solve the inequality |2h-3| >1

The best-fit line for a data set is found using the least-squares regression method, which identifies the linear equation that minimizes the residual errors. The equation is in the form y = mx + b, where m is the slope, and b is the y-intercept.

The question seeks to determine the linear function equation that best fits a given data set. To find the best-fit line, also known as the least-squares regression line, we typically analyze data points and use statistical methods to determine the equation that minimizes the sum of the squares of the residuals (the differences between the observed values and the values predicted by the model). The given options suggest that we are looking for a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept.

The equation of the best-fit line provided in the reference material, ý = -173.51 + 4.83x, indicates the method to determine both the slope (4.83) and the y-intercept (-173.51). This can be compared with the provided options to identify which one has a slope (or multiplier for x) closest to 4.83 and y-intercept closest to -173.51. In practice, students would use numerical and conceptual methods rather than graphing to interpret the data in multi-dimensional space when there are more than two variables involved.

Answer:

see explanation

Step-by-step explanation:

Given

q = [tex]\frac{p}{r}[/tex] + s ( subtract s from both sides )

q - s = [tex]\frac{p}{r}[/tex]

Multiply both sides by r

r(q - s) = p

Answer:

2 31/32   cups used

Step-by-step explanation:

We have 4 3/8 cups cherries

Change this to an improper fraction

4 3/8 = (8*4+3)/8 = 38/8

We use 5/8 of the cherries

38/8 *5/8

190/64

Change this back to a mixed number

64 goes into 190 2 times

190 - 128 =62  left over

2 62/64

2 31/32   cups used

Answer:

$290.00

Step-by-step explanation:

The equation would be 890-600=290 because if you subtract the base amount from the final savings it would give you how much she saved altogether.  

Hope this helps! :)

Answer:

How is that possible

Step-by-step explanation:

So..... what is the question ?

ANSWER

[tex]g(x) = \sin(x +4) - 4[/tex]

EXPLANATION

The basic sine function is

[tex]f(x) = \sin(x) [/tex]

The transformed sine function has equation

[tex]g(x) = a \sin(bx +c ) + d[/tex]

where a=1 is the amplitude

2π/b=2π is the period

c/b= 4 is the horizontal shift 4 units left.

d=-4 is a downward vertical shift of 4 units.

The required sine function is:

[tex]g(x) = \sin(x +4) - 4[/tex]

Answer:

see explanation

Step-by-step explanation:

The exponential function is of the form

y = a [tex]b^{x}[/tex]

Substitute the given points into the equation to find a and b

Using (0, 4), then

4 = a[tex]b^{0}[/tex] ⇒ a = 4

Using (1, 24), then

24 = 4 [tex]b^{1}[/tex] ⇒ b = 6

Exponential function is

y = 4 × [tex]6^{x}[/tex]

The equation of the exponential function that passes through the points (0,4) and (1,24) is y = 4(6)^x.

To find the equation of the exponential function that passes through the points (0,4) and (1,24), we can use the general form of an exponential function: y = ab^x, where a is the initial value and b is the growth/decay factor.

Using the point (0,4), we plug in x=0 and y=4 to get the equation 4 = ab^0, which simplifies to a = 4.

Using the point (1,24), we plug in x=1, y=24, and a=4 to get the equation 24 = 4b^1, which simplifies to b = 6.

Therefore, the equation of the exponential function is y = 4(6)^x.

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Still second graph from top down is the good one

There is approximately 1 second per second

You’re welcome

Approximately one

Per one

Answer:

4x² - 2x

Step-by-step explanation:

5x² + x - 2x - x² - x

can be simplified:  5x² - x² - 2x + x - x = 4x² - 2x

Answer:

3x^2

Step-by-step explanation:

five x squared

5x^2

plus x

+x

minus two x squared

-2x^2

minus x​

-x

All together

5x^2 +x-2x^2 -x

Combine like terms

5x^2-2x^2 +x-x

3x^2

Answer:

70

Step-by-step explanation:

From 8, we want to choose 4.  So:

₈C₄ = 8! / (4! (8-4)!)

₈C₄ = 8! / (4! 4!)

₈C₄ = (8×7×6×5×4×3×2×1) / (4×3×2×1 × 4×3×2×1)

₈C₄ = (8×7×6×5) / (4×3×2×1)

₈C₄ = 70

There are 70 different teams you can form.

Answer:

Step-by-step explanation:

Put x = -4 to f(x) = -x - 2:

f(-4) = -(-4) - 2 = 4 - 2 = 2

Answer is

New perimeter = 112

See photo

Answer:

A = 78.5 in ^2

Step-by-step explanation:

Area of a circle = pi * r^2

The radius is d/2

r= 10/2

r =5

A = pi * r^2

Substitute r=5

A = pi *(5)^2

A = 25 pi

We know that pi is approximated by 3.14

A = 25 (3.14)

A = 78.5 in ^2

Answer:

The approximate difference in the growth rate of the two populations is 40%.

