The diagonals of parallelogram ABCD intersect at P. Which statements must be true? Select all that apply.

Answer:

Set up the equation ... 60 + 40X = total charges... where X is the number of hours (6.5)

60 + 40(6.5) = ?

60 + 260 = ?

320 = total charges

The total area of the two circles will be 168316.9 square feet.

The circle is defined as a two-dimensional figure having a fixed point and the number of the points is traced around the curved path at an equal distance from the fixed point. The overall figure is called a circle.

The area of the circle is calculated by the formula:-

Area = πr²

Given that the south side of the highway needed to be compacted in order to create two circles of various sizes for a specific four-leaf clover. The two circles on the north side of the road have a 128-foot radius, whereas the two on the south side have a 102-foot radius.

The total area will be calculated as:-

Area = 2 x π x 128² + 2 x π x 102²

Area = 102943.25 + 65370.25

Area = 168316.9 square feet

Hence, the total area will be 168316.9 square feet.

To know more about circle follow

https://brainly.com/question/14068861

#SPJ9

Step-by-step explanation:

for z -> 3 (3z - 2) -> (3×3 - 2) = 7

The evaluation of the cubic function represented by the graph can be presented as follows;

a. The equation of the function, S = a·t³ + b·t² + c·t + d, indicates that the equation is a cubic equation

b. i. d = -5

ii. The three equations are;

a + b + c = 8...(1)

8·a + 4·b + 2·c = 4...(2)

27·a + 9·b + 3·c = 0...(3)

iii. a = 2, b = -12, and c = 18

c. The student is expected to be in debt for 2 years, 4 months and 3 days

A cubic function is a degree three polynomial that can be expressed in the form; f(x) = a·x³ + b·x² + c·x + d.

The specified function can be presented as follows;

S = a·t³ + b·t² + c·t + d

a. A feature of the graph that indicates that a cubic equation is the appropriate model, is the largest power of the input time variable t in the function is 3, which is the same as the power of a cubic function.

b. i. The value of d can be found by plugging in t = 0, in the function; S = a·t³ + b·t² + c·t + d

From the table in the question, we get;

At t = 0, S = -5

Therefore;

S = a×0³ + b×0² + c×0 + d = -5

d = -5

The value of d = -5

b. ii. The simultaneous equations can be obtained by plugging in the values of t from the table into the function for S as follows;

S = a·t³ + b·t² + c·t + d

S = a·t³ + b·t² + c·t - 5

When t = 1, we get;

S = a·1³ + b·1² + c·1 - 5 = 3

a + b + c - 5 = 3

a + b + c = 3 + 5 = 8

When t = 2, we get;

S = a·2³ + b·2² + c·2 - 5 = 3

8·a + 4·b + 2·c - 5 = -1

8·a + 4·b + 2·c = -1 + 5 = 4

When t = 3, we get;

S = a·3³ + b·3² + c·3 - 5 = 3

27·a + 9·b + 3·c - 5 = -5

27·a + 9·b + 3·c = -5 + 5 = 0

iii. Solving the system of equations using a graphing calculator, indicates that we get;

c. Plugging in the values into the specified equation, we get;

S = 2·t³ - 12·t² + 18·t - 5

The solution of the above equation can be found as follows;

2·t³ - 12·t² + 18·t - 5 = 0

Based on an online tool, the Newton Raphson method indicates that a solution of the equation is; t ≈ 0.35821, which indicates that a factor of the equation, 2·t³ - 12·t² + 18·t - 5 = 0 is; (x - 0.35821)

(2·t³ - 12·t² + 18·t - 5) ÷ (x - 0.35821) ≈ 2·t² - 11.28356·t + 13.95804

The other solutions are therefore;

t ≈ 1.83, and t ≈ 3.81

The student is expected to be in debt at time t = 0, and from the graph, cross the x-axis out of depth first at time, t ≈ 0.35821 of a year

The student will be in dept again between t ≈ 1.83 and t ≈ 3.81

The total time the student is expected to be in debt is therefore;

Learn more on cubic functions here: https://brainly.com/question/2456468

#SPJ1

Answer:

[tex] \frac {3}{8} + \frac{2}{8} = \frac{5}{8} = 1 \frac{3}{8} [/tex]

[tex] = \frac{5}{ \\ 8} = 1 \frac{3}{8} [/tex]

Answer: B

Step-by-step explanation:

The number 7.787887888 is option (C) not a rational number, it has a pattern which is predictable, but not repeating

The given number is 7.787887888

The rational numbers is a number that can be expressed as the p/q format, where p and q are integers and p will not be equal to zero. So the rational number is the ratio of the two integers.

