Two identical gardens are to be weeded, each by a two-person team. Team A includes one gardener who could weed the garden in 2 h and another who could weed the garden in 4 h. Team B includes two gardeners, either of whom could weed the garden in 3 h. Which team will finish first? Explain.

Another point on the line is (-9, 7). Ultimately, the choice of which point to use depends on the context or specific requirements of the problem you are solving.

To determine which point to use from the equation y - 7 = 3(x + 9), we need more information.

The equation provided represents a linear equation in the form y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Without additional context or specific instructions, we can choose any point that satisfies the equation to use as a reference.

For example, if we let x = 0, we can solve the equation for y:

y - 7 = 3(0 + 9)

y - 7 = 3(9)

y - 7 = 27

y = 27 + 7

y = 34

So, one point on the line is (0, 34).

Alternatively, if we let x = -9, we can solve the equation for y:

y - 7 = 3(-9 + 9)

y - 7 = 3(0)

y - 7 = 0

y = 7

So, another point on the line is (-9, 7).

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X=90 ....angles in a semi-circle

Angle B=A ...Radii

Answer:

a. 30 b. indeterminate, unless you're given the measure of either of the other sides.

Step-by-step explanation:

a. lazy solution: it's a 3-4-5 right triangle scaled up (18 is 3*6, 24 is 4*6, last side will be 5*6= 30. Less than lazy solution: it's a right triangle, pythagorean theorem applies:

[tex]x^2= 18^2+24^2 = 324+576 = 900\\x= 30[/tex]

b.problem is indeterminate as long as you don't know the measure of any of the other sides. the 30-60 triangle is half of an equilateral triangle and x is [tex]\sqrt3[/tex] times the short side, or [tex]\frac{\sqrt3} 2[/tex] times the long side. It's easily shown by mirroring the triangle along the vertical side, and if the short leg measures k, the hypotenuse measures 2k, and the vertical side measures [tex]x^2+k^2=(2k)^2\\x^2+k^2 = 4k^2\\x^2 = 3k^2 \implies x=\sqrt3\ k[/tex]

From the attached image, it can be seen that triangle PQR is an isosceles triangle and therefore option (A), option (B), option (C)  and option (D) are all correct.

An isosceles triangle has 2 sides equal meaning 2 opposite angles are also equal.

Let us assume the following:

PR = 1cm

QR = 1cm

PQ = 2cm

cos P = adj/hyp

         = PR/PQ = 1/2

cos Q = adj/hyp

          = QR/PQ = 1/2

Therefore cos P and cos Q are equal.

sin P = opp/hyp

        = QR/PQ = 1/2

sin Q = opp/hyp

         = PR/PQ = 1/2

Also sin P and sin Q are equal.

From this analogy, we can deduce the following:

sin P = sin Q = 1/2

cos P = cos Q = 1/2

sin P = cos Q = 1/2

cos P = sin Q = 1/2

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The correct answer is (j - k)(x) = 10 + x.

To find the difference in the amount of money between Joel's and Kevin's accounts, we subtract the value of Kevin's account (k(x)) from Joel's account (j(x)).

(j - k)(x) = (25 + 3x) - (15 + 2x)

            = 25 - 15 + 3x - 2x

            = 10 + x

This expression represents how much more money is in Joel's account compared to Kevin's account after x weeks.

Therefore, the correct function is (j - k)(x) = 10 + x.

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Holly's expression is equal to 864, and Jim's expression is equal to 36. So, Jim's expression is 828 less than the other expression.

Holly's notebook:

6 × (24 ÷ 2)²

= 6 × (12)²

= 6 × 144

= 864

Jim's notebook:

6 × 24 ÷ 2²

= 6 × 24 ÷ 4

using PEMDAS

P = parenthesis

E = exponents

M = multiplication

D = Division

A = Addition

S = Subtraction

6 × 24 ÷ 4

= 144 ÷ 4

= 36

Therefore, Jim's expression is less than Holly's expression.

