Three friends go grocery shopping together, and each buys the same kind of
oranges. LaMar buys 2 pounds (lb) and pays $1.00. Enrico buys 4 pounds and
pays $2.00. Anna buys 3 pounds and pays $1.50.
Identify the aranh and unit price that represent the orange costs.

The value of y is 18

Similar triangles have the same corresponding angle measures and proportional side lengths. The angles of the two triangle must be equal and it not necessary they have equal sides.

Therefore the corresponding angles of similar triangles are congruent and the ratio of corresponding sides of similar triangles are equal.

Therefore;

14/21 = 12/y

14y = 21 × 12

14y = 252

divide both sides by 14

y = 252/14

y = 18

Therefore the value of y is 18.

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Answer:

27

Step-by-step explanation:

9x3 right so 27

The law of sines can be solved for the following cases:

• AAS

• ASA

• SSA (But this can be ambigous)

The law of cosines can be solved for the following cases:

• SAS

• SSS

Thererefore, the correct options are A, C, E, D and F

Answer:

15 just the answer because of the value given above

Answer: Value of A is 5.

From the sample we conclude that:

the probability of an elk being infected is 0.14.

To find out how many of the total are infected we multiply the total by this probability, then:

Therefore, 1120 elks are likely to be infected.

Answer:

12.9

Step-by-step explanation:

tan⁡θ=opp/adj

tan 24° = x/29

x = 29 tan 24°

x = 12.9

Answer:

Not C, Not A, most likely B

Step-by-step explanation:

Its less than 90 because its and acute, meaning its smaller, so you can already knock off C.

The probabilities are:

a. P(A) = 0.35

b. P(B|A) ≈ 0.349

c. P(A ∩ B) ≈ 0.122

d. P(A^c ∩ B) ≈ 0.228

e. P(B) = 0.35

f. P(A|B) = 0.349

g. A and B are independent.

Yes, it is reasonable to treat A and B as though they were independent because P(A) * P(B) = P(A ∩ B).

We have,

Given:

Total number of components (n) = 1000

Number of defective components (d) = 350

a.

P(A) is the probability that the first component drawn is defective:

P(A) = d/n = 350/1000 = 0.35

b.

P(B|A) is the probability that the second component drawn is defective given that the first component drawn is defective:

Since one defective component has already been drawn, the total number of components is now 999, and the number of defective components remaining is 349.

P(B|A) = Number of defective components remaining / Total number of components remaining = 349/999 ≈ 0.349

c.

P(A ∩ B) is the probability that both the first and second components drawn are defective:

P(A ∩ B) = P(A) * P(B|A) = 0.35 * 0.349 ≈ 0.122

d.

P(\(A^c\) ∩ B) is the probability that the first component drawn is not defective (complement of A) and the second component drawn is defective:

\(P(A^c)\) is the probability that the first component drawn is not defective:

\(P(A^c)\) = 1 - P(A) = 1 - 0.35 = 0.65

Since the first component drawn is not defective, the total number of components remaining is now 999, and the number of defective components remaining is still 350.

P(\(A^c\) ∩ B) = P(\(A^c\)) * P(B) = 0.65 * (350/999) ≈ 0.228

e.

P(B) is the probability that the second component drawn is defective:

P(B) = Number of defective components / Total number of components

= 350/1000

= 0.35

f.

P(A|B) is the probability that the first component drawn is defective given that the second component drawn is defective:

P(A|B) = P(A ∩ B) / P(B)

= (0.35 * 0.349) / 0.35

= 0.349

g.

To determine if A and B are independent, we need to compare

P(A) * P(B) with P(A ∩ B).

P(A) * P(B) = 0.35 * 0.35 = 0.1225

P(A ∩ B) = 0.122

Since P(A) * P(B) = P(A ∩ B), A and B are independent events.

It is reasonable to treat A and B as independent because the probability of A and the probability of B are not affected by each other.

The occurrence or non-occurrence of A does not impact the probability of B.