Here the given number is 7.787887888.

So this is an non terminating number

But here we can see that there is a pattern which is predictable but its not repeating

Therefore, it is not a rational number ,but it has a pattern which is predictable, but not repeating

Learn more about rational number here

brainly.com/question/24540810

#SPJ4

The perimeter of the figure after a dilation with a scale factor of 4 is

Suppose the initial measurement of a figure was x units.

And let the figure is scaled and new measurement is of y units.

Since the scaling is done by multiplication of some constant, that constant is called scale factor. Let that constant be 's'.

Then we have:

[tex]s \times x = y\\s = \dfrac{y}{x}\\[/tex]

Thus, scale factor is the ratio of the new measurement to the old measurement.

Given;

The perimeter= 12units

Scale factor=4

Now,

Dilation with the given scale factor;

= 12*1/4

=12/4

=3

Therefore, dilation by the given scale factor will be 3.

Learn more about scale factor here:

https://brainly.com/question/11178083

#SPJ9

a)

The total number of possible 3​-card poker hands is 22100

b)

The number of possible black flushes is 2600

c)

The probability of being dealt a black flush is 0.1176

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Number of cards = 52

Number of cards in hand = 3

Combination formula.

[tex]^nC_r[/tex] = n! / r! (n -r)!

a)

The total number of possible 3​-card poker hands.

= [tex]^{52}C_3[/tex]

= (52 x 51 x 50) / (3 x 2)

= 22100

b.

Number of black cards (spades and clubs) = 13 + 13 = 26

The number of possible black flushes.

= [tex]^{26}C_3[/tex]

= (26 x 25 x 24) / (3 x 2)

= 2600

c.

The probability of being dealt a black flush.

From (a) and (b)

= 2600/22100

= 0.1176

Thus,

The total number of possible 3​-card poker hands = 22100

The number of possible black flushes = 2600

The probability of being dealt a black flush = 0.1176

Learn more about probability here:

https://brainly.com/question/14099682

#SPJ9

Just ten more days and I'll be in London!

Answer:

Just ten more days and I'll be in London!

Answer:

you are to use patagorious theory

Answer:

[tex]a \sqrt[5]{b} [/tex]

Step-by-step explanation:

solution Given:

[tex] \sqrt[5]{ {a}^{3} {b}^{2} } \times \sqrt[5]{ {a}^{2}{b }^{ - 1} } [/tex]

since i indices rule if the power is same it can be multiplied or divided.

[tex] \sqrt[5]{ {a}^{3} {b}^{2} \times {a}^{2} {b}^{ - 1} } [/tex]

since power is added of like terms in multiplication

[tex] \sqrt[5]{ {a}^{3 + 2} {b}^{2 - 1} } [/tex]

again simplifying

[tex] \sqrt[5]{ {a}^{5} b} [/tex]

by using indices formula

[tex] \sqrt[x]{ {a}^{y} } = {a}^{ \frac{y}{x} } [/tex]

we get

[tex]a \sqrt[5]{b} [/tex]

Answer:

[tex]a \sqrt[5]{b}[/tex]

Step-by-step explanation:

Given expression:

[tex]\sqrt[5]{a^3b^2} \times \sqrt[5]{a^2b^{-1}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]

[tex](a^3b^2)^{\frac{1}{5}} \times (a^2b^{-1})^{\frac{1}{5}}[/tex]

As the exponents are the same,

[tex]\textsf{apply exponent rule} \quad a^n \cdot c^n=(a \cdot c)^n:[/tex]

