please help me thank you

The values of a and b of the exponential function are 10000 and 0.6 respectively

We are given that the exponential function is expressed in general form as; f(x) = abˣ

where;

a is a non-zero real number called the initial value

b is any positive real number such that

b ≠ 1.

The domain of f is all real numbers.

The range of f is all positive real numbers if a > 0.

The range of f is all negative real numbers if a < 0.

The y-intercept is (0, a)

The horizontal asymptote is; y = 0.

We are told that this exponential function passes through the coordinate points (0, 10000) and (3, 2160).

At coordinate point (0, 10000), we have;

10000 = ab⁰

a = 10000

Now, at the coordinate point (3, 2160), we have;

2160 = 10000(b)³

2160/10000 = b³

0.216 = b³

b = ∛0.216

b = 0.6

Thus, we can conclude that the values of a and b of the given exponential function are respectively 10000 and 0.6.

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Answer:4x/5-1/5 = y

Step-by-step explanation:

We need to get y by itself

4x+2=5y+3

subtract 3 from both sides

4x-1=5y

divide both sides by 5

4x/5-1/5 = y

Answer:

[tex]4x + 2 = 5y + 3[/tex]

[tex]5y + 3 = 4x + 2[/tex]

[tex]5y = 5x + 2 - 3[/tex]

[tex]5y = 4x - 1[/tex]

[tex] \frac{5y}{5} = \frac{4x - 1}{5} [/tex]

[tex]y = \frac{4x - 1}{5} [/tex]

The province's population is growing at the rate of  58.34 %

Rate of change is used to mathematically describe the percentage change in value over a defined period of time, and it represents the momentum of a variable. The calculation for ROC is simple in that it takes the current value of a stock or index and divides it by the value from an earlier period.

Given:

Initial Population = 4.2 million

Population after 20 years = 6.65 million

Change in population = 6.65 - 4.2 = 2.45 million

Rate at which the province's population growing is

= [tex]\frac{Change in population}{Inital Population}[/tex] x100 %

= [tex]\frac{2.45}{4.2}\\[/tex] x 100%

= 58.34 %

Thus the province's population is growing at the rate of  58.34 %

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It is to be noted that the determination of whether or not there is a significant difference between the two groups will be done using a t test.

A t-test is a statistical test that juxtaposes two samples' means. It is used in hypothesis testing, using a null hypothesis that the variance in group means is zero and an alternative hypothesis that the difference is not zero.

The conditions to use the t test are:

The degrees of freedom (k) to be utilized for this text will be derived using the conservative method given below:

df = [(s₁²/n₁) + (s₂²/n²)/[((s₁²/n₁)²/((n₁-1)) + (s₂²/n₂)²/((n₂-1))]

= [(3.0952/15) + (6.4095/15)]² / [((3.0952/15)²/14) + ((6.4095/15)²/14)]

= 24.965

Hence,

df ≈ 24 (if approximated to the floor)

Recall the the standard deviation of the population are unequal and unknown. This thus requires that we utilize the two-sample unpooled t-test.

Here, H₀ is given as;

[tex]t = \frac{\bar{x_{1} -\bar{x_{2}}}}{\sqrt{\frac{s_{1}^{2} }{n_{1} } + \frac{S_{2}^{2} }{n_{2}} } } \sim t_{df}[/tex]

t = [(3.33333 - 4.13333)]/√[(3.0952/15) + (6.4095/15)]

= - 0.8/√0.6337

t = - 1.005

The 95% confidence interval is computed using the following formula:

[tex](\bar x_{2} - \bar x_{1}) \pm t_\alpha_/_2_,_df \left({\sqrt{\frac{S_{1}^{2} }{n_{1} } + \frac{S_{2}^{2} }{n_{2}} } } \right)[/tex]

= - 0.8 ± t₀.₀₂₅,₂₄ (√0.6337)

= - 0.8 ± 2.064 (√0.6337)

= -2.4429, 0.8429

To derive the 90% interval, we state:

[tex](\bar x_{2} - \bar x_{1}) \pm t_\alpha_/_2_,_df \left({\sqrt{\frac{S_{1}^{2} }{n_{1} } + \frac{S_{2}^{2} }{n_{2}} } } \right)[/tex]

= - 0.8 ± t₀.₀₅₀,₂₄ (√0.6337)

= - 0.8 ± 0.685 (√0.6337)

= -2.162, 0.562

From the intervals computed, we must fail to reject H₀

H₀ : μ₁ = μ₂

It is clear from the above intervals computed from that the differences between the mean of both groups is significant. This is because, zero is included on the two intervals.