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Answer: Landing on X and heads, landing on Y and heads, landing on Z and heads, landing on X and tails, landing on Y and tails, landing on Z and tails

Step-by-step explanation:

       There are three possible spinner options and 2 possible coin options. 3 * 2 = 6, leading to 6 possible outcomes.

       The spinner could land on X, Y, or Z.

       The coin could land on heads or tails.

       If we type out all of these possibilities (each spinner section and heads, each spinner section and tails) we end up with;

       ➜ Landing on X and heads

       ➜ Landing on Y and heads

       ➜ Landing on Z and heads

       ➜ Landing on X and tails

       ➜ Landing on Y and tails

       ➜ Landing on Z and tails

(a). The distance QR is equal to 45.3 using the cosine rule.

(b) Bearing of Q from P is 315°

Bearing is usually measured in degrees, with 0° indicating the reference direction (usually North), and increasing clockwise to 360°. It refers to the direction or angle between a reference direction and a point or object.

(a). Let ∆PQR be the triangle formed with bearings so that:

angle P = 45° + 40° {alternate angles from Q and R respectively to P}

angle P = 85°

PQ = 25km

PR = 40km

The distance QR is calculated using the cosine rule as follows:

QR² = 25² + 40² - 2(25)(40)cos85° {cosine rule}

QR² = 2225 - 174.3115

QR = √2050.6885 {take square root of both sides}

QR = 45.2845

(b) Bearing of point Q from P is the angle measured from the north of P to the straight line distance between Q and P

Bearing of Q from P = 45° + 270° = 315°

Therefore, the distance QR is equal to 45.3 using the cosine rule. Bearing of Q from P is 315°

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Step-by-step explanation:

volume of any type of pyramid :

1/3 × base area × height

FYI (not needed to solve the problem) :

base area is a pentagon.

the area of a pentagon is

1/2 × p × a

p is the perimeter (5 × side length) of the pentagon.

a is the apothem (the direct - right-angled- distance from the center of the pentagon to the center of a side).

volume of any type of regular prism :

base area × height

since the sides of the pentagon are the same, also their base areas are the same.

the height is the same.

so, when we compare both formulas, we see that the only difference is the factor 1/3.

the volume of the pyramid is 1/3 the volume of the prism.

therefore,

volume prism = volume pyramid × 3 = 435.7 × 3 =

= 1,307.1 cm³

I cannot describe the pattern in the sequence of artwork without visual representation.

Let's analyze each pattern:

The pattern appears to be adding 7 to each number to get the next number.

The next three numbers would be:

29, 36, 43.

The pattern alternates between adding 2 and subtracting 1.

The next three numbers would be:

11, 10, 12.

The pattern increments by 3 each time.

The next three numbers would be:

15, 18, 21.

The pattern alternates between squaring and taking the square root of the previous number.

The next three numbers would be:

1, 8, 1.

The pattern doubles each time.

The next three numbers would be:

64, 128, 256.

The pattern multiplies each number by 3 to get the next number.

The next three numbers would be:

243, 729, 2187.

As a text-based AI model, I am unable to draw diagrams.

I can describe the next diagram in each pattern:

The next diagram would consist of three rows, each containing four dots arranged in a square.

The next diagram would consist of a single dot positioned 7 units below the bottom dot of the previous diagram.

The next diagram would consist of two vertical lines with three dots each.

The next diagram would consist of a single dot positioned 4 units above the top dot of the previous diagram.

The next diagram would consist of a row of six dots arranged in a straight line.

The next diagram would consist of four rows, each containing three dots arranged in a square.

A text-based AI model, I am unable to see or analyze images or diagrams.

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log₂ 24 can be expressed as 3 + log₂ 3 in terms of prime factors, using the properties of logarithms.

To express log₂ 24 in terms of prime factors, we can use the properties of logarithms and the fact that any positive integer can be expressed as a product of prime factors.

