HELP please explain to me how to get this.
Which of the following represents a function?

Let's do the usual thing and make t the years since 1950.   We'll just abbreviate a billion B.

f(1950-1950)=39.4 B

f(2000-1950) =2025.2 B

Our exponential form for f will be

[tex]f = a e^{kt}[/tex]

[tex]39.4 \textrm{ B} = a e^{ 0 k} = a[/tex]

[tex]2025.2 \textrm{ B} = a e^{50 k}[/tex]

Dividing

[tex]\dfrac{2025.2}{39.4} = e^{50 k}[/tex]

[tex]50 k = \ln \dfrac{2025.2}{39.4}[/tex]

[tex]k = \frac 1 {50} \ln \dfrac{2025.2}{39.4} \approx 0.0787932[/tex]

Our function is

[tex]f = 39.4 \textrm{ B } e^{0.0787932 t }[/tex]

Since [tex]e^{0.0787932} \approx 1.08198[/tex]

[tex]f = 39.4 \textrm{B } 1.08198^t }[/tex]

around 8.2 % annualized growth.

Final answer:

An exponential function modeling U.S. federal budget growth between 1950 and 2000 is based on the formula f(t) = a ×[tex]b^t[/tex], where 'a' is the initial value in 1950 ($39.4 billion) and 'b' is the growth factor, calculated from the data in 2000 ($2025.2 billion). Solving the equations gives us the function [tex]f(t) = 39.4 * (51.4^{(1/50)})^t.[/tex]

Explanation:

We can model the growth of the U.S. federal budget using an exponential function, given the data from 1950 and 2000. First, we identify the years as our variable 't' where t=0 corresponds to the year 1950. We'll use the formula for exponential growth, which is f(t) = a × b^t, where 'a' is the initial amount, 'b' is the growth factor, and 't' is the time in years.

From the question, we have two data points: the budget in 1950 (t=0) is $39.4 billion, which gives us our 'a' value. In 2000 (t=50), the budget is $2025.2 billion. Plugging these values into our exponential function, we get two equations:

f(0) = 39.4 = a × [tex]b^0[/tex] which simplifies to a = 39.4.

f(50) = 2025.2 = 39.4 × b^50.

To find the value of 'b', we solve the second equation:

2025.2 = 39.4 ×  [tex]b^{50[/tex]
Divide both sides by 39.4:
51.4 = [tex]b^{50[/tex]
Take the 50th root of both sides:
b =[tex]51.4^(1/50).[/tex]

Now that we know both 'a' and 'b', we can write the exponential function that models the federal budget from 1950 to 2000:

[tex]f(t) = 39.4 * (51.4^{(1/50)})^t.[/tex]

Keep in mind that this model does not account for complexities like inflation or changing economic conditions. It provides a simplified view of the growth of the federal budget over this particular time period.

Answer:

66

Step-by-step explanation:

divide 264/4=66

Answer:

C) 66 jumps

Step-by-step explanation:

Dana can jump 264 times in 4 minutes

Divide 364 by 4 to see how many times she can jump in one minute

264/4 = 66

Answer:

It does not converge.

Step-by-step explanation:

Given is an infinite geometric series whose first term is a = 4/7 and common ratio is r = 7/6.

The series ∑a·rⁿ converges if we have |r| < 1.

And the series ∑a·rⁿ diverges if we have |r| > 1.

But we can easily check that |r| = 7/6 > 1.

It means the given series diverges, i.e. does not converge.

Hence, option D is correct answer, i.e. It does not converge.

Answer:

D. it does not converge

Answer:

Correct choice is D

Step-by-step explanation:

Given the system of two equations:

[tex]\left\{\begin{array}{l}4x+y=8\\6x-9y=12\end{array}\right..[/tex]

Fro mthe first equation

[tex]y=8-4x.[/tex]

Substitute into the second equation [tex]8-4x[/tex] instead of y:

[tex]6x-9(8-4x)=12.[/tex]

Note that [tex]8-4x=-4x+8,[/tex] then the second equation will take look

[tex]6x-9(-4x+8)=12.[/tex]

Answer:

The growth factor is option c. 1.03 per year

Step-by-step explanation:

Growth rate: r = 3% = 3 / 100 → r = 0.03

Growth factor: b = 1+r

Replacing r by 0.03 in the formula above:

b = 1+0.03

b = 1.03

Answer: The growth factor is 1.03 per year

Final answer:

Ali's fish weighs 25/6 lb more than Lisa's fish.