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Answer:

4.6 minutes

Step-by-step explanation:

Average = the sum of the numbers/ the number of numbers

Plug in the numbers: 2+3+6+8+4/5 = 23/5 = 4.6 minutes

Answer:

None of these is not true

The solution to the inequality expression is x>5 and the correct representation is a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

Inequality expressions are expression not separated by an equal sign

Given the following inequality expression

–3(2x – 5) < 5(2 – x)

Expand

-6x + 15 < 10 - 5x

Collect the like terms

-6x + 5x < 10 -15

-x < -5

x > 5

Hence the solution to the inequality expression is x>5 and the correct representation is a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

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The equation for a circle is:

[tex](x-a)^{2} + (y-b)^{2} + = r^{2}[/tex]

Where (a,b) is the circle's center and r is the circle's radius.

First, we can find the center point of the circle. Because the two points from the problem are the endpoints of a diameter, the midpoint of the line segment is the center point of the circle.

The formula to find the mid-point of a line segment giving the two endpoints is:

M = [tex](\frac{x_{1} + x_{2} }{2}[/tex], [tex]\frac{y_{1} + y_{2} }{y} )[/tex]

Where M is the midpoint and the given points are:

[tex](x_{1}, y_{1} )[/tex] and [tex](x_{2} , y_{2})[/tex]

Substituting the values from the two points in the problem gives:

[tex]M = (\frac{11+9}{2}[/tex],[tex]\frac{-2+4}{2} )[/tex]

[tex]M = (\frac{11+9}{2}[/tex],[tex]\frac{2-4}{2})[/tex]

[tex]M = (\frac{20}{2} , \frac{2}{2})[/tex]

[tex]M = (10,1)[/tex]

The area of the interior above the polar axis is -0.858 square units

The area bounded by a polar curve between θ = θ₁ and θ = θ₂ is given by

[tex]A = \int\limits^{\theta_{2} }_{\theta_{1} } {\frac{1}{2}r^{2} } \, d\theta[/tex]

Now, since we have the curve r = 1 - sinθ and we want to find the area of the interior above the polar axis, we integrate from θ = 0 to θ = π, since this is the region above the polar axis.

So, [tex]A = \int\limits^{\theta_{2} }_{\theta_{1} } {\frac{1}{2}r^{2} } \, d\theta\\= \int\limits^{\pi}_{0} {\frac{1}{2}(1 - sin\theta)^{2} } \, d\theta\\= \int\limits^{\pi}_{0} {\frac{1}{2}[1 - 2sin\theta + (sin\theta)^{2}] } \, d\theta\\= \int\limits^{\pi}_{0} {\frac{1}{2}\, d\theta - \int\limits^{\pi}_{0} 2sin\theta \, d\theta+ \int\limits^{\pi}_{0} (sin\theta)^{2} } \, d\theta\\[/tex]

[tex]A = \int\limits^{\pi}_{0} {\frac{1}{2}\, d\theta - 2\int\limits^{\pi}_{0} sin\theta \, d\theta+ \int\limits^{\pi}_{0} \frac{(1 - cos2\theta)}{2} } \, d\theta\\= \int\limits^{\pi}_{0} {\frac{1}{2}\, d\theta - 2\int\limits^{\pi}_{0} sin\theta \, d\theta+ \int\limits^{\pi}_{0} \frac{1}{2} } \, d\theta -\int\limits^{\pi}_{0} \frac{cos2\theta}{2} } \, d\theta\\[/tex]

[tex]A = \int\limits^{\pi}_{0} \, d\theta - 2\int\limits^{\pi}_{0} sin\theta \, d\theta -\int\limits^{\pi}_{0} \frac{cos2\theta}{2} } \, d\theta\\= [\theta]_{0}^{\pi} - 2[-cos\theta]^{\pi} _{0} - [\frac{sin2\theta}{4}]_{0}^{\pi} \\= [\theta]_{0}^{\pi} + 2[cos\theta]^{\pi} _{0} - [\frac{sin2\theta}{4}]_{0}^{\pi}\\= [\pi - 0] + 2[cos\pi - cos0] - \frac{ [sin2\pi - sin0]}{4}\\= \pi + 2[-1 - 1] - \frac{ [0 - 0]}{4}\\= \pi + 2[-2] - \frac{ [0]}{4}\\= \pi - 4 - 0\\= \pi - 4\\= 3.142 - 4\\= -0.858[/tex]

So, the area of the interior above the polar axis is -0.858 square units

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The smallest possible prime number x is 17.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.

given, Two-thirds of a number x is at least 10.

