I need help please! I’m struggling

By evaluating the exponential equation for the population:

P(x) = 200*(1.2)^x

We will get:

a) 240 badgers

b) 288 badgers

We know that the number of badgers increases by 20% each year, that increase after x years is given by the exponential equation:

P(x) = A*(1 + 20%/100%)^x

P(x) = A*(1.2)^x

Where A is the initial amount.

Here we know that the initial population of badgers is 200, then we have:

P(x) = 200*(1.2)^x

a) To find the population after one year, we need to evaluate the exponential equation in x = 1, we will get:

P(1) = 200*1.2^1 =240

b) The population after 2 years is:

P(2) = 200*1.2^2 = 288

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The required linear model is y = 5800 + 324x.

What is a linear equation?

Equations whose variables have a power of one are called linear equations.

Given, a bakery sells 5800 muffins in 2010

the bakery sells 7420 muffins in 2015

So, the number of muffins sold after 2010 through 2015:

7,420 - 5,800 = 1,620

Then, the sales per year:

1,620 muffins sold since 2010 / 5 years = 324 muffins per year.

Then our linear model will be:

y = 5800 + 324x

Hence, the required linear model is y = 5800 + 324x.

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Answer:

Step-by-step explanation:

(x+4)(x+5) = 0

x = -4

x = -5

Weight represents the top 10% of the zucchinis is 5.9

The formula for calculating a z-score is z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

We're looking for:

Weight is 10% of zucchinis at the top.

Top 10% = 90% of the population

90th percentile Z score is 1.282.

Hence

1.282 = x - 5 / 0.7

1.282 × 0.7 = x - 5

0.8974 = x - 5

x = 5 + 0.8974

x = 5.8974

5.9 ounces, roughly.

The top 10% of the zucchinis have a weight of 5.9 ounces.

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The length of each side of the sign will be 14.81-inch approx.

It is assumed that an Octagon sign is created by cutting out triangles from a square's corners, and that the stop sign's overall length is 36 inches. Since we are aware that squares have right angles on all four sides, we can use Pythagoras' theorem to solve for the side of the sign in the image below.

           [tex]s^{2} =x^{2} +x^{2} \\s^{2}=2x^{2} ...................Eq.1[/tex]

Also, it is a square. So, the measurement of length from side to side

            [tex]2x+s=36....................Eq.2[/tex]

solving Eq.1 we get,

[tex]s=\sqrt{2} x[/tex]...putting this value in Eq.2,

            [tex]s=36-2x\\\\\sqrt{2} x=36-2x\\\\x=\frac{36}{2+\sqrt{2} }[/tex]

Putting this value of x in Eq.1,

          s = 14.8

Hence, The length of each side of the sign will be 14.81-inch approx.

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Answer:

Hope this helps you out

Step-by-step explanation:

After 9 weeks, the sunflower would be 39 inches tall.

After w weeks, the sunflower would be 15 + (2 * w) inches tall.

Answer:

216.025 I think

Answer: S=237.5 in

Step-by-step explanation:

S=2(5)(6,5)+2(6.5)(7.5)+2(5)(7.5)

S=6,5(10)+97.5+7.5(10)

S=65+97.5+75

S=237,5 in

The recursive equation for f( n ) is  f( n-1 ) + 3.75

Any term of a sequence in terms of its preceding terms is a recursive equation. The equation can be defined as a mathematical statement made up of expressions. For example, b (n )  = 2b ( n-1 ) + 4 is a recursive equation.

As per the question,

As we know,

⇒   f ( n )   =   total cost

                =   g × n + c

    f ( n )   =   3.75 ( n ) + 2.55

Replace n with n - 1,

⇒   f ( n - 1 )   =   3.75 ( n - 1 )  +  2.55

⇒   f ( n - 1 )   =   3.75 n  -  3.75  +  2.55

⇒   f ( n - 1 )   =   3.75 n  +  2.55  -  3.75

⇒   f ( n - 1 )   =   f ( n )  -  3.75

⇒   f ( n )   =   f ( n - 1 )  +  3.75

Therefore, f( n-1 ) + 3.75 is the recursive equation for f ( n ).

