Question 4 Multiple Choice Worth 2 points
What is the rate of change and initial value for the linear relation that includes the points shown in the table?
XY
3
4
5
67
89
O Initial value: 1, rate of change: 2
O Initial value: 1, rate of change: 1
O Initial value: 2, rate of change: 2
O Initial value: 3, rate of change: 2
action

Answer:

5/18

Step-by-step explanation:

Let's say the original packaging was 1 lb of packaging for $1.

The cost was $1/lb.

Then the weight went down by 10% and the price went up by 15%.

Now 0.9 lb of packaging cost $1.15.

The new unit cost is $1.15/(0.9 lb)

The difference is

$1.15/(0.9 lb) - $1/lb =

= $1.15/(0.9 lb) - $0.9/(0.9 lb)

= $0.25/(0.9 lb)

=$25/(90 lb) = $5/(18 lb)

The price went up by 5/18.

Answer:

The p -value for the hypothesis test is 0.003.

Step-by-step explanation:

In this case, a paired t-test would be used to determine whether the drug  increases blood pressure.

The hypothesis can be defined as follows:

H₀: The drug has no effect on blood pressure, i.e. d = 0.

Hₐ: The drug increases blood pressure, i.e. d > 0.

The information provided is:

[tex]n=32\\\bar d=2.5\\S_{d}=4.8[/tex]

The test statistic is:

[tex]t=\frac{\bar d}{S_{d}/\sqrt{n}}[/tex]

  [tex]=\frac{2.5}{4.8/\sqrt{32}}\\\\=2.9463\\\\\approx 2.95[/tex]

The degrees of freedom of the test is:

[tex]df=n-1=32-1=31[/tex]

The p-value of the test is:

[tex]p-value=P(t_{31}>2.95)=0.003[/tex]

*Use a t-table.

Thus, the p -value for the hypothesis test is 0.003.

A t-test is an inferential statistic that is used to see if there is a significant difference in the means. The p-value for the hypothesis test is 0.003.

A t-test is an inferential statistic that is used to see if there is a significant difference in the means of two groups that are connected in some way.

As it is given that 32(n) subjects in the study had an average change in blood pressure of 2.5([tex]\bar d[/tex]) with a standard deviation of 4.8([tex]S_d[/tex]).

Now, in order to solve the problem we need to use t-test, the test will determine whether the blood pressure increases or not under the influence of the drug.

The hypothesis for the test can be defined as:

H₀: The drug has no effect on blood pressure, therefore, d = 0.

Hₐ: The drug has increased blood pressure, therefore, d>0.

The test static is:

[tex]t = \dfrac{\bar d}{\dfrac{S_d}{\sqrt n}}\\\\\\t = \dfrac{2.5}{\dfrac{4.8}{32}} = 2.946 \approx 2.95[/tex]

Further, the degree of freedom of the test can be written as,

[tex]d_f=n-1 = 32-1=31[/tex]

Thus, the p-value of the test is:

[tex]p-value = P(t_{31} > 2.95)\\\\\text{Using the t-table}\\\\p-value = 0.003[/tex]

Hence, the p-value for the hypothesis test is 0.003.

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Answer:

-7 and -4

Step-by-step explanation:

The graph of the function f(x) = (x + 4)⁶ (x + 7)⁵ cross the X axis at x = -4 and x = -7.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given is a function,

f(x) = (x + 4)⁶ (x + 7)⁵

When the function cross the X axis, the value of the function will be 0.

Let f(x) = 0

(x + 4)⁶ (x + 7)⁵ = 0

This implies that, either x + 4 = 0 or x + 7 = 0

x + 4 = 0 ⇒ x = -4

x + 7 = 0 ⇒ x = -7

Hence the roots are -4 and -7 where the function crosses the X axis.

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Answer:

Maximum =  756

Minimum =  600

Step-by-step explanation:

A square is a shape that has the large areas of a defined perimeter out of available rectangles. It implies they want the two parentheses to be as similar in value. as a result, to establish the maximum value of P.