So,

2/3 x ≥ 10

x ≥ 15

First prime number that is bigger than 15 is 17.

therefore, The smallest possible prime number x is 17.

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12 inches

A regular polygon is any 2-D shape where all the sides and angles are congruent.

Regular Hexagon

As denoted by the prefix "hexa-", hexagons have 6 sides and internal angles. The perimeter is equal to all 6 sides added together. However, we know that these sides must be congruent because it is a regular hexagon.

Solving for Perimeter

We can create an equation that describes the perimeter of this shape, with "x" representing the length of one side.

Since all the sides are equal we can use multiplication instead of addition. To solve this equation, divide both sides by 6.

This means that all sides must be 12 inches.

The graphed piecewise function is the one in option B.

On the graph, we can see that on the lowest part we have a closed dot at x = 1

And the above part has a open dot at x = 1.

Then the piecewise function is of the form:

Such that the above part seems to be quadratic, and the part below seems to have a larger degree.

With that, we can conclude that the correct option is:

Which is option b.

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The length and width of the rectangle are 5 inches and 1 inches respectively.

The length and width of the rectangle can be found as follows;

l = 3 + 2w

area of a rectangle = lw

where

Therefore,

5 = lw

5 = (3 + 2w)w

5 = 3w + 2w²

2w² + 3w - 5 = 0

Hence,

2w² + 3w - 5 = 0

Therefore,

w = 1  and w = - 5 / 2

width = 1 inches

length =  3 + 2(1) = 5 inches

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Answer:

30624; 1514,6; a1,6.

Answer:

the rectangles area is 24 meters

Step-by-step explanation:

area = length x width

length is 6 using the words long and width is 4

Answer:

area = 24 cm²

Step-by-step explanation:

The area of a rectangle can be found using the formula:

[tex]\boxed {area = length \times width}[/tex].

Substituting the values into the equation:

[tex]area = 6 \space\ cm\times 4 \space\ cm[/tex]

       ⇒ [tex]\bf 24 \space\ cm^2[/tex]

Answer:

87.5%

Step-by-step explanation:

Given:

Area of triangle NCM

⇒ 1/2 × base × height

⇒ 1/2 × CN × CM

⇒ 1/2 × 5 × 4

⇒ 10cm²

Length of rectangle ⇒ 10

Breadth of the rectangle ⇒ 8

↓

Area of rectangle ⇒ Length × Breadth

Area of rectangle ⇒ 10 × 8 = 80cm²

Area of shaded region ⇒ Area of rectangle  -  Area of triangle

Area of shaded region ⇒ 80 - 10 = 80cm²

Percentage of the shaded region = Shaded/complete rectangle × 100

⇒ 70/80 × 100 = 87.5

⇒ The percent of the area of the rectangle shaded is therefore 87.5%.

Answer:

A

Step-by-step explanation:

the sum to n terms of a geometric series is

[tex]S_{n}[/tex] = [tex]\frac{a_{1}(r^{n}-1) }{r-1}[/tex] , then for n = 7

S₇ = [tex]\frac{-1(2^{7}-1) }{2-1}[/tex] = [tex]\frac{-1(128-1)}{1}[/tex] = - 1 (127) = - 127

The piece-wise linear functions can be written as follows:

A linear function is modeled by:

y = mx + b

In which:

For x equal or less than -2, the line passes through (-3,-3) and (-2,-2), hence the rule is:

[tex]f(x) = x, x \leq -2[/tex].

For x greater than -2 up to 1, the y-intercept is of -7, and the line also passes through (1,-8), hence the rule is:

[tex]f(x) = -x - 7, -2 < x \leq 1[/tex].

For x greater than 1, the function goes through (2,-5) and (3,-3), hence the slope is:

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

The rule is:

y = 2x + b.

When x = 2, y = -5, hence:

-5 = 2(2) + b

b = -9.

Hence:

[tex]f(x) = 2x - 9, x > 1[/tex].

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Answer:

u = -225

Step-by-step explanation:

36 - u = 261

-u = 261 - 36

-u = 225

u = -225

The line segment in the figure can be named as: IYM and MYI.