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Answer:

a.) c(t)=44t+48

b.) the total initial cost of setting up a website and maintaining it for 6 months is $312

Step-by-step explanation:

h

After solving the given fraction, the resultant fraction is (A) 1 15/21.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole.

A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

A fraction appears in the numerator or denominator of a complex fraction.

The numerator of a proper fraction is less than the denominator.

So, we have:

2 4/7 * 2/3

Now, solve the fraction as follows:

2 4/7 * 2/3

14+4/7 * 2/3

18/7 * 2/3

36/21

1 15/21

Therefore, after solving the given fraction, the resultant fraction is (A) 1 15/21.

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The two equations that can be used to determine the number of hits that he had each year are given as follows:

His hits by team are divided as follows:

Then the total number of hits is obtained by the sum of the number of hits that he obtained with each of the three teams, as follows:

t = 2098 + 702 + 210 = 3010.

Then the amount of hits that he obtained each year is obtained applying the proportion, dividing t by 18, as follows:

a = t/18.

Hence the result is given as follows:

a = t/18 = 3010/18 = 167 hits per year.

The options are given by the image shown at the end of the answer.

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Triangle ABC to be isosceles we need to prove that opposite pair of sides of triangle ABC are congruent to each other.

Explanation :

Let us consider a triangle ABC,

To prove : Triangle ABC is an isosceles triangle.

In triangle ADC and triangle ADB,

m ∠CAD ≅ m ∠BAD ( AD bisect angle A )

AD = DA ( common side )

m ∠ADC ≅ m ∠ADB ( each 90° )

By Angle side angle (ASA ) theorem ,

ΔADC ≅ΔADB

By congruence parts congruent triangles :

AC ≅ AB

Therefore, by congruence parts congruent triangles side AC ≅ AB implies ABC is an isosceles triangle.

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Population after 95 years is more than 28 billion.

What is a growth rate?

The growth rate of a value (such as GDP, turnover, earnings, etc.) gauges how much it has changed over time (month, quarter, year). The percentage is a fairly universal way to communicate it.

Here, we have

The present size of the population is 7 billion.

Assuming that the population starts growing from the age of "0"

The number of people after 30 years is equal to two times the present population i.e 14 billion

The number of people after 60 years is equal to two times the population after 40 years i.e 28 billion

Hence, the population after 95 years is more than 28 billion.

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The gradient of the line in the given graph is 1/2.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

From the graph, let us consider two points from where the line is passing.

(-2, 3) and (2, 5).

Gradient is nothing but slope of the line.

m=5-3/2-(-2)

=2/4

=1/2

Hence, the gradient of line in the given graph is 1/2.

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In order to break even,

Total charge for x glasses =  Per day cost

1.25x = 0.6x  + 15

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

Let x be the number of  glasses of lemonade Jennifer needs to sell each day

Total charge for x glasses = 1.25x

It costs her $0.60 to make each glass of lemonade:

=> For x glasses, cost = 0.6x

Per day cost = 0.6x  + 15

In order to break even,

Total charge for x glasses =  Per day cost

1.25x = 0.6x  + 15

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By reading the graph we can see that k(x) = 80 for x ∈ (5, 6]

Look at the graph and try to identify the line where y = 80, now move to the right until you hit the graph of k(x) (red graph).

Now, move downwards until you intercept the x-axis, that value in the x-axis is the input that gives k(x) = 80.

In this case, there is a set of values.

The open circle means taht the value does not belong to the set.

The closed circle means taht the value does belong to the set.

Then k(x) = 80 for all the values of x in the set:

(5, 6]

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The area of the rectangular park is 143360 square yards.

It is the conversion of one unit to another unit with its standard conversion.

Example:

1 hour = 60 minutes

1 minute = 60 second

1 km = 1000 m

We have,

Scale drawing of a rectangular park:

Wide = 5 inches

Length = 7 inches

Actual rectangular park:

Wide = 320 yards

Length = 448 yards

Now,

5 inches = 320 yards

7 inches = 7/5 x 320 yards

7 inches = 7 x 64 yards

7 inches = 448 yards

Now,

The area of the actual park.

= Length x Wide

=  448 x 320

= 143360 square yards.

Thus,

143360 square yards is the area of the actual park.

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Answer:

1. 20 minutes (segment A)

2. 40 minutes (segment B)

3. 10 minutes (segment C)

4. 10 minutes (Segment D  minus Segment B)

5. Segments C & E (approaching x axis)

6. Segment A (greatest slope)

7. 115 minutes

Answer:

A. The y-intercept of the graph of f is at (0, 100).

D. The value of f when x = 5 is less than 1.

E. The value of f is never 0.

The first two statements are not true because the function f is defined by the equation f(x) = 100 • e^-x, where e^-x is the base of the natural logarithm (commonly known as "e") raised to the power of -x. Since e is always greater than 1, the value of e^-x will always be between 0 and 1, so the function f will always decrease as x increases. This means that statements B and C are not true.

Step-by-step explanation:

Answer:

7) d (21)

6) a (102)

Step-by-step explanation:

For the first question, we should start with what we know first:

When angles are complementary then, their angles add up to 90.

So here we have 69 + something = 90.

We find out that the missing angle (angle B) is 21.

For this second question, we know that a straight line has an angle of 180. Here we have a straight line, but only part of the angle in which we only have 78.

Since we know 78 + x = 180

Then we can figure out that x = 102.

The possible values of k are -0.56, -3.56, -2, and -1.

We have the equation of the parabola, y=0.5(x-3)(x+k)

When we Substitute x=0, we get that y=0.5*(-3) * k  for instance y = -1.5k

So, the y-intercept is (0,-1.5k).

We will now substitute y=0, 0=0.5(x-3)(x+k) for instance  0=0.5(x-3)(x+k) x=3 and x=-k

So, the x-intercepts are (3,0) and (-k,0).

We can see that 'k' cannot be 0 or -3 since height = 0 if k=0, which is not conceivable. If k = -3, the base is also 0, which is not feasible.

We know that area of a triangle is 1/2*base*height

when we substitute we will get

1.5=1/2*(3+k) *(1.5k)

3=4.5k+1.5k^2

k=-0.56 and k=-3.56

or

1.5=1/2*(-3-k) *(1.5k)

3=-4.5k-1.5k^2

k=-2 and k=-1

hence the possible values of k will be -0.56, -3.56, -2, and -1.

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Your question is incomplete, most probably the full question was:

The area of the triangle formed by x− and y− intercepts of the parabola y=0.5(x−3)(x+k) is equal to 1.5 square units. Find all possible values of k.

The prove the SAS congruence rule,  two sides and one angles between the includes sides of the triangle and the two sides and one angles between the includes sides of the another triangle should be equal

The SAS congruence rule is used to prove the congruence of the one triangle angle and another triangle.

SAS congruence rule stands for the side-angle-side congruence rule of triangles.

Side-angle-side rule of congruence states that if two sides and one angles between the includes sides of the triangle is equal to the two sides and one angles between the includes sides of the another triangle, then the both the triangles are congruent

Therefore, to prove the SAS congruence rule two sides and one angle of both triangle should be equal

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The equation of a line passes through (6,1) is 3x - 2y = 16.

Here we have to find the equation of a line.

Data given:

Point = (6,1)

The equation of another line is 2x + 3y = 18

From the given equation we can find the slope;

So we have

3y = -2x + 18

y = -2/3x + 18/3

So the slope is -2/3

As the line is perpendicular, so the slope of the line perpendicular to it will be 3/2

The general formula of the line is:

(y - y1) = m(x-x1)

(x1, y1) is the point

The point is (6,1 ) and the slope is 3/2

Now put that in the equation we get:

(y - 1) = 3/2(x - 6)

2y - 2 = 3x - 18

3x - 2y = 16

Therefore the equation is 3x - 2y = 16.