And to establish the minimum value, to have the greatest difference for them. 1 + 2 + 3 ... +10=55, which wasn't even but which can be split as similarly as possible into 27 and 28 which have a product of 756. In this question it can be done in a variety of ways, one of which is:

(1 + 3 + 5 + 8 + 10) ×  (2 + 4 + 6 + 7 + 9) = 756

At the very least, the biggest difference can be created if one term is made of the smallest numbers, while the other full of the highest, or:

(1 + 2 + 3 + 4 + 5) × (6 + 7 + 8 + 9 + 10)=600

Answer:

43

Step-by-step explanation:

it looks the same as the other side

The required angle b is 43°.

It is required to find the  measure of angle b.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle and corner whether constituting a projecting part or a partially enclosed space.

Given:

The measure of angle b is 43° due to vertically opposite angle.

Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines. Vertically opposite angles are equal to each other. These are sometimes called vertical angles.

Therefore, the required angle b is 43°.

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Answer:

b

Step-by-step explanation:

i solved it in my head.

Answer:

4 cm^2

4 cm

Step-by-step explanation:

8/2 = 4

4/2 = 2

each side of the square is 2 cm

sqrt. 16 = 4

4 cm

Answer: B. rectangular pyramid

Answer:

x = 4

x = -10

Step-by-step explanation:

(x + 3)² = 49

Take the square root of both sides.

x + 3 = ±7

The equation is x + 3 = 7 or x + 3 = -7.

x + 3 = 7

Subtract 3 on both sides.

x = 4

x + 3 = -7

Subtract 3 on both sides.

x = -10

Answer:

x₁ = -10

x₂ = 4

Step-by-step explanation:

(x + 3)² = 49

x + 3 = ± 7

x + 3 = -7 → x = -10

x + 3 = 7 → x = 4

Hope this helps! :)

Answer:

7.5 mL

Step-by-step explanation:

If it decays exponentially then you divide the previous number by 4 to get the next number and 30 divided by 4 is 7.5mL.

Answer:

115/5 23 so 20% =23 23x4 =92

Answer:

144 cm^2

Step-by-step explanation:

8x6+4x10+4x8+4x6

48+40+32+24

80+40+24

120+24

144

Answer:

2 cm

10 cm

Step-by-step explanation:

14/7 = 2

This helps to find because area of rectangle = bh or base times height.

A = 1/2 bh

30 = 1/2 b 6

30 = 3b

b = 10

Answer:

b = 2 cm

b = 10 cm

Step-by-step explanation:

Area of a Rectangle: A = lw

Area of a Triangle: A = 1/2bh

We are given area and length, so simply plug it in:

14 = 7w

w = 2 cm

We are given area and height, so simply plug it in:

30 = 1/2(6)(b)

30 = 3b

b = 10 cm

Answer:

c

Step-by-step explanation:

area of a circle = πr²

area = A²

A =√ 12π

A = 2 √ 3π

Answer:

Cada perro caliente cuesta 5,500 pesos y cada hamburguesa cuesta 7,000 pesos.

Step-by-step explanation:

Sea x el precio de los perros calientes y y el precio de las hamburguesas.

Escribiendo los datos de la primera familia en forma de ecuación tenemos:

[tex]4x+3y=43,000[/tex] (4 perros calientes y 3 hamburguesas cuestan 43,000 pesos)

Escribiendo los datos de la segunda familia:

[tex]5x+y=34500[/tex] (5 perros calientes y 1 hamburguesa cuestan 34,500 pesos)

Vamos a resolver este sistema de ecuaciones por el método de suma y resta:

[tex]4x+3y=43,000\\5x+y= 34,500[/tex]

Multiplicando la segunda ecuación por -3 y sumando ambas tenemos:

[tex]4x+3y=43,000\\-15x-3y= -103,500\\\\-11x=-60,500\\x=-60,500/-11\\x= 5,500[/tex]

Por lo tanto, un perro caliente cuesta 5,500 pesos.

Ahora sustituimos este valor en nuestra segunda ecuación para encontrar el precio de las hamburguesas:

[tex]5x+y=34500\\5(5,500)+y=34,500\\27,500 +y=34,500\\y=34,500-27,500\\y=7,000[/tex]

Por lo tanto, las hamburguesas cuestan 7,000 pesos cada una

Answer:

Solution,

[tex] \frac{5}{8} = \frac{12}{g} \\ or \: 5 \times g = 12 \times 8 \: ( \: cross \: multiplication) \\ or \: 5g = 96 \\ or \: g = \frac{96}{5} \\ g = 19.2[/tex]

Hope this helps..