Explanation:

To find out how much more Ali's fish weighs compared to Lisa's fish, we need to subtract the weight of Lisa's fish from the weight of Ali's fish.

Ali's fish weighs 9 and 1/2 lb, which can be rewritten as 19/2 lb. Lisa's fish weighs 5 and 1/3 lb, which can be rewritten as 16/3 lb.

Now, subtracting the weight of Lisa's fish from Ali's fish, we have:

Ali's fish weight - Lisa's fish weight = (19/2) lb - (16/3) lb = (57/6) lb - (32/6) lb = 25/6 lb.

Therefore, Ali's fish weighs 25/6 lb more than Lisa's fish.

Answer:

$573

Step-by-step explanation:

955* 0.60=573

or

10% of 955= 95.5

50% of 955=477.5

477.5=95.5=573

The sale price of the computer is given by the equation A = $ 573

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the sale price of the computer after the price reduction be A

Now , the equation will be

The initial sale price of the computer = $ 955

The price reduction percentage on computer = 40 %

So , the sale price after reduction A = initial sale price of the computer - ( price reduction percentage x initial sale price of the computer )

Substituting the values in the equation , we get

The sale price after reduction A = 955 - ( 40/100 ) x 955

On simplifying the equation , we get

The sale price after reduction A = 955 - 382

The sale price after reduction A = $ 573

Therefore , the value of A is $ 573

Hence , the price of the computer is $ 573

To learn more about equations click :

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Answer:

You will want to set up the ratio for each and set them equal to each other. Then you can cross multiply to verify if you get the same answer. Another strategy is to set up each ratio and then reduce to lowest terms to see if you get the same fraction.

Step-by-step explanation:

Answer:

sin = √2/2, cos = -√2/2, tan = cot = -1

csc = √2, sec = -√2

Step-by-step explanation:

Angle runs around unit circle (where x^2+y^2=1)

from (1,0) to (-√2/2,√2/2)

Greetings!

Answer:

2370 miles can be travelled

Step-by-step explanation:

If 474 miles can be travelled in 1 hour, this means that to find the total amount in 5 hours we can simply multiply this value by 474:

474 * 5 = 2370

So it can travel 2370 miles!

Final answer:

To create a rectangular field with the same perimeter but a smaller area than the original 115 yards by 75 yards field, one could have a field that is 130 yards long and 60 yards wide.

Explanation:

To find the length and width of another rectangular field that has the same perimeter as a 115 yards by 75 yards field but a smaller area, we first calculate the perimeter of the original field:

Perimeter = 2(length + width) = 2(115 yd + 75 yd) = 2(190 yd) = 380 yd

To have a smaller area, the new field cannot be a square (which would maximize the area) and the sides need to have a greater difference in their measurements while still adding up to half of the original perimeter:

Let's assume the new length is 130 yards, to find the new width: 380 yd / 2 - 130 yd = 60 yd

Therefore, a new rectangular field could be 130 yards long and 60 yards wide.

Answer: choice A only

(1,-2) is the only solution (from the list of choices)

====================================

Explanation:

Let's go through each answer choice. We'll plug the coordinates in one at a time.

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Choice A has the point (1,-2) so x = 1 and y = -2 pair up together

y < -|x|

-2 < -|1|

-2 < -1

This is a true statement as -2 is to the left of -1 on the number line. So (1,-2) is one solution. Let's see if there are others.

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Choice B) plug in (x,y) = (1,-1)

y < -|x|

-1 < -|1|

-1 < -1

False. A number is not smaller than itself. So we can cross B off the list.

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Choice C) plug in (x,y) = (1,0)

y < -|x|

0 < -|1|

0 < -1

This is false because -1 is smaller than 0. Cross choice C off the list.

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Only choice A is a solution point for this inequality. If we were to graph the inequality, we would see only point A is in the shaded region while the other points are outside the shaded region.

