Please answer this question!! 20 points and brainliest!

Answer:

Step-by-step explanation:

(a) The given numbers can be put directly into the form ...

... f(t) = (initial value) · (ratio)^(t/(time to achieve that ratio))

Here, we have an intial value of $100, and a ratio of $184.50/$100 = 1.845. The time to achieve that multiplication is 10 years (1967 to 1977). So, the equation can be written ...

... f(t) = 100·1.845^(t/10)

(b) You want to find f(38).

... f(38) = 100·1.845^(38/10) = 100·1.845^3.8 ≈ 1025.15 . . . dollars

Final answer:

Using the provided CPI data, an exponential function is found to model the change in cost of goods over time. The estimated cost of the same goods in 2005, using this model, is approximately $1019.03, illustrating changes in purchasing power and the cost of living.

Explanation:

The question involves finding an exponential function to model the Consumer Price Index (CPI) data and estimate the cost of goods in a future year based on past data. The data provided includes the cost of the same goods being $100 in 1967 (t=0) and $184.50 in 1977. An exponential function of the form y = abt can be used, where y represents the cost of goods, t represents the year, and a and b are constants to be found.

Given that the goods cost $100 in 1967, our initial condition gives us a as $100. We then use the information from 1977 (t=10) to solve for b. Plugging in the values, we get $184.50 = 100*b10, which solves to b approximately equal to 1.0653. Therefore, the exponential function modeling the CPI data is y = 100(1.0653)t.

To estimate the cost of goods in 2005, we substitute t with 38 (2005 - 1967), resulting in an estimated cost of goods y ≈ 100(1.0653)³⁸ ≈ $1019.03. This estimation illustrates how the Consumer Price Index can indicate changes in purchasing power and the cost of living over time.

Answer:

[tex]\log_4{(16384)}=7[/tex]

Step-by-step explanation:

The base of the exponent is the base of the logarithm. The exponent is the logarithm. The value the exponential expression is equal to is the argument of the logarithm.

Answer:

26, 37

Step-by-step explanation:

1,3,5,7,9,11

17 + 9 = 26

26 + 11 = 37

Answer:

-5/3

Step-by-step explanation:

Parallel lines are lines which have the exact same slope but different y-intercepts. We can find the slope by converting to slope-intercept form, y=mx+b from standard form.

We convert by using inverse operations to isolate y.

5x+3y=7

5x-5x+3y=7-5x

0x+3y=-5x+7

3y=-5x+7

[tex]\frac{3y}{3} =\frac{-5x+7}{3} \\y=\frac{-5}{3}x+\frac{7}{3}[/tex].

The slope is -5/3. SInce parallel lines have the same slope, the slope for a parallel line will be -5/3.

Answer:

y + g = 12 ,2y + 3g = 16

y =12-g

Substitute y =12-g in the equation 2y + 3g = 16.

2(12-g)+ 3g = 16

24-2g+3g=16

24+g=16

g=16-24

g= -8

Substitute g= -8 in the equation y =12-g.

y =12-(-8)

=12+8

y =20

Step-by-step explanation:

The value of variable y is 20 and value of variable g is -8.

Two or more expressions with an Equal sign is called as Equation.

The given system of equations are  y+ g = 12 and 2y + 3g = 16

y+g=12

y=12-g...(1)

2y+3g=16..(2)

Substitute 1 in equation 2

2(12-g)+3g=16

24-2g+3g=16

Add the like terms

24+g=16

g=16-24

g=-8

Now substitute the g value in equation y+g=12

y-8=12

Add 8 on both sides

y=20

Hence, the value of variable y is 20 and value of variable g is -8.

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None of these questions have anything to do directly with the polynomial remainder theorem. The theorem says that the remainder upon dividing a polynomial [tex]p(x)[/tex] by [tex]x-c[/tex] is given by the value of [tex]f(c)[/tex].

For these questions, all you really have to do is evaluate the given polynomials at the given points, and IMO is much less work.

Question 2: [tex]f(5)=4(5)^2-5(5)+2=77[/tex]

Question 3: [tex]f(4)=3(4)^4-8)4)^2-2(4)+12=644[/tex]

Question 4: Here you have check the value of [tex]h(x)[/tex] and 2 and -2, then interpret them as points in the coordinate plane, [tex](x,h(x))[/tex].

[tex]h(-2)=2(-2)^5-4(-2)^4-2(-2)^2+15=-121[/tex]

[tex]h(2)=2(2)^5-4(2)^4-2(2)^2+15=7[/tex]

Question 5: Same as in question 4, but you have to check [tex]h(x)[/tex] at -4, -3, -2, -1.