Thus,

The probabilities are:

a. P(A) = 0.35

b. P(B|A) ≈ 0.349

c. P(A ∩ B) ≈ 0.122

d. P(A^c ∩ B) ≈ 0.228

e. P(B) = 0.35

f. P(A|B) = 0.349

g. A and B are independent.

Yes, it is reasonable to treat A and B as though they were independent because P(A) * P(B) = P(A ∩ B).

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Step-by-step explanation:

therefore, the correct option should be A.

Answer:

mean = 24

Step-by-step explanation:

the mean is calculated as

mean = \(\frac{sum}{count}\)

the sum of the data set is

sum = 12 + 13 + 15 + 28 + 28 + 30 + 42 = 168

there is a count of 7 in the data set , then

mean = \(\frac{168}{7}\) = 24

The matching expressions are:

\(i) 3a x 4 = C (12a)\\ii) a^2 x a = A (a^3)\\iii) 6 × 1/2 a^2 = D (3a^2)\)

i) 3a x 4 can be represented as C (12a) since multiplying 3a by 4 gives 12a.

ii) a^2 x a can be represented as A (a^3) since multiplying a^2 by a gives a^3.

iii) \(6 \times 1/2 a^2\) can be represented as D (3a^2) since multiplying 6 by 1/2 and then by a^2 gives 3a^2.

To understand the matching expressions, let's break down each one:

i) 3a x 4:

This expression represents multiplying a variable, 'a', by a constant, 4. The result is 12a, which matches with C (12a).

ii) a^2 x a:

This expression represents multiplying the square of a variable, 'a', by 'a' itself. This results in a^3, which matches with A (a^3).

iii) 6 × 1/2 a^2:

This expression involves multiplying a constant, 6, by a fraction, 1/2, and then multiplying it by the square of 'a', a^2. The final result is 3a^2, which matches with D (3a^2).

Therefore, the matching expressions are:

i) 3a x 4 = C (12a)

ii) a^2 x a = A (a^3)

iii) 6 × 1/2 a^2 = D (3a^2)

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Answer:

Deductive reasoning is a method of logical thought that begins with a general concept and arrives at a particular conclusion. It is often referred to as top-down thought or shifting from general to particular.

Step-by-step explanation:

Here are some examples:

deductive reasoning is a type of logical thinking that starts with the general idea and reaches a specific conclusion

Answer:

\(f(d)=\left\{ \begin{matrix} 11 & \text{for} & 0< d\leq 4 \\-3+3.5d & \text{for}& d > 4 \end\)

Step-by-step explanation:

Cost of first 4 kilometers ride = 11 pesos.

So, for the first 4 km, the fair is constant i.e.

for 1 km the fare is 11 pesos,

for 2 km the fair is also 11 pesos,

similarly, for 3 km of 4 km, the fare is 11 pesos.

Hence, for the distance \(0\geq d\geq 4\), the fair function,

\(f(d)=11\cdots(i)\)

After 4 km, there is an increment of $ 3.50 for each kilometer.

So, the fare function up to 5 kilometers,

\(f(d)=11+3.5=14.5\)

So, the fare function up to 6 kilometers, i.e for the distance \(5<d\leq6\),

\(f(d)=11+2\times3.5=18\)

This can be arranged as the fare function up to 6 km,

\(f(d)=11+(6-4)\times3.5=18\)

Similarly, the fare function up to \(d\) kilometer \((n>4)\),

\(f(d)=11+(d-4)\times3.5\)

\(\Rightarrrow f(d)=-3+3.5d\cdots(ii)\)

Hence, from equations (i) and (ii),

\(f(d)=\left\{ \begin{matrix} 11 & \text{for}\; 0< d \leq 4 \\-3+3.5d & \text{for}\; d > 4 \end\)

Answer:

  $142.32, profit on sale of the policy

Step-by-step explanation:

You want to know the expected value of a $280,000 life insurance policy sold for $270, if the probability the insured will live for the year is 0.999544.