The dashed boundary line does not count as the shaded region. This visually confirms why point B does not work.

After evaluating each point against the inequality y < -|x|, only point A (1, -2) satisfies the condition, making it the correct answer.

To determine which point is a solution for the inequality y < -|x|, we need to check if the y-value of each point is less than the negative absolute value of its corresponding x-value.

Therefore, the correct answer is point A (1, -2), as it is the only point where the y-value is less than the negative absolute value of the x-value.

[tex]t_1=4\\t_n=-3t_{n-1}\\\\t_2=-3\cdot4=-12\\t_3=-3\cdot(-12)=36\\t_4=-3\cdot36=-108[/tex]

Answer:

D

Step-by-step explanation:

The domain is the set of all x-values. We know the domain by finding the start and stop point of the function on the x-axis. The domain is all the values in between if the function is continuous without any breaks.

Here the function begins at x=-5 and ends at x=6.

We write the domain as [tex]-5\leq x\leq 6[/tex].

Answer is D.

Answer:

In your first picture

7) -40

14) 200

Step-by-step explanation:

The symbol in the picture is asking for multiplication. Typically for these, teachers encourage the use of the multiplication button on a calculator, but otherwise you need to know the basic steps of multiplication.

Answer:

7) -40

14) 200

Step-by-step explanation:

Answer:

275

Step-by-step explanation:

To find out how many more, we find the difference between the two values. We use the math operation subtraction to find the difference.

Friday had 537 and Saturday had 812. We subtract 812-537= 275.

275 more people attended Saturday than Friday.

A value which x represent in the function when determining the population after 6 years is 6.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

[tex]f(x)=a(b)^x[/tex]

Where:

In this context, we can reasonably infer and logically deduce that the variable x in the standard form of the equation of an exponential function represent time, which can either be measure in years, months, days, hours, minutes, or seconds.

In conclusion, x represents 6 in the exponential function when determining the population after 6 years.

Complete Question:

An initial population of 8 wolves increases by 9% each year. The function [tex]f(x) = ab^x[/tex] models this situation. Which value does x represent in the function when determining the population after 6 years?

Answer:

x = 22 tan 31

x is approximately equal to 13.22

Step-by-step explanation:

We know from trigonometric functions that

tan A = opposite side/ adjacent side

tan 31 = x / 22

Multiply each side by 22

22 tan 31 = x

13.2189332

x is approximately equal to 13.22

[tex]\dfrac{1}{2}h(b_1+b_2)=A\qquad\text{multiply both sides by 2}\\\\h(b_1+b_2)=2A\qquad\text{divide both sides by }\ h\neq0\\\\b_1+b_2=\dfrac{2A}{h}\qquad\text{subtract}\ b_2\ \text{from both sides}\\\\\boxed{b_1=\dfrac{2A}{h}-b_2}\to\boxed{F.}[/tex]

The first hexagon: 2, 2, 3, 4, 6, 7

The second hexagon: 3, 3, a, b, c, d

The hexagons are similar. Therefore the sides are in proportion.

[tex]\dfrac{a}{3}=\dfrac{3}{2}[/tex]     multiply both sides by 3

[tex]a=\dfrac{3}{2}=4.5[/tex]

[tex]\dfrac{b}{4}=\dfrac{3}{2}[/tex]    multiply both sides by 4

[tex]b=\dfrac{3}{2}\cdot4=6[/tex]

[tex]\dfrac{c}{6}=\dfrac{3}{2}[/tex]     multiply both sides by 6

[tex]c=\dfrac{3}{2}\cdot6=9[/tex]

[tex]\dfrac{d}{7}=\dfrac{3}{2}[/tex]    multiply both sides by 7

[tex]d=\dfrac{21}{2}=10.5[/tex]

The perimeter:

[tex]P=4.5+6+9+10.5=30[/tex]

Answer:

36

Step-by-step explanation:

The previous answerer forgot to add the two 3's to the sum so the correct answer it 36

Answer:

a. -1, odd; 2, even

b. [tex](x+1)(x-2)^2[/tex]

c. odd likely 3

Step-by-step explanation:

A polynomial graph has several features we look for to determine the equations.