[tex]h(-4)=72[/tex]

[tex]h(-3)=46[/tex]

[tex]h(-2)=26[/tex]

[tex]h(-1)=12[/tex]

- - -

If you insist on using the polynomial remainder theorem, it's a question of polynomial division. For instance, in question 2 you'd compute

[tex]\dfrac{4x^2-5x+2}{x-5}=4x+15+\dfrac{77}{x-5}\implies4x^2-5x+2=(4x+15)(x-5)+77[/tex]

so the remainder is 77, as we found by simply computing [tex]f(5)[/tex].

Answer:

$1237.50

Step-by-step explanation:

r = 4.5% = 0.045

I = prt

I = 5500*0.045*5

= $1237.50

Answer:

(0,3)

Step-by-step explanation:

g(x) = f(x + 2) – 3

This is a shift of 2 to the left  and  a shift of 3 down

x moves from 2   to 2 units left  (-2)  so it becomes 0

y moves from 6 to 3 units down (-3) so it becomes 3

Answer:

the answer is B. or (0,3)

Step-by-step explanation:

This can be represented by the inequality:

3x + 0.75 ≥ 4.5

Inequality shows the non-equal comparison between two numbers or mathematical expressions.

Let x represent the price of milk per gallon.

Since the price of milk tripled, and then rose another $0.75 per gallon, hence:

Price of milk = 3x + 0.75

The price is now is AT LEAST $4.50 per gallon, hence this can be represented by the inequality:

3x + 0.75 ≥ 4.5

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Answer:

57 pounds weight is 95 percent of the limit .

Step-by-step explanation:

Formula

[tex]Percentage = \frac{Part\ value\times 100}{Total\ value}[/tex]

As given

A rocking horse has a weight limit of 60 pounds .

Here

Percentage = 95%

Total value = 60 pounds

Put in the formula

[tex]Percentage = \frac{Part\ value\times 100}{Total\ value}[/tex]

[tex]95 = \frac{Part\ value\times 100}{60}[/tex]

[tex]Part value = \frac{95\times 60}{100}[/tex]

[tex]Part value = \frac{5700}{100}[/tex]

Part value = 57 pounds

Therefore 57 pounds weight is 95 percent of the limit .

Answer:

57 pounds is 95 percent of the limit.

Step-by-step explanation:

Given the statement: A rocking horse has a weight limit of 60 pounds.

⇒Weight limit of rocking horse  = 60 pounds.

To find what weight is 95 percent of the limit.

Let x be the weight.

then;

x = 95% of 60

[tex]x = \frac{95}{100} \times 60[/tex]

or

x = [tex]\frac{95 \times 60}{100} = \frac{5700}{100} = 57[/tex]

therefore, 57 pounds is 95 percent of the limit.

Answer:

D

Step-by-step explanation:

The other ones don't make sense. The answer is 3.5x+x=9.90

[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-3}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-3-4}{0-0}\implies \cfrac{-7}{0}\impliedby und efined[/tex]

when the slope of the points is undefined, is a flag that is a vertical line.

Check the picture below.

Hi there! :)

Step-by-step explanation:

[tex]Slope=\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}[/tex]

[tex]\frac{(-3)-4}{0-0}=\frac{-7}{0}=0[/tex]

Therefore, the slope is 0.

Undefined.

Final answer is 0.

I hope this helps you!

Have a nice day! :)

-Charlie

:D

Answer:

(5c-7)(c+2)

Step-by-step explanation:

Answer:

A point of sale transaction occurs when an ATM withdrawal is made- TRUE.

Step-by-step explanation:

A point of sale transaction occurs when an ATM withdrawal is made - This is TRUE.

A point of sale is the point when a transaction is finalized. This transaction is based on any form of payment like - cash, debit cards, credit cards etc.

Answer:

x = - 1

x1 = - 3

x2 = 3

Step-by-step explanation:

x^2(x + 1) - 9(x + 1)    = f(x)                  x + 1 is a common factor

(x + 1) [ x^2 - 9]          = f(x)                 factor x^2 - 9

(x + 1)(x - 3)(x + 3)

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

x + 1 = 0

x = - 1

x - 3 = 0

x = 3

x + 3 = 0

x = - 3

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

Answer

x = - 1

x1 = - 3

x2 = 3

Question:

What are the zeros of the polynomial function?

Step-by-step explanation:

Hope this helps!