Step-by-step explanation:

The general exponential growth model is

[tex]y=a(1+r)^t[/tex]

Where, a is initial value, r is growth rate and t is time.

In the given graph, red curve passing through the points (2,22.5) and (3,33.75).

[tex]22.5=a(1+r)^2[/tex]           .... (1)

[tex]33.75=a(1+r)^3[/tex]           .... (2)

Divide the equation (2) by equation (1).

[tex]1.5=1+r[/tex]

[tex]0.5=r[/tex]

The graph rate of red curve is 50%.

In the given graph, purple curve passing through the points (7,19.4) and (8,21.4).

[tex]19.4=a(1+r)^7[/tex]           .... (3)

[tex]21.4=a(1+r)^8[/tex]           .... (4)

Divide the equation (4) by equation (3).

[tex]1.1031=1+r[/tex]

[tex]0.1031=r[/tex]

[tex]0.1\approx r[/tex]

The graph rate of red curve is 10%.

The approximate difference in the growth rate of the two populations is

[tex]50-10=40\%[/tex]

Therefore the approximate difference in the growth rate of the two populations is 40%.

Answer:

A = 36.75 cm^2

Step-by-step explanation:

The area of a trapezoid is found by

A = 1/2 (b1+b2) *h

where b1 and b2 are the bases and h is the height

A = 1/2 (12+9) *3.5

A = 1/2(21)*3.5

A = 36.75 cm^2

hope it helps you!!!!!!!!!!!

Answer:

m∠2 = 56°

Step-by-step explanation:

Given;

m∠1 = 10x + 4 and m∠2 = 5x - 4

Angles 1 and 2 are supplementary angles meaning that they add up to 180°

i.e,

(10x + 4) + (5x - 4) = 180°

10x + 5x + 4 - 4 = 180°

15x = 180°

x = 180/15 = 12

m∠2 = 5(12)° - 4° = 60° - 4° = 56°

Answer:

D=2R R=D/2  Circumference = 2πR  Area: πR^2

Step-by-step explanation:

the answer would be 0.03%

The number that is equivalent of 3% is 0.03

From the question, we have the following parameters that can be used in our computation:

Number = 3%

Express the percentage as division

So, we have

Number = 3/100

When the division is evaluated, we have the following

Number = 0.03

Hence, the equivalent of 3% is 0.03

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Answer:

6

Step-by-step explanation:

Given data:

x=area

f(x)=the length of one side of the square

Also the model of f(x)= [tex]\sqrt{x-1} +1[/tex]

Now determining length of one side of the square f(x), when Area x of square is 26:

Putting the value x=26 in given equation of f(x)

f(x)= [tex]\sqrt{26-1} +1[/tex]

   = [tex]\sqrt{25} +1[/tex]

  = 5 +1

   = 6

Hence length of one side of the square f(x) is 6, when Area x of square is 26 !

Answer with explanation:

x= Area

f(x)= The length of one side of the square

Model Determined by Sam to approximate the side of a square is

    [tex]f(x)=\sqrt{x-1} +1[/tex]

It is given that , Area(x) = 26 Square Unit

 Substituting the value of , x in above equation

    [tex]f(x)=\sqrt{26-1} +1\\\\f(x)=\sqrt{25} +1\\\\f(x)=5+1\\\\f(x)=6[/tex]

So, Side length of Square According to model created by Sam = 6 unit

Answer:

A (0,0)

Step-by-step explanation:

When a function intersects the y-axis then the point of intersection is called y-intercept of the function,

Also, for y-intercept x = 0.

That is, if f(x) is the function then its y-intercept is (0, f(0) )

By the given table for x = 0, f(x) = 0

Hence, the y-intercept of the given function is (0,0),

Option A is correct.

Answer:

A trust

Step-by-step explanation:

Answer:

Correct choice is 1) [tex]5a^2 (b-c)-5d(b-c)[/tex].

Step-by-step explanation:

Given expression is : [tex]5a^2b-5a^2c-5db+5dc[/tex]

Now we need to factor it by completing square to match the correct choice.

[tex]5a^2b-5a^2c-5db+5dc[/tex]

Make two groups having first two terms and last two terms then find GCF of each.

[tex]=5a^2(b-c)-5d(b-c)[/tex]

Hence correct choice is 1) [tex]5a^2 (b-c)-5d(b-c)[/tex].

Answer: option B

Step-by-step explanation:

The circumference of a circle can be calculated with this formula:

[tex]C=2\pi r[/tex]

Where "C" is the circumference of the circle and "r" is the radius of the circle.

The area of a circle can be calculated with:

[tex]A=\pi r^2[/tex]

Where "r" is the radius.