[tex](a^3b^2a^2b^{-1})^{\frac{1}{5}}[/tex]

Collect like terms:

[tex](a^3a^2b^2b^{-1})^{\frac{1}{5}}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex](a^{(3+2)}b^{(2-1)})^{\frac{1}{5}}[/tex]

Simplify the exponents:

[tex](a^5b^1)^{\frac{1}{5}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^bc^d)^n=(a^b)^n \cdot (c^d)^n:[/tex]

[tex](a^5)^{\frac{1}{5}} \cdot (b^1)^{\frac{1}{5}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]a^{\frac{5}{5}} \cdot b^{\frac{1}{5}}[/tex]

Simplify:

[tex]a^1 \cdot b^{\frac{1}{5}}[/tex]

[tex]a \cdot b^{\frac{1}{5}}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{\frac{1}{n}}=\sqrt[n]{a}:[/tex]

[tex]a \sqrt[5]{b}[/tex]

Answer:a

Step-by-step explanation:

Using the distributive property of matrix multiplication A(cu) = 0, which implies that cu also satisfies the equation Ax = 0 for any scalar c.

We have given that Ax = 0, where A is an m × n matrix and x is an n-dimensional vector in Rn.

To show that A(cu) = 0 for any scalar c, we can use the distributive property of matrix multiplication, which states that A(B + C) = AB + AC for any matrices A, B, and C of appropriate dimensions.

Let us substitute cu for x in the equation Ax = 0, then we get:

A(cu) = A(c × u)

Using the distributive property, we can write:

A(c × u) = c × A(u)

Since u satisfies the equation Ax = 0, we have:

A(u) = 0

Substituting this into the above equation, we get:

c × A(u) = c × 0 = 0

Therefore, we have shown that A(cu) = 0, which implies that cu also satisfies the equation Ax = 0 for any scalar c.

Learn more about the matrix at

https://brainly.com/question/28180105

#SPJ4

It looks like 1) adjacent angles.

The length of the dotted line would be 7.922 ft.

What is the diameter of the circle?

The diameter of a circle is the distance across the circle through its center. It is equal to twice the length of the radius, which is the distance from the center of the circle to any point on the circle.

In mathematical terms, if d represents the diameter of a circle, and r represents its radius, we have the formula:

d = 2r

In the given circle, for finding the inner diameter we have to remove the thickness of the circle from outer diameter, we get

q = 17.708 - 4.893 - 4.893

By solving this, we get

q = 7.922

Hence, the length of the dotted line would be 7.922 ft.

To learn more about the diameter of the circle, visit:

https://brainly.com/question/10907234

#SPJ1

a).The function1 changes at greater rate of 45.

b). At x = 1; the function1 = 45 and function2 = 50.

c).The functions are equal to 90 at x = 2.

A function in the equation form "y = mx + c" represents a straight line in a two-dimensional coordinate system. "y" and "x" are variables representing the coordinates of points on the line, "m" is the slope of the line, and "c" is the y-intercept, which is the point at which the line crosses the y-axis.

The slope "m" represents the rate at which the line rises or falls as x increases. The y-intercept "c" determines the location of the line along the y-axis. This equation is known as the slope-intercept form of a linear equation.

For the function1, when y = 0 and x = 0, we can solve for c and m as follows:

0 = 0m + c

c = 0

when y = 90 and x = 2;

90 = 2m + 0

m = 45

Hence, the function1 with y = 45x changes at a greater rate of 45.

At x = 1:

for function1;

y = 45(1) + 0 = 45

for function2;

y = 40(1) + 10 = 50.

At the point when x = 2:

for function1;

y = 45(2) + 0 = 90

for function2;

y = 40(2) + 10 = 90.

Therefore, the function1 changes at greater rate of 45. At x = 1; the function1 = 45 and function2 = 50. The functions are equal to 90at x = 2.

Know more about function here:https://brainly.com/question/24148225

#SPJ1

14. The mean of  the Zoo-venir Stand sales is of 23.9, representing the quotient between the sum of all the amounts and the number of observations.