In this graph, there are two real zeros: -1,2

We can write them in intercept or factored form as (x+1) and (x-2).  

Because the graph crosses the x-axis at -1, it's multiplicity is odd likely 1. However, the graph does not cross at 2 and has an even multiplicity likely 2.

The graph is ends up and is a sideways s so is positive with an odd degree.

This means the function has a degree of 3 or higher with the degree being odd.

Answer:      " r  =  a  +  b  -  s "  .

_____________________________________________________

Step-by-step explanation:

_____________________________________________________

Given:  

a + b = s + r ;  Solve for:  "r" ;  that is; rewrite the equation in terms of:  " r " .

_____________________________________________________

Subtract "s" from each side of the equation;  

   to isolate "r" on one side of the equation:

_____________________________________________________

    →      a + b - s  =  s + r - s  ;

    →   to get:

   →       a + b - s  =  r  ;

____________________________________________________

 ↔   " r = a + b - s "  .

____________________________________________________

   →  which is the answer.

____________________________________________________

Hope this helps!

 Best wishes to you!

____________________________________________________

Answer:4.-37 5.-6 6.-33 11.-20 12.-16

13.19

Step-by-step explanation:

Answer:

1. -41

2. -40

3. -4

4. -37

5. -24

6. -33

8. -47

9. 14

10. 59

11. -20

12. -16

13. 19

Answer:

SSS can be used to prove that the given triangles are congruent.

Step-by-step explanation:

In the given two triangles ΔADC and ΔABC,

Hence, ΔADC ≅ ΔABC by Side-Side-Side (SSS) congruence.

SSS congruence-

If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Answer: y-7 = 4(x+3), choice B

============================================

Point slope form is generally

y-y1 = m(x-x1)

we have m as the slope and (x1,y1) as the point this line goes through. In this case,

m = 4

(x1,y1) = (-3,7) so x1 = -3 and y1 = 7

So,

y-y1 = m(x-x1)

y - 7 = 4(x - (-3))

y - 7 = 4(x + 3)

which is why choice B is the answer

Point-slope form:

y - y₁ = m(x - x₁)    "m" is the slope

Since you know:

m = 4

(x₁ , y₁) = (-3,7)

You can plug it into the equation

y - y₁ = m(x - x₁)  

y - 7 = 4(x - (-3))

y - 7 = 4(x + 3)

Your answer is the 2nd choice

Answer: False

Step-by-step explanation:

45-45-90 is a special triangle because there is a specific relationship between the legs and the hypotenuse: a - a - a√2

So, If the leg of the 45-45-90 triangle is 12, then the hypotenuse (labeled as x in your drawing) will be 12√2.

Hey there!

"Which is equivalent to [tex]80\frac{1}{4}[/tex]?"

In order for you to solve this particular equation, you multiply the front number from the denominator, then whatever that outcome is, add to the nominator

So,  

[tex]80\frac{1}{4}[/tex]

[tex]80(4) = 320[/tex]

[tex]320 +1 = 321[/tex]

[tex]4[/tex] stays the same

[tex]\boxed{Answer: \frac{321}{4}}[/tex]

If you want the decimal form, simplify the  the mixed  to a improper then you should get a outcome of: [tex]80.25[/tex]

For percentage do the fraction out of [tex]100[/tex] then solve it from there ([tex]0.8025[/tex]) would be the percentage form

Good luck on your assignment and enjoy your day!

~[tex]LoveYourselfFirst:)[/tex]

[tex]80\frac{1}{4}[/tex] is equivalent to the decimal number 80.25, which can also be expressed as the improper fraction 321/4.

The question asks for an equivalent of the number [tex]80\frac{1}{4}[/tex].  To find this, we can convert the mixed number to an improper fraction or decimal. Since 1/4 is a standard fraction that is equivalent to 25 percent, we can express 1/4 as 0.25. Adding this to 80, we get an equivalent decimal number of 80.25. Another way to express 80 1/4 would be as an improper fraction, which would be [tex]\frac{321}{4}[/tex] because 80 times 4 equals 320, plus the numerator 1 equals 321.