First, let's find the prime factorization of 24.

24 can be divided by 2, so we have 24 = 2 × 12.

12 can be divided by 2, so we have 12 = 2 × 6.

6 can be divided by 2, so we have 6 = 2 × 3.

Therefore, the prime factorization of 24 is 2 × 2 × 2 × 3, or 2³ × 3.

Now, using the properties of logarithms, we can express log₂ 24 as the sum of logarithms of its prime factors.

log₂ 24 = log₂ (2³ × 3)

According to the properties of logarithms, we can separate the factors inside the logarithm as individual terms:

log₂ (2³ × 3) = log₂ 2³ + log₂ 3

Since log₂ 2³ is equal to 3, we can simplify the expression further:

log₂ (2³ × 3) = 3 + log₂ 3

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Answer:

Step-by-step explanation:

D is the answer. See attachment for reason.

a. The number halfway between 3.6 and 9.6 is 6.6.

b. The number halfway between 1.1 and 1.5 is 1.3.

c. The number halfway between 7.26 and 7.28 is 7.27.

To find the number halfway between 3.6 and 9.6, we can add the two numbers and divide by 2:

(3.6 + 9.6) / 2 = 13.2 / 2 = 6.6

The number halfway between 3.6 and 9.6 is 6.6.

To find the number halfway between 1.1 and 1.5, we can use the same approach:

(1.1 + 1.5) / 2 = 2.6 / 2 = 1.3

The number halfway between 1.1 and 1.5 is 1.3.

To find the number halfway between 7.26 and 7.28, we can apply the same method:

(7.26 + 7.28) / 2 = 14.54 / 2

= 7.27

The number that is between 3.6 and 9.6:

(3.6 + 9.6) / 2 = 13.2 / 2 = 6.6

6.6 is the number that falls between 3.6 and 9.6.

We can apply the same strategy to determine the value that lies between 1.1 and 1.5:

(1.1 + 1.5) / 2 = 2.6 / 2

= 1.3

1.3 is the number that falls between 1.1 and 1.5.

We can use the same procedure to determine the number that is halfway between 7.26 and 7.28:

(7.26 + 7.28) / 2 = 14.54 / 2

= 7.27

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2/9 is the probability that the teacher will choose two girls

To calculate the probability of choosing two girls from the class

we need to determine the total number of possible outcomes and the number of favorable outcomes.

Total number of outcomes: Since the teacher is choosing two students from a class of 10, the total number of outcomes is given by the combination formula C(10, 2), which is calculated as:

C(10, 2) = 10! / (2!(10 - 2)!) = 10! / (2! × 8!) = (10 × 9) / (2 × 1) = 45

Number of favorable outcomes

We want to choose two girls from the 5 girls in the class.

The number of ways to choose 2 girls from 5 is given by the combination formula C(5, 2), which is calculated as:

C(5, 2) = 5! / (2! × (5 - 2)!) = 5! / (2! × 3!) = (5× 4) / (2× 1) = 10

Therefore, the number of favorable outcomes is 10.

The probability of choosing two girls is given by the number of favorable outcomes divided by the total number of outcomes:

Probability = Number of favorable outcomes / Total number of outcomes = 10 / 45 = 2 / 9

Hence, the probability that the teacher will choose two girls is 2/9.

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A. P(E) = 1/5

B. P(F) = 1/5

C. P(G) = 1/5

D.  The probability of selecting either "Eben" or "Frank" is 2/5.

A: To find the probability of selecting the name "Eben," we need to determine the fraction of the total possible outcomes that result in selecting "Eben." Since there are a total of five names to choose from, the probability of selecting "Eben" can be expressed as:

P(E) = (Number of favorable outcomes) / (Total number of possible outcomes)

In this case, there is only one favorable outcome (selecting "Eben"), and there are five possible outcomes (choosing any of the five names). Therefore:

P(E) = 1/5

B: Similarly, to find the probability of selecting the name "Frank," we can apply the same approach. The probability of selecting "Frank" can be expressed as:

P(F) = (Number of favorable outcomes) / (Total number of possible outcomes)

Again, there is only one favorable outcome (selecting "Frank"), and there are five possible outcomes (choosing any of the five names). Thus:

P(F) = 1/5

C: To find the probability of selecting the name "Evelyn," we follow the same method as above. The probability of selecting "Evelyn" is:

P(G) = (Number of favorable outcomes) / (Total number of possible outcomes)

Once again, there is only one favorable outcome (selecting "Evelyn"), and there are five possible outcomes (choosing any of the five names). Therefore:

P(G) = 1/5

D: To find the probability of selecting either event E or event F (P(E U F)), we can add their individual probabilities and subtract the probability of their intersection (P(E ∩ F)). The probability of the union can be calculated as follows:

P(E U F) = P(E) + P(F) - P(E ∩ F)

Since event E and event F are independent, the probability of their intersection is zero (no name can be both "Eben" and "Frank" simultaneously). Therefore:

P(E U F) = P(E) + P(F) - 0

= P(E) + P(F)

= 1/5 + 1/5

= 2/5

Thus, the probability of selecting either "Eben" or "Frank" is 2/5.

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Answer: quotient: x+7 remainder: -5

(a) A formula to calculate the amount after n months: 1,500(1 + nx0.0046)

(b)  the amount owed after 14 months = $1596.6

Given that,

Principal amount =  P  = $1,500

interest of grown = R = 5.5%

Now we can write is,

5.5% = 5.5/100

        =  0.055

We know that,

The simple interest formula,

A = P(1 + rt)

Where,

A represents Amount after T years

R represents rate of interest

T is time in year

Now,

Since 1 month = 1/12 years

                        = 0.084

Therefore amount after 1 month be

A = 1,500(1+0.055x0.084)

  = 1,500(1+0.0046)

  = 1506.93

Amount after 2 month be

A =  1,500(1+ 2 x 0.055x0.084)

  = 1,500(1+2x0.0046)

Amount after 3 month be

A =  1,500(1+ 2 x 0.055x0.084)

  = 1,500(1 + 3x0.0046)

Hence amount of  n months = 1,500(1 + nx0.0046)

Hence,

The amount after 14 months,

=  1,500(1 + 14x0.0046)

= $1596.6

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After calculating the average of numbers here, the average of the four odd numbers from [tex]8 \ to \ 15[/tex] is greater than the average of the four even numbers.

The step-by-step solution to this is given below:

To determine which average is greater, let's calculate the averages of the even and odd numbers separately.

The four even numbers from [tex]8 \ to \ 15 \ are \ 8, 10, 12, and \ 14[/tex]. To find their average, we sum them up and divide by [tex]4[/tex]:

[tex]\[\text{Average of even numbers} = \frac{8 + 10 + 12 + 14}{4} = \frac{44}{4} = 11\][/tex]

The four odd numbers from [tex]8 \ to \ 15 \ are \ 9, 11, 13, and \ 15.[/tex] Similarly, we calculate their average:

[tex]\[\text{Average of odd numbers} = \frac{9 + 11 + 13 + 15}{4} = \frac{48}{4} = 12\][/tex]

Now, the next step will be comparing the two averages, we find that the average of the four odd numbers, [tex]12[/tex], is greater than the average of the four even numbers, [tex]11[/tex].

Therefore, the average of the four odd numbers from [tex]8 \ to \ 15[/tex] is greater than the average of the four even numbers.