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The value of f(g(2)) is output of the function g(2) is in the input of f(x) which

is equal to 1.

When the output of one function is given to the input of another function they are called composite functions.

In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).

From the graphs f(x) = -x + 5 and g(x) = x².

Now, f(g(2)) is the output of g(2) is the input of f(x).

g(2) = (2)².

g(2) = 4.

Now, f(g(2)) = -(4) + 5.

f(g(2)) = 1.

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The solution to this problem is , we reject null hypothesis  R H0 at  p value =0.005 .

The likelihood of rejecting the null hypothesis when it is true is the significance level, often known as alpha or. A significance level of 0.05, for instance, represents a 5% likelihood of drawing the incorrect conclusion that a difference exists when there isn't one.

Given that Hippocrates magazine states that 35 percent of all Americans take multiple vitamins regularly.

Persons surveyed = 750

Of those survived no of persons who took multiple vitamin = 296

Sample proportion = p =0.395

q =1-p = 0.605

[tex]H_{0}\\[/tex] : p= 0.35

[tex]H_{A}[/tex] : p ≠ 0.35

(Two tailed test)

Assuming H0 is true standard error = [tex]\sqrt{(0.35 * 0.65)/750}[/tex]

=>0.0174

p difference = 0.045

Test statistic = 0.045/0.0174

=>2.58

p value = 0.005 for right tailed

Reject H0:

Therefore , we reject  R H0 at  p value =0.005 .

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The  balloon's vertical distance above the ground is 300.19 feet.

What is angle of depression?

If the line of sight is directed downward from the horizontal line, then an angle is created with the horizontal line. The angle produced between the horizontal line and the observer's line of sight is known as the angle of depression if the object being observed is below the observer's level.

Given that a balloon make 22° angle with a fixed point. The horizontal distance of the balloon along the ground is 743 feet.

Here need to find the vertical distance.

To find the vertical distance, use tangent of 22°. The tangent of angle is the ratio of vertical distance to horizontal distance.

Therefore,

tan 22° = vertical distance/ horizontal distance

tan 22° = vertical distance/ 743

Multiply both sides by 743:

vertical distance = 743 × tan 22°

vertical distance = 300.191

vertical distance = 300.19 ( rounding to the nearest hundredth)

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Answer:

The right answer is C.

Step-by-step explanation:

The parent function is:

[tex]f(x)=x^3[/tex]

If something is subtracted from variable [tex]x[/tex] it means the graph shifted toward right and something is added to [tex]y[/tex] value then the graph is shifted up.

[tex]f(x)=(x-8)^3[/tex]

graph shifted toward right by [tex]8[/tex] units right

[tex]f(x)=(x-8)^3+3[/tex]

graph shifted toward right by [tex]3[/tex] units up

Thus the new function is:

[tex]g(x)=(x-8)^3+3[/tex]

The cost per month is 39.96, the setup fee is 24.94, and the equations are x  = 39.96  and 6x + y = 264.70.

A formula known as an equation uses the equals sign to denote the equality of two expressions.

Given data:

A company offers premium cable for 39.96 per month plus a one-time set fee,

The total cost for setup and 6 months I'd 264.70

Write the equation as shown below,

The number of months × price per month + one-time setup fee = total cost

Calculate the equations,

x = number of months, y = setup fees

1 × x + y = 39.96 ⇒ x  = 39.96  (y = 0 for one month)

6 × x + y = 264.70 ⇒ 6x + y = 264.70

Solve the above equation by the elimination method

x = 39.96  and y = 24.94

Therefore, the cost per month is 39.96, the setup fee is 24.94, and the equations are x  = 39.96  and 6x + y = 264.70.

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