The insurance company expects to have to pay the $280,000 death benefit for 0.000456 of the policies issued. That means their expected payout on any one policy is ...

  0.000456 × $280,000 = $127.68

The company gets a premium of $270 for the policy, so the expected value of the policy to the company is ...

  $270 -127.68 = $142.32

The expected value of the policy to the company is $142.32.

This represents its profit from sale of the policy.

__

Additional comment

Of course, the company has expenses related to the policy, perhaps including a commission to the agent selling it, and expenses related to handling claims. That is to say that not all of the difference between the premium and the average death benefit is actually profit. It is what might be called "contribution margin."

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Olivia would be able to get 11 toppings.

Steps:

8.00 / .75 = 10.6

Round~

11

You're welcome!!!

Answer:

Jack $1800 Blake $7400

Step-by-step explanation:

a) The parametric equations of the line are: x(t) = −2 + 3t, y(t) = 4 − 2t, z(t) = 3 + 4t and The symmetric equation of the line are: (x + 2)/3 = (y − 4)/−2 = (z − 3)/4

b) The line intersects yz-plane at (0, 8/3, 17/3)

The given points on the line are:

(x₁, y₁, z₁) = (−2, 4, 3)

(x₂, y₂, z₂) = (1, 2, 7)

The direction ratios of this line are:

⟨a, b, c⟩ = ⟨x₂ − x₁, y₂ − y₁, z₂ − z₁⟩

             = ⟨1 + 2, 2 − 4, 7 − 3⟩

             = ⟨3, −2, 4⟩

a) Parametric equations of the line:

These are given by:

x(t) = x₁ + at = −2 + 3t

y(t) = y₁ + bt = 4 − 2t

z(t) = z₁ + ct = 3 + 4t

Symmetric equation of the line:

This is given by:

              (x − x₁)/a = (y − y₁)/b = (z − z₁)/c

              (x + 2)/3 = (y − 4)/−2 = (z − 3)/4

b) When a line intersects the yz-plane, its x-coordinate is zero.

Using the parametric equations of the part (a):

                                   x = 0

                          −2 + 3t = 0

                                  3t = 2

                                    t = 2/3

Substitute this in the parametric equations corresponding to y and z as well:

                                   y = 4 −2t

                                      = 4 − 2(2/3)

                                      = 8/3

                                   z = 3 + 4t

                                      = 3 + 4(2/3)

                                      = 17/3

Hence, the required point is: (x, y, z) = (0, 8/3, 17/3)

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Answer:

143 should be correct

Step-by-step explanation:

hope this helps

Answer:

Step-by-step explanation:

250x^3-16

2(125x^3-8)

2[(5x)^3-(2)^3]

2(5x-3)[(5x)^2+5x*3+(2)^2]

2(5x-3)(25x^2+15x+4)

The measure of distance x, that is, the distance between a point P and the point of horizon, is equal to 284.372 miles.

In this problem we must determine the distance between a point P located about earth's circumference and the point of horizon, located on earth's circumference. Since the line between these two points is tangent to earth, then, distance x can be found by Pythagorean theorem:

x = √[(3959 mi + 10.2 mi)² - (3959 mi)²]

x = 284.372 mi

The distance x is equal to 284.372 miles.

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Answer:

(120^2+120^2)^0.5 = 169.705m

Step-by-step explanation:

Pythagorean Theorem

Problem 1

Reason: We start at 0 and move 4 units left. This is represented by 0+(-4) or 0-4. That simplifies to -4. Then add on 7 to move 7 units to the right to arrive at 3 as the final destination.

=============================================

Problem 2

Reason: We start at 0 and move 8 units to the right. That is represented by +8 or simply 8. Then the +3 will move us 3 more units to the right to get to 11 on the number line. This is one visual way to see why 8+3 = 11.

Answer:

\(-3 \le h \le 1\).

Step-by-step explanation:

Apply the property of absolute values: if \(a \ge 0\), then \(|x| \le a \iff -a \le x \le a\). By this property, \(|- 3\, h - 6 | \le 3\) is equivalent to \(-3 \le -3\, h - 6\le 3\). That's the same as saying that \(-3\, h - 6 \ge -3\) and \(-3\, h - 6 \le 3\).

Add \(6\) to both sides of both inequalities:

\(-3\, h \ge 3\) and \(-3\, h \le 9\).

Divide both sides of both inequalities by \((-3)\). Note that because \(-3 < 0\), dividing both sides of an equality by this number will flip the direction of the inequality sign.

Both inequalities are supposed to be true. Combining the two inequalities to obtain:

\(-3 \le h \le 1\).

Answer:

1, 33.3

2, 81.9

3, 240

4, the farmer sold 33.3 of his crops

5, 750 students are enrolled.

Answer:

1. 8 is 33.3333333% of 24. 2.  63% of 130 is 81.9. 3. 36 is 15% of 240. 4. 30.72% of crops. 5. 750 students

Step-by-step explanation:

Hope this helped you!! Give brainliest.

Answer:

82 degrees

Step-by-step explanation:

It took 3 hours for it to go from 78 to 72.

Which is a rate of -2 degrees per hour

We want to know what the temperature was two hours before it was 78 degrees so we'd do 78 - (-2) which is 82

Answer:

The volume of the box is maximized when x = 0.53 cm

Therefore,  x = 0.53 cm  and the Maximum volume = 1.75 cm³

Step-by-step explanation:

Please refer to the attached diagram:

The volume of the box is given by

\(V = Length \times Width \times Height \\\\\)

Let x denotes the length of the sides of the square as shown in the diagram.

The width of shaded region is given by

\(Width = 3 - 2x \\\\\)

The length of shaded region is given by

\(Length = \frac{1}{2} (5 - 3x) \\\\\)

So, the volume of the box becomes,

\(V = \frac{1}{2} (5 - 3x) \times (3 - 2x) \times x \\\\V = \frac{1}{2} (5 - 3x) \times (3x - 2x^2) \\\\V = \frac{1}{2} (15x -10x^2 -9 x^2 + 6 x^3) \\\\V = \frac{1}{2} (6x^3 -19x^2 + 15x) \\\\\)

Take the derivative of volume and set it to zero.

\(\frac{dV}{dx} = 0 \\\\\frac{dV}{dx} = \frac{d}{dx} ( \frac{1}{2} (6x^3 -19x^2 + 15x)) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\0 = \frac{1}{2} (18x^2 -38x + 15)\\\\18x^2 -38x + 15 = 0\\\\\)

We may solve the quadratic equation using the quadratic formula.

\($x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$\)

The values of coefficients a, b, c are

\(a = 18 \\\\b = -38 \\\\c = 15 \\\\\)

Substituting the values into quadratic formula yields,

\(x=\frac{-(-38)\pm\sqrt{(-38)^2-4(18)(15)}}{2(18)} \\\\x=\frac{38\pm\sqrt{(1444- 1080}}{36} \\\\x=\frac{38\pm\sqrt{(364}}{36} \\\\x=\frac{38\pm 19.078}{36} \\\\x=\frac{38 + 19.078}{36} \: or \: x=\frac{38 - 19.078}{36}\\\\x= 1.59 \: or \: x = 0.53 \\\\\)

Volume of box when x = 1.59:

\(V = \frac{1}{2} (5 - 3(1.59)) \times (3 - 2(1.59)) \times (1.59) \\\\V = -0.03 \: cm^3 \\\\\)

Volume of box when x = 0.53:

\(V = \frac{1}{2} (5 - 3(0.53)) \times (3 - 2(0.53)) \times (0.53) \\\\V = 1.75 \: cm^3\)

As you can see, the volume of the box is maximized when x = 0.53 cm

Therefore,  x = 0.53 cm  and the Maximum volume = 1.75 cm³