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The value of x is 24.426 degrees when the opposite side is 9 and adjacent side is 20  and value of x is 58.211 degrees degrees when the adjacent side is 17 and hypotenuse is 32

In the given triangle

We have to find the missing angle x

By tan function we know that tan is a ratio opposite side and adjacent side

tanx=9/20

tanx=0.45

x=tan⁻¹(0.45)

x=24.426 degrees

For example 2, we find x by using cosine function which is a ratio of adjacent side and hypotenuse

cosx=17/32

cosx=0.53

x=cos⁻¹(0.53)

x=58.211 degrees

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The inclination of the line represented by the equation y = x + 3 is 1, and the inclination of the line represented by the equation 3x - 2y = 6 is 3/2.

To determine the inclination (or slope) of a straight line, we can examine the coefficients of the variables x and y in the equation of the line.

The inclination represents the ratio of how much y changes with respect to x.

Equation: y = x + 3

In this equation, the coefficient of x is 1, which means that for every increase of 1 in x, y also increases by 1.

This indicates that the inclination of the line is positive, meaning it slopes upwards as x increases.

Since the coefficient of x is 1, the inclination can be expressed as 1/1 or simply 1.

Equation: 3x - 2y = 6

To determine the inclination, we need to rearrange the equation in slope-intercept form (y = mx + b), where m represents the slope.

First, isolate y:

-2y = -3x + 6

Divide the entire equation by -2 to solve for y:

y = (3/2)x - 3

Now we can observe that the coefficient of x is 3/2.

This indicates that for every increase of 1 in x, y increases by 3/2. Therefore, the inclination of this line is positive, indicating an upward slope.

The inclination can be expressed as 3/2.

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Answer:

4th option

Step-by-step explanation:

using the rule of exponents

• [tex]a^{m}[/tex] ×[tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

then

[tex]x^{9}[/tex] × x = [tex]x^{9}[/tex] × [tex]x^{1}[/tex] = [tex]x^{(9+1)}[/tex] = [tex]x^{10}[/tex]

Then

[tex]\sqrt[3]{x^{10} }[/tex] ≡ [tex]\sqrt[3]{x^9 . x}[/tex]

Answer:

  C.  4 cm²

Step-by-step explanation:

You want the maximum possible area of a quadrilateral inscribed in a semicircle.

The figure is symmetrical about a vertical line, so the area will be maximized when the area of half the quadrilateral is maximized. The area of the quadrilateral in the right half of the figure is the product of the x- and y-coordinates of the corner point on the circle.

For coordinates (x, y), the area is A=xy. The graph of this function is a hyperbola, symmetric about the line y=x. The larger the value of A, the farther the graph is from the origin.

The maximum possible value of A will be found where the graph of xy=A is tangent to the circle. That point of tangency will lie on the circle and on the line y = x.

The equation for the semicircle is ...

  x² +y² = 2²

When x=y, this is ...

  x² +x² = 4

  x² = 2

This is the area of the quadrilateral in the right half of the figure.

The entire quadrilateral has an area twice this, or 2·2 = 4 (square cm).

The maximum possible area of the quadrilateral is 4 cm².

__

Additional comment

You will notice the figure is half of a figure of a whole circle with a square inscribed. This is not a coincidence.

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The area of a triangle is:

12x² -18x - 12

The area of a triangle can be calculated using the formula:

A = 1/2 * b * h

where b is the base and h is the height of the triangle

We have:

b = -6x + 3

h =  4(x - 2) = 4x - 8

substituting into the formula:

A = 1/2 * (6x + 3) * (4x - 8)

A = 1/2 * (24x² -48x + 12x - 24)

A = 1/2 * (24x² -36x - 24)

A = 12x² -18x - 12

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The six ordered pairs for the function f(x) = -x^2 + 3x + 2 are:

(-2, -8), (-1, -2), (0, 2), (1, 4), (2, 4), (3, 2).

To find six ordered pairs for the function [tex]f(x) = -x^2 + 3x + 2[/tex], we can substitute different x-values into the function and evaluate the corresponding y-values.

Let's choose six x-values and calculate the corresponding y-values:

When x = -2:

[tex]f(-2) = -(-2)^2 + 3(-2) + 2 = -4 - 6 + 2 = -8[/tex]

Therefore, the ordered pair is (-2, -8).