Good luck on your assignment...

Answer:

Step-by-step explanation:

5/8=12/g

*8      *8

5=12*8/g

*g    *g

5g=12*8=96

:5              :5

g=96/5

g=19.2

Answer: 28

Step-by-step explanation:

The shape is grouped into 4 identical parallelograms.  

Thus, as the combined area of the figure is 308, you can divide 308/4 to get 77.  Thus, each parallelogram has an area of 77.

Then, divide 14/2 to get that the height of each parallelogram is 7.  

The area of a parallelogram is l*w.  Thus, because l = 7, each parallelogram has a width of 11 because 77/7 = 11.  

Then, simply add 11+11+6 to get y.

Hope this helps <3

Answer:

12 meters

Step-by-step explanation:

Draw a picture of the two pathways 30° apart.  Add a circle representing the illumination of the light on one of the pathways.  Draw a line from the center of the circle to the last point where it intersects the pathway without lights.

This forms a triangle.  One leg is x, the length of the pathway without lights.  Another leg is 5n, where n is an integer.  This represents how far the light is from where the pathways meet.  The third and final leg is 6, the radius of the illumination.

Use law of cosine to solve:

6² = x² + (5n)² − 2x(5n) cos 30°

36 = x² + 25n² − 5√3 xn

0 = x² − 5√3 xn + 25n² − 36

In order to have a solution, the discriminant must be greater than or equal to 0.

b² − 4ac ≥ 0

(-5√3 n)² − 4(1)(25n² − 36) ≥ 0

75n² − 100n² + 144 ≥ 0

144 − 25n² ≥ 0

144 ≥ 25n²

144/25 ≥ n²

12/5 ≥ n

So n must be an integer less than 12/5, or 2.4.  Therefore, the largest value of n is 2.  Substituting:

0 = x² − 5√3 x(2) + 25(2)² − 36

0 = x² − 10√3 x + 64

Solve with quadratic formula:

x = [ 10√3 ± √(300 − 4(1)(64)) ] / 2(1)

x = (10√3 ± √44) / 2

x = 5√3 ± √11

x ≈ 5.34 or 11.98

We want the larger value of x.  So approximately 12 meters of the pathway without lights is illuminated.

Answer:

Step-by-step explanation:-

-

-8239910.76

For this question, the time given confuses me.  I know the rate of return is just total return divided by divided by investment, Assuming that Matt received the $400 in dividends as cash payouts, and they weren't reinvested into buying shares of the stock, then his total return over two years was $500, Now, if Matt's dividends were reinvested into the stock - and if you have a 401(k) or IRA, that's what usually happens - then his ROI would have been only 6% because he only made a profit of $100 on an investment of $1500. Note:  In the real world, in current market conditions, Matt probably would have got about a 5% return on a good stock, and Bella would have received about 0.05% on a savings account.

hope this helped you ;)

Matt probably would have got about a 5% return on a good stock.

The rate of return is just the total return divided by investment.

Consider that Matt received the $400 in dividends as cash payouts, and they weren't reinvested into buying shares of the stock, then his total return over two years was $500.

Now, if Matt's dividends were reinvested into the stock then his ROI would have been only 6% because he only made a profit of $100 on an investment of $1500.

In the real, current market conditions, Matt probably would have got about a 5% return on a good stock, and Bella would have received about 0.05% on a savings account.

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Answer:

√3 + 1

Step-by-step explanation:

Step below are self-explanatory

Answer:

4 lb

Step-by-step explanation:

Answer:

4 AND 2

Step-by-step explanation:

Answer:

Hello!

______________________

This question is very easy.

2 + 2 = 4

1 + 1 = 2

Step-by-step explanation: Add.

Hope this helped you!

Answer:

Around 10/3 or 3.33 times farther.