15. The range of the Zoo-venir Stand sales is of 30, representing the difference between the highest number and the lowest number.

Considering the key format of the stem-and-leaf plot, the observations are given as follows:

12, 13, 13, 13, 14, 15, 15, 16, 17, 20, 21, 21, 22, 22, 23, 24, 25, 25, 25, 26, 27, 27, 28, 29, 29, 32, 34, 34, 37, 41, 42.

The mean is given by the sum of all observations divided by the number of observations, hence it's value is of: 23.9.

The range is the difference between the highest observation and the lowest observation, hence it is of:

42 - 12 = 30.

More can be learned about mean and range of data-sets at https://brainly.com/question/14532771

#SPJ1

The volume of the Cone A will be 4m³.

What is a cone?

A cone is a shape constructed by connecting a common point, known as the apex or vertex, to all the points of a circular base using a collection of line segments (which does not contain the apex). The height of the cone is the distance from the vertex to the base. The radius of the circular base has been measured. The slant height is the length of the cone from the apex to any point on the perimeter of the base. Based on these values, formulae for the cone's surface area and volume have been developed. The cone in the illustration is characterised by its height, radius of base, and slant height.

Volume of cone=πr²h where r=radius of base and h=height of cone

Curved surface area=πrL , where L=slant height

Now,

As given Cone B is the image of cone A after dilation by a scale factor of 1/4. If the volume of cone B is 1 m³

After dilation volume also decreases/increases with respect to scale factor of dilation. Here scale factor is 1/4

and Then volume of A=1*4

=4 m³

hence,

          The volume of the Cone A will be 4m³.

To know more about cone visit the link

https://brainly.com/question/16394302?referrer=searchResults

#SPJ1

Answer: it is actually 64m^3

Step-by-step explanation:

i did it and this was the right answer

Answer:

Step-by-step explanation:

m∠2 = 90° - 56° = 34°. So, m∠1 = m∠2 = 34°

here the answers

The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.

What is meant by continuous compounding?

If compound interest is calculated and reinvested into the balance of an account across an essentially unlimited number of periods, continuous compounding is the mathematical limit that compound interest can reach. Continuous compounding determines interest by assuming constant compounding across an infinite number of periods, as opposed to computing interest on a finite number of periods, such as annually or monthly.

Given,

rate per period  = 3%

Principal amount = $1000

Compounding is done after 1,5 and 20 years.

But we are asked to find the amount after continuous compounding after 1 year.

The formula of the amount after continuous compounding is:

[tex]A = Pe^{rt}[/tex]

where A = amount after continuous compounding

        r = rate of period

     t = time period

    P  = principal amount

[tex]A = Pe^{rt} = 1000e^{0.03*1}[/tex] = $1030.45

Annual yield formula (AYP) = [tex](1+\frac{r}{n} )^n-1[/tex]

n = times it compounds per year = 365

r = 0.03

AYP = [tex](1+\frac{0.03}{365} )^{365}-1 = 0.0304[/tex]

                                  = 3.04%

Therefore The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.

To learn more about compounding, follow the link.

https://brainly.com/question/30460031

#SPJ1

Answer:

So, Darmal needs to work more than 8.96 hours to earn more than $128.

Step-by-step explanation:

The situation represented by the inequality 14.25x > 128 is B. Darmal earns $14.25 per hour at his job. How many hours does he need to work to earn more than $128?

The inequality states that the product of 14.25 and x (representing the number of hours worked) is greater than 128. Solving for x, we can find the number of hours Darmal needs to work to earn more than $128:

14.25x > 128

x > 128 / 14.25

x > 8.96

So, Darmal needs to work more than 8.96 hours to earn more than $128.

Answer:

≈29.93 [units].

Step-by-step explanation:

according to the attachment the required perimeter is:

P=2*6+4.25*2+3.1415*3=12+8.5+9.4245=29.9245 [units].

The table that represents a linear relationship that is also proportional is; Table 2

A proportional relationship is defined as one where there is multiplying or dividing between the two numbers. A linear relationship can be a proportional one (for example y = 2x is proportional), but usually a linear equation has a proportional component plus some constant number (for example y = 2x + 3).