When x = -1:

[tex]f(-1) = -(-1)^2 + 3(-1) + 2 = -1 - 3 + 2 = -2[/tex]

Therefore, the ordered pair is (-1, -2).

When x = 0:

[tex]f(0) = -(0)^2 + 3(0) + 2 = 0 + 0 + 2 = 2[/tex]

Therefore, the ordered pair is (0, 2).

When x = 1:

[tex]f(1) = -(1)^2 + 3(1) + 2 = -1 + 3 + 2 = 4[/tex]

Therefore, the ordered pair is (1, 4).

When x = 2:

[tex]f(2) = -(2)^2 + 3(2) + 2 = -4 + 6 + 2 = 4[/tex]

Therefore, the ordered pair is (2, 4).

When x = 3:

[tex]f(3) = -(3)^2 + 3(3) + 2 = -9 + 9 + 2 = 2[/tex]

Therefore, the ordered pair is (3, 2).

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Answer:

x = - 3, x = 1

Step-by-step explanation:

x² + 2x - 3 = 0

consider the factors of the constant term (- 3) which sum to give the coefficient of the x- term (+ 2)

the factors are + 3 and - 1 , since

3 × - 1 = - 3 and + 3 - 1 = + 2 , then

(x + 3)(x - 1) = 0 ← in factored form

equate each factor to zero and solve for x

x + 3 = 0 ( subtract 3 from both sides )

x = - 3

x - 1 = 0 ( add 1 to both sides )

x = 1

solutions are x = - 3 , x = 1

Each radio requires 2 batteries, and each flashlight requires 6 batteries.

To solve this problem using the substitution method, we need to determine how many batteries each radio and flashlight need. Let's assume the number of batteries needed for a flashlight is represented by 'f', and the number of batteries needed for a radio is represented by 'r'.

From the given information, we can create two equations:

Equation 1: 12f + 6r = 84 (Karen's usage of batteries)

Equation 2: 5f + 10r = 50 (Jin's usage of batteries)

To solve the system of equations, we can use the substitution method. First, we'll solve Equation 1 for 'f' in terms of 'r':

12f = 84 - 6r

f = (84 - 6r)/12

f = 7 - (r/2)

Now, we substitute this expression for 'f' into Equation 2:

5(7 - (r/2)) + 10r = 50

35 - 5(r/2) + 10r = 50

35 - (5r/2) + 10r = 50

35 + (20r - 5r)/2 = 50

35 + 15r/2 = 50

15r/2 = 15

15r = 30

r = 2

Now that we have the value of 'r' as 2, we can substitute it back into Equation 1 to find the value of 'f':

12f + 6(2) = 84

12f + 12 = 84

12f = 72

f = 6

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The number of choir students that performed in at least 3 concerts is given as follows:

16 students.

An histogram is a graph that shows the number of times each element of x was observed, or the number of observations in each range of a data-set.

Hence, for this problem, the meaning of the histogram is given as follows:

Hence the number of choir students that performed in at least 3 concerts is given as follows:

9 + 4 + 3 = 16 students.

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The measure of angle cbd in regular octagon ABCDEFGH is 22.5°.

We are given that;

The octagon ABCDEFGH

Now,

To find the measure of angle CBD. Since ABCDEFGH is a regular octagon, triangle BCD is an isosceles triangle with BC = BD2. Therefore, the base angles of triangle BCD are congruent and have the same measure. Let x be the measure of angle CBD. Then, we have:

x + x + 135° = 180° (sum of angles in a triangle)

2x + 135° = 180°

2x = 180° - 135°

2x = 45°

x = 45°÷2

x = 22.5°

Therefore, by the angle the answer will be 22.5°.

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it will be A .......................................

Answer:

The answer is

-5.79×10²³,6.88×10‐²³,5.73×10²³,57.8×10²²,5.83×10²³

Step-by-step Explanation: