrt(x^2) =±sqrt(4)

x = ±2

Answer:

50k

Step-by-step explanation:

Answer:

9 m

Step-by-step explanation:

Given that

Width of rectangular flower garden, w = 4 m

Perimeter of rectangular flower garden, p = 26 m

To find:

Length of Lisa's flower garden = ?

Solution:

First of all, let us understand perimeter, length and width of a rectangle.

Let ABCD be a rectangle. Please refer to the attached image.

Opposite sides of a rectangle are equal to each other.

AB = CD = Length  

Let the length be [tex]l[/tex] m.

BC = DA = Width = 4 m

Perimeter of a closed image is equal to the sum of all the sides of the image.

So, perimeter of ABCD:

[tex]p = AB + BC + CD + DA \\\Rightarrow \bold{ p = 2 \times (Length +Width)}[/tex]

[tex]26 = 2 \times (l +4)\\\Rightarrow 2l =26-8\\\Rightarrow \bold{l = 9 m}[/tex]

Answer:

Step-by-step explanation:

½ of 5¼

½×(21/4)

=21/8

=2⅝ hours

Answer:

2 5/8

Step-by-step explanation:

you would divide 5 1/4 by 2 :

5 divided by 2 =2 1/2

1/4 divided by 2=1/8

then make the numbers have the same denomanator

1/2, 2/4, 4/8

1/8,

then you add

2 4/8+1/8=2 5/8

Answer:

A. 70.69 is the correct answer.

Step-by-step explanation:

Given:

Two lines:

[tex]3x - 4y + 5 = 0 \\2x + 3y -1 = 0[/tex]

To find:

Angle between the two lines = ?

Solution:

Acute Angle between two lines can be found by using the below formula:

[tex]tan \theta = |\dfrac{(m_1 - m_2)}{ (1 + m_1m_2)}|[/tex]

Where [tex]\theta[/tex] is the acute angle between two lines.

[tex]m_1, m_2[/tex] are the slopes of two lines.

Slope of a line represented by [tex]ax+by+c=0[/tex] is given as:

[tex]m = -\dfrac{a}{b }[/tex]

So,

[tex]m_1 = -\dfrac{3}{- 4} = \dfrac{3}{4}[/tex]

[tex]m_2 = -\dfrac{2}{ 3}[/tex]

Putting the values in the formula:

[tex]tan \theta = |\dfrac{(\dfrac{3}{4}- (-\dfrac{2}{3}))}{ (1 + \dfrac{3}{4}\times (-\dfrac{2}{3 }))}|\\\Rightarrow tan \theta = |\dfrac{\dfrac{3}{4}+\dfrac{2}{3}}{ (1 -\dfrac{1}{2})}|\\\Rightarrow tan \theta = |\dfrac{\dfrac{17}{12}}{ \dfrac{1}{2}}|\\\Rightarrow tan \theta = \dfrac{17}{6}\\\Rightarrow \theta = tan^{-1}(\frac{17}{6})\\\Rightarrow \theta = \bold{70.69^\circ}[/tex]

So, correct answer is A. 70.69