(2,4) because y2 is 1 = 2x

Answer:

A. 33

B. k=32

C. 1

D. [tex]\pm 1,\ \pm 2,\ \pm 4[/tex]

E. [tex]B=-2,\ D=5[/tex]

Step-by-step explanation:

In all parts for the quadratic equation [tex]ax^2+bx+c=0[/tex] use Vieta's formulas

[tex]x_1+x_2=-\dfrac{b}{a},\\ \\x_1\cdot x_2=\dfrac{c}{a},[/tex]

where [tex]x_1,\ x_2[/tex] are the roots of the quadratic equation.

A. For the equation [tex]x^2-5x-4=0,[/tex]

[tex]x_1+x_2=5,\\ \\x_1\cdot x_2=-4.[/tex]

Then

[tex](x_1+x_2)^2=x_1^2+2x_1\cdot x_2+x_2^2,\\ \\5^2=x_1^2+x_2^2+2\cdot (-4),\\ \\x_1^2+x_2^2=25+8=33.[/tex]

B. One of the roots of [tex]x^2+12x+k=0[/tex] is twice the other root, then [tex]x_2=2x_1.[/tex] By the Vieta's formulas,

[tex]x_1+x_2=3x_1=-12,\\ \\x_1\cdot x_2=2x_1^2=k.[/tex]

Then [tex]x_1=-4[/tex] and [tex]k=2x_1^2=2\cdot (-4)^2=2\cdot 16=32.[/tex]

C. The sum of the roots of the quadratic  [tex]4x^2-4x-4[/tex] is [tex]-\dfrac{b}{c}=-\dfrac{-4}{4}=1.[/tex]

D. Note that

[tex](Ax+B)(Cx+D)=ACx^2+x(AD+BC)+BD,[/tex]

then [tex]AC=a=4.[/tex] If [tex]A,\ B,\ C,\ D[/tex] are integers, then you should check [tex]A=\pm 1,\ \pm 2,\ \pm 4.[/tex]

E. Consider [tex]3x^2 - x - 10 = (x + B)(3x + D).[/tex] Note that

[tex]x_1+x_2=\dfrac{1}{3},\\ \\x_1\cdot x_2=-\dfrac{10}{3}.[/tex]

Then

[tex]x_1=2,\ x_2=-\dfrac{5}{3}.[/tex]

Then [tex]3x^2 - x - 10 = (x -2)(3x+5),[/tex] hence [tex]B=-2,\ D=5.[/tex]

A. The sum of the squares of the roots is 33, B. k = 32, C. The sum of the roots is 1, D. The possible values he should check are ±1, ±2, ±4, E. The ordered pair (B, D) is (2, -5).

Let's solve each part of the problem step-by-step:

A. First, find the roots of the quadratic equation using Vieta's formulas:

Now, the sum of the squares of the roots is given by: (α² + β²) = (α + β)² - 2αβ. Substituting the known values:
Hence, α² + β² = 25 - (-8) = 25 + 8 = 33.

B. Let the roots be α and 2α. Using Vieta's formulas again:

C. The sum of the roots is given by -b/a:

D. The quadratic can be written as 4x² + bx + c. The coefficient of x² on the right-hand side must be AC. Since a = 4:

E. The quadratic can be factored as (x + B)(3x + D). Let's determine B and D:

Thus, the ordered pair (B, D) is (2, -5).

Answer:0.85c

Step-by-step explanation:

Answer:

0.85c

Step-by-step explanation:

i did the diagnostic

Answer:-

[tex]11.4 + 0.5y = 9.9 + 0.6y[/tex] , then the two states have the same population.

Step-by-step explanation:

Let y represents the number of years

As per the statement:

In 2000, Ohio's population was 11.4 million and and increasing by 0.5 million each year.

⇒ [tex]11.4 + 0.5y[/tex]

and

also, it is given that: Michigan's population was 9.9 million, increasing by 0.6 million each year.

⇒ [tex]9.9 + 0.6y[/tex]

When two states have the same population.

then the equation : [tex]11.4 + 0.5y = 9.9 + 0.6y[/tex].

Answer:

In 15 years the population will be same.

Step-by-step explanation:

Let y represent the number of years.

In 2000, Ohio's population was 11.4 million and and increasing by 0.5 million each year.

[tex]x=11.4+0.5y[/tex]

Michigan's population was 9.9 million, increasing by 0.6 million each year.

[tex]x=9.9+0.6y[/tex]

We have to tell that when will the two years have the same population, so we will put both equations equal.

[tex]11.4+0.5y=9.9+0.6y[/tex]

=> [tex]11.4-9.9=0.6y-0.5y[/tex]

=> [tex]0.1y=1.5[/tex]

So, y = 15

Therefore, in 15 years the population will be same.