Table 1:

The proportions are;

-3/2, 0/3, 3/4

They are not equal and so not proportional

Table 2:

The proportions are;

-2/4 and -1/2

They are equal and so are proportional

Table 3:

The proportions are;

0/-2, 1/1 and 2/4

They are not equal and so not proportional.

Table 4:

The proportions are;

-4/0, 0/1 and 4/2

They are not equal and so not proportional.

Read more about Proportional Relationship at; https://brainly.com/question/12242745

#SPJ1

Answer:

Step-by-step explanation:

The correct answer is D. m∠6 + m∠7 = 180°.

When a transversal cuts two parallel lines, corresponding angles are equal and alternate interior angles are supplementary. This means that the sum of alternate interior angles is equal to 180°. In this diagram, ∠6 and ∠7 are alternate interior angles, so it is necessarily true that m∠6 + m∠7 = 180°.

The other options are not necessarily true. Option A states that m∠1 = m∠7, but this is only true if the two lines being cut by the transversal are perpendicular. Option B states that m∠3 = m∠6, but this is only true if the two lines being cut by the transversal are parallel. Option C states that m∠5 + m∠8 = 90°, but this is only true if the two lines being cut by the transversal are perpendicular.

(a) When q = 0 or q = 1, we get p = 0.5, but for other values of q, the optimal value of p is different.

(b) When q = 1, the expected score is 1, which is the maximum possible score.

(c) The optimal value of p also depends on the value of q in this case.

a) The expected score of the meteorologist can be expressed as the weighted average of the two possible scores, where the weights are the probabilities of it raining or not raining:

Expected score = p(1 - (1 - q)^2) + (1 - p)(1 - q^2)

To maximize the expected score, we need to differentiate it with respect to p, set the derivative equal to zero, and solve for p. This gives:

2q(1 - q) = 1 - 2p

Solving for p, we get:

p = (1 - 2q + 2q^2) / 2

So the optimal value of p depends on the value of q. When q = 0 or q = 1, we get p = 0.5, but for other values of q, the optimal value of p is different.

b) If the meteorologist chooses p = q, then the expected score simplifies to:

Expected score = q(1 - (1 - q)^2) + (1 - q)(1 - q^2)

= q^3 + (1 - 2q)q^2 + (1 - q)

To find the maximum expected score, we can take the derivative of this expression with respect to q, set it equal to zero, and solve for q. This gives:

3q^2 - 4q + 1 = 0

This quadratic equation has two roots: q = 1/3 and q = 1. When q = 1, the expected score is 1, which is the maximum possible score. When q = 1/3, the expected score is (8/27), which is the maximum score for any value of q between 0 and 1.

c) If the payoffs are {1 - (1 - p)^2, 1 - 1.1p^2}, then the expected score of the meteorologist is:

Expected score = p(1 - (1 - q)^2) + (1 - p)(1 - 1.1q^2)

To maximize this expected score, we can differentiate it with respect to p, set the derivative equal to zero, and solve for p. This gives:

2.2q^2 - 2q + 1 = 2p

Solving for p, we get:

p = (2.2q^2 - 2q + 1) / 2

So, in this scenario, the value of q also affects the ideal value of p.

To learn more about expected score here:

https://brainly.com/question/28000192

#SPJ4

Answer: 3

Step-by-step explanation:

Took the test

The factors of given polynomial are (x+3), (x-3), (x+2) and (x-2).

The factors are the polynomials which are multiplied to produce the original polynomial.

The given polynomial is x⁴-13x²+36

Here, x⁴-13x²+36 can be written as x⁴-9x²-4x²+36

= x²(x²-9)-4(x²-9)

= (x²-9)(x²-4)

= (x²-3²)(x²-2²)

By using the identity a²-b²=(a+b)(a-b)

So, (x+3)(x-3)(x+2)(x-2)

Therefore, the factors are (x+3), (x-3), (x+2) and (x-2).

To learn more about the factorisation of polynomial visit:

https://brainly.com/question/16789195.

#SPJ1