If we have three points on a line segment, the point on the middle will be the alphabet in the center when naming the line, while the alphabets of both endpoints can be written either at the beginning or ending.

Given the figure above, Y will be at the center. The endpoints are I and M. Therefore, the line segment can be named as: IYM and MYI.

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Answer:

  D. y+5=2(x−4)

Step-by-step explanation:

The point-slope form of the equation of a line is useful for writing an equation for a line through a given point with a given slope.

The point-slope form of the equation of a line is ...

  y -k = m(x -h) . . . . . . line through point (h, k) with slope m

We want a line through point (h, k) = (4, -5) with slope m = 2. Putting these numbers into the form gives ...

  y -(-5) = 2(x -4)

  y +5 = 2(x -4) . . . . . . simplifying the signs

The function g(x) is g(x)= (3x)^2

The complete question is in the image

From the graph in the image, we have:

f(x) = x^2

The function f(x) is stretched by a factor of 3 to form g(x).

This means that:

g(x) = f(3x)

So, we have:

g(x)= (3x)^2

Hence, the function g(x) is g(x)= (3x)^2

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The equation of the quartic function is f(x) = x⁴ - 18 · x² + 6 · x + 72.

Herein we must construct at least a polynomial that satisfies all conditions described in the statement. According to the fundamental theorem of algebra, quartic functions may have no real roots, two real roots or four real roots, which means that one of the roots must have a multiplicity of 2.

The root with a multiplicity of 2 is x = 3 and both x = - 4 and x = - 2 have only a multiplicity of 1, then we have the following expression by using the factor form of the definition of polynomials:

f(x) = (x - 3)² · (x + 4) · (x + 2)

Now we expand the expression to get the standard form:

f(x) = (x² - 6 · x + 9) · (x² + 6 · x + 8)

f(x) = x⁴ - 6 · x³ + 9 · x² + 6 · x³ - 36 · x² + 54 · x + 8 · x² - 48 · x + 72

f(x) = x⁴ - 18 · x² + 6 · x + 72

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The monthly payments for this add on interest loan are of $164.71.

Given Information and Formula Used

It is given that for an add on interest loan,

Principal Amount, p = $8,276.17

Annual Interest Rate, r = 5.7%

Term of the loan, T = 5.5 years

The formula for simple interest is given as follows,

I = (p)(r)(t)/100 ............... (1)

The formula for total amount of add on interest is given by,

A = p + I ....................... (2)

Computing the Interest

Substitute the given values of p, r, and t in the formula (1) of interest to get,

I = (8276.17)(5.7)(5.5)/100

I = 259457.9295/100

I = $2,594.58

Computing the Monthly Payment for Add-on Interest Loan

Substituting the values of p and I in the formula (2), we obtain the total amount as,

A = $ (8276.17 + 2594.58)

A = $ 10,870.75

Monthly payment for the add on interest loan = A/t(in months)

=  $ (10,870.75/66)

= $164.71

Therefore, monthly payments of $164.71 are to be made for the add on interest loan.

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Using proportions, it is found that they must win 19 of their next 30 games.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

We want a win-to-loss proportion of 2:1, which is equivalent to a win-to-total proportion of 2:3. We have that:

Hence:

[tex]\frac{5 + x}{36} = \frac{2}{3}[/tex]

3(5 + x) = 72

15 + 3x = 72

3x = 57

x = 19.

The Rangers must win 19 of their next 30 games.

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The solution to the question is 265.

Logarithm of a number A is the exponent or power or index n, a given number called the base B would be raised to give the number A.

So n is the logarithm of A to base B.

Analysis:

log 2( log2(x-9)) = 3

log2(x-9) = [tex]2^{3}[/tex]

log2(x-9) = 8

x-9 = [tex]2^{8}[/tex]

x-9 = 256

x = 256 + 9

x = 265

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The rate if he went three years without an accident based on the information about the insurance is $552.15.

From the information given, his basic insurance cost is $613.50 per year and his insurance company offers a typical "safe-driver discount.

The amount will be:

= 613.50 - (20.45 × 3)

= 552.15

In conclusion, the rate is $552.15.

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If you randomly purchase one item, the probability it will last longer than 9 years is; 11.12%

The formula for Z-score is;

z = (x' - µ)/σ

where;

x' = sample mean

µ = population mean

σ = standard deviation

Thus;

z = (9 - 7.9)/0.9

z = 1.22

From online p-value from z-score calculator, we have;

probability = 0.1112 = 11.12%

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