Answer: [tex]\bold{Y = 450e^{(.054t)}}[/tex]

Step-by-step explanation:

The general formula for decay is:

[tex]A = Pe^{rt}[/tex]  ; where:

Given:

Equation:

[tex]Y = 450e^{(.054t)}[/tex]

Answer:

your answer is 8/40 but is reduced to 1/5

Step-by-step explanation:

Answer:

B Every rational number has a decimal representation that either repeats or terminates.

Step-by-step explanation:

A rational number is a number that can be written as a fraction of integers. As a decimal, a rational number either terminates or repeats.

Answer: B Every rational number has a decimal representation that either repeats or terminates.

Every rational number has a decimal representation that either repeats or terminates.  Option B is correct.

In mathematics, a rational number is a number that can be described as the result of a fraction of value or does not have face value.

An irrational number is a type of real number that cannot be represented as a simple fraction or the values that have face value are irrational numbers. Example: √2, √3, and π are all irrational.

here,
From definition,

Rational numbers are the fractional values that give decimal values and every rational number has a decimal representation that either repeats or terminates.

Thus, option B is correct.

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Answer: 25% of the ice cream must be eaten to insure it does not overflow the cone when it melts.

Step-by-step explanation:

1. You must calculate the area of spherical scoop of ice cream  with the following formula for calculate the volume of  a sphere:

[tex]Vs=\frac{4}{3}r^{3}\pi[/tex]

Where [tex]r[/tex] is the radius ([tex]r=\frac{8cm}{2}=4cm[/tex])

[tex]Vs=\frac{4}{3}(4cm)^{3}\pi=268.08cm^{3}[/tex]

2. Now, you need to calculate the volume of the sugar cone with the following formula:

[tex]Vc=\frac{1}{3}r^{2}h\pi[/tex]

Where [tex]r[/tex] is the radius ([tex]r=\frac{8cm}{2}=4cm[/tex]) and [tex]h[/tex] is the height ([tex]h=12cm[/tex]):

[tex]Vc=\frac{1}{3}(4cm)^{2}(12cm)\pi=201.06cm^{3}[/tex]

3. When the ice cream melt, the percent of the cone that will be filled is:

[tex]P_f=(\frac{201.06cm^{3}}{268.08cm^{3}})100=75[/tex]%

4. Therefore, the percent of the ice cream that must be eaten to insure it does not overflow the cone when it melts, is:

[tex]P_e=100[/tex]%[tex]-75[/tex]%

[tex]P_e=25[/tex]%

Final answer:

To ensure the melted ice cream does not overflow the cone, 75% of the ice cream must be eaten. This is calculated by finding the volumes of the ice cream sphere and the cone and comparing them to get the percentage that can fit into the cone without overflowing.

Explanation:

The student's question involves determining what percent of a spherical scoop of ice cream (with a diameter of 8 cm) must be eaten to ensure it does not overflow a sugar cone (also with a diameter of 8 cm and 12 cm deep) when the ice cream melts. The ice cream and the cone have the same diameter, so they have the same base area. To prevent overflow, the volume of the melted ice cream must be less than or equal to the volume of the cone.

To solve this, we must first calculate the volume of the spherical scoop of ice cream, which can be determined using the formula for the volume of a sphere: V = (4/3)πr³. Subsequently, we need to calculate the volume of the cone using the formula for the volume of a cone: V = (1/3)πr²h. We shall compare these volumes to find out the percentage of ice cream that must be eaten.

Let's calculate the volume of the sphere (ice cream):
V_s = (4/3)π(4 cm)³ = (4/3)π(64 cm³) = 256π/3 cm³

Now let's calculate the volume of the cone:
V_c = (1/3)π(4 cm)²(12 cm) = (1/3)π(16 cm²)(12 cm) = 64π cm³

To prevent overflow, the volume of melted ice cream should be the same or less than the volume of the cone. Therefore, the portion which would fit into the cone without overflowing when melted is:
percent = (V_c / V_s) × 100 = (64π / 256π/3) × 100 = 75%

This means that 75% of the ice cream must be eaten to ensure it does not overflow the cone when it melts.

As per the given values, the opponent received 686 votes.

Total votes received by Mayor = 2058.

To find out how many votes the opponent received, we need to determine the ratio of votes received between the new mayor and her opponent. Given that the new mayor received three votes for every vote received by her opponent, we can set up the equation:

3x = 2058

where x represents the number of votes received by the opponent. To solve for x, we divide both sides of the equation by 3:

x = 2058 ÷ 3

= 686

Therefore, the opponent received a total of 686 votes.

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