Step-by-step explanation:

We simply divide the larger distance by the smaller distance to find our ratio:

2(10⁸)/6(10⁷)

10/3

*Remember when you divide exponents, you subtract them

Answer:

16.59

Step-by-step explanation:

Given:

[tex](ax+b)(bx+a)=26x^2+\Box\cdot x+26[/tex]

Expanding the left hand side, we have:

[tex](ax+b)(bx+a)=abx^2+a^2x+b^2x+ab\\=abx^2+(a^2+b^2)x+ab\\=26x^2+\Box\cdot x+26\\ab=26 \implies b=\frac{26}{a}[/tex]

Therefore:

[tex]a^2+b^2=a^2+\dfrac{26}{a} =\dfrac{a^3+26}{a}[/tex]

To find the minimum value, we take the derivative and solve for its critical point.

[tex]\frac{d}{da} (\frac{a^3+26}{a})=\frac{2a^3-26}{a^2}\\$Setting the derivative equal to zero, we have:\\2a^3-26=0\\2a^3=26\\a^3=13\\a=\sqrt[3]{13}[/tex]

Recall that:

[tex]\Box=a^2+b^2=\dfrac{(\sqrt[3]{13}) ^3+26}{\sqrt[3]{13}}\\=\dfrac{13+26}{\sqrt[3]{13}}\\\\\Box=16.59[/tex]

The minimum possible value of the coefficient of x is 16.59.

Answer:

173

Step-by-step explanation:

For sympliciy let the box equal y.

Expanding the left side we get (a*x+b)(b*x+a) = (a*b*(x)^2 + (a^2 + b^2)x + a*b). Hence we have that  (a*b*(x)^2 + (a^2 + b^2)x + a*b) = 26*(x)^2 + x*y + 26. Scince the coefficients of like terms in our equation must be equal, ab=26. Hence (a,b) = (1,26),(26,1),(-1,-26),(-26,-1),(2,13),(13,2),(-2,-13),(-13,-2). Since a^2 + b^2 = y we can see that the only 2 values of y are 677 and 173 (by simply plug in the values of (a,b)), taking the smaller of the two our answer is [173].

Answer:

Option D is correct.

The equation with roots 3 plus or minus square root 2 is x² - 6x + 7

Step-by-step explanation:

The roots of the unknown equation are

3 ± √2, that is, (3 + √2) and (3 - √2)

The equation can then be reconstructed by writing these roots as the solutions of the quadratic equation

x = (3 + √2) or x = (3 - √2)

The equation is this

[x - (3 + √2)] × [x - (3 - √2)]

(x - 3 - √2) × (x - 3 + √2)

x(x - 3 + √2) - 3(x - 3 + √2) - √2(x - 3 + √2)

= x² - 3x + x√2 - 3x + 9 - 3√2 - x√2 + 3√2 - 2

Collecting like terms

= x² - 3x - 3x + x√2 - x√2 - 3√2 + 3√2 + 9 - 2

= x² - 6x + 7

Hope this Helps!!!

Answer:

Option (1). 17

Step-by-step explanation:

Length of a segment having coordinates (x₁, y₁) and (x₂, y₂) is given by the formula,

d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Coordinates of points A and C are (4, 3) and (19, 11).

To get the length of segment AC we will substitute the coordinates in the formula,

AC = [tex]\sqrt{(19-4)^2+(11-3)^2}[/tex]

     = [tex]\sqrt{(15)^2+8^2}[/tex]

     = [tex]\sqrt{225+64}[/tex]

     = [tex]\sqrt{289}[/tex]

     = 17

Therefore, length of segment AC = 17 units.

Option (1) will be the answer.

Answer: CPCTC

Step-by-step explanation:

because in the step before that it was proved that the triangles were congruent and CPCTC is used after they are proved congruent.

By CPCT [Corresponding Part of congruent Triangle]

<h=<j

hope i helped

-lvr

Answer:

2.5

Step-by-step explanation:

1/2x5=?

5/2=?

2.5=?

Answer:

[tex]\boxed{2.5}[/tex]

Step-by-step explanation:

=> [tex]\frac{1}{2} of 5[/tex]

The word "of" means "to multiply"

=> [tex]\frac{1}{2} * 5[/tex]

=> [tex]\frac{1*5}{2}[/tex]

=> [tex]\frac{5}{2}[/tex]

=> 2.5