Knowing the area, you can solve for the radius:

[tex]r^2=\frac{9\pi cm^2}{\pi }\\\\r=\sqrt{\frac{9\pi cm^2}{\pi } }\\\\r=3cm[/tex]

Substituting into  [tex]C=2\pi r[/tex], you get that the circumference of this circle is:

 [tex]C=2\pi (3cm)=6\pi\ cm[/tex]

Answer:

B

Step-by-step explanation:

The area (A) of a circle = πr² ← r is the radius

here A = 9π, hence

πr² = 9π ( divide both sides by π )

r² = [tex]\frac{9\pi }{\pi }[/tex] = 9

r = [tex]\sqrt{9}[/tex] = 3

The circumference (C) of a circle is C = 2πr, hence

C = 2π × 3 = 6π → B

Answer:

x=25

Step-by-step explanation:

x+y=100 (y being number of 8¢ stamps)

12x+ 8y = 900

-----------------------------------

y = 100-x

12x + 8y = 900

----------------------------------------

12x + 8(100-x) = 900

12x + 800 - 8x = 900

12x - 8x = 900 - 800

4x = 100

x=25

Answer:

Part 1) The segment length indicated is [tex]6.4\ units[/tex]

Part 2) The segment length indicated is [tex]19\ units[/tex]

Step-by-step explanation:

Let

x------> the segment length indicated

Part 1)

Applying the Pythagoras Theorem

[tex](13+x)^{2}=13^{2}+14.4^{2}\\ \\ (169+26x+x^{2})=169+207.36\\ \\x^{2}+26x-207.36=0[/tex]

Solve the quadratic equation by graphing

The solution is [tex]x=6.4\ units[/tex]

see the attached figure N 1

Part 2)

Applying the Pythagoras Theorem

[tex]x^{2} =11.4^{2}+(7.6+7.6)^{2}\\ \\ x^{2}=129.96+231.04\\ \\x^{2}=361\\ \\x=19\ units[/tex]

Answer:

The root of [tex]\sqrt{2y-5} +8 = 4[/tex] is 10.5.

Step-by-step explanation:

Given that,

[tex]\sqrt{2y-5} +8 = 4[/tex]

As we have a square root term along with a single term on left side. We will move the single term on right side.

[tex]\sqrt{2y-5}  = 4-8[/tex]

[tex]\sqrt{2y-5}  = -4[/tex]

Taking the square on both sides, we get

[tex](\sqrt{2y-5})^2  = (-4)^2[/tex]

Square will cancel the impact of square root, therefore:

[tex]({2y-5})  = 16[/tex]

[tex]2y = 16+5[/tex]

[tex]2y = 21[/tex]

[tex]y = \frac{21}{2}[/tex]

[tex]y = 10.5[/tex]

Therefore, the root of [tex]\sqrt{2y-5} +8 = 4[/tex] is 10.5.  

Answer:

See below.

Step-by-step explanation:

The graph of the quadratic equation is a parabola or u shaped graph. It has a vertex at (-1,-3) since h=-1 and k=-3 in the vertex form. It is also facing down since the leading coefficient is negative.

The graph of the equation y = -(x + 1)2 -3 is a downward opening parabola with the vertex at (-1, -3).

The graph of the equation y = -(x + 1)2 -3 is a downward opening parabola. The coefficient in front of the quadratic term, in this case, -1, determines the direction of the opening. If the coefficient is negative, the parabola opens downward.

Additionally, the vertex of the parabola is (-1, -3) since the equation is in vertex form. The vertex is the highest or lowest point on the graph. Therefore, the graph of the equation y = -(x + 1)2 -3 will be a downward opening parabola with the vertex at (-1, -3).

Answer:

Step-by-step explanation:

the lawn above is 40 x 60= 2400 ft^2

one bag of seed that costs $2.50 and it covers 1200 ft^2

if your lawn is 2400 ft^2 you divide it by the 1200 ft^2

                            2400 ft^2 / 1200 ft^2 = 2

so if 1 bag covers 1200 ft^2 then you will need 2 bags to cover 2400 ft^2.

at $2.50 a bag your answer will be, B.

Answer is B

Area = area of rectangle + area of that small areched shape

Area is little bit more than (60*40)=2400

Which is covered by 2 bags (2400/1200) =2

Cost of 2 bags is 2.5*2=5

So..you have to choose what is more than 5 with little amout..which is 5.51

Answer:

Step-by-step explanation:

f(x) = x⁵ – 8x⁴ + 16x³

As x approaches +∞, the highest term, x⁵, approaches +∞.

As x approaches -∞, x⁵ approaches -∞ (a negative number raised to an odd exponent is also negative).

Now let's factor:

f(x) = x³ (x² – 8x + 16)

f(x) = x³ (x – 4)²

f(x) has roots at x=0 and x=4.  x=4 is a repeated root (because it's squared), so the graph touches the x-axis but does not cross at x=4.

The graph crosses the x-axis at x=0.

Answer:

Part 1. B

Part 2. 4, 0

Step-by-step explanation: Edge 2023