ΔABC with vertices A(-3, 0), B(-2, 3), C(-1, 1) is rotated 180° clockwise about the origin. It is then reflected across the line y = -x. What are the coordinates of the vertices of the image?

 4 +2 +4 = 10 blocks total

2 are blue so you have a 2/10 which reduces to  1/5 probability of picking blue

To calculate the probability of choosing a blue block from a bag, divide the number of blue blocks by the total number of blocks. In a bag with 4 red, 2 blue, and 4 green blocks, the probability is 2/10, which simplifies to a 20% chance of picking a blue block.

The question is about calculating the probability of selecting a blue block from a bag containing a mix of different colored blocks. When finding the probability of an event, the formula to use is the number of ways the event can happen divided by the total number of outcomes. In the case of the blue block, if a bag has 4 red, 2 blue, and 4 green blocks, there are

To calculate the probability of choosing a blue block, you divide the number of blue blocks by the total number of blocks:

Probability(Blue) = Number of Blue Blocks / Total Number of Blocks
Probability(Blue) = 2 / 10
Probability(Blue) = 0.2 or 20%

The final result is that there is a 20% chance of picking a blue block from the bag.

Final answer:

The least common multiple (LCM) of 3, 4a, 5b, and 6ab is 60ab, calculated by prime factorizing each term and identifying the highest power of each prime factor.

Explanation:

The least common multiple (LCM) of 3, 4a, 5b, and 6ab is calculated by finding the LCM of the individual components.

Prime factorize each term: 3 = 3, 4a = 2*2*a, 5b = 5*b, 6ab = 2*3*a*b.

Identify the highest power of each prime factor: LCM = 2*2*3*5*a*b = 60ab.

Answer:

D. (3.5, 3)

Step-by-step explanation:

Just something simple

F= kx

 so to get k divide both sides by x

 so k = F/x

Quadrilateral DEFG is not a rhombus because the four sides do not all have the same length.

The coordinates of the vertices of quadrilateral DEFG are D(-2, 5), E(2, 4), F(0, 0), and G(-4, 1). To determine if DEFG is a rhombus, we need to observe the properties of a rhombus. A rhombus has opposite sides that are parallel and all four sides have the same length. Using the distance formula, we calculate the lengths of the four sides of DEFG:

As we can see, the lengths of DEFG's sides are not all the same. Therefore, DEFG is not a rhombus.

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Hence, the product is:

[tex]\dfrac{z(z+2)}{z+3}[/tex] such that: z≠ -1,0 and -3.

We are asked to represent the product in the simplest form along with the restrictions applied to z.

We have to evaluate the expression:

[tex]\dfrac{z^2}{z+1}\times \dfrac{z^2+3z+2}{z^2+3z}\\\\=\dfrac{z^2}{z+1}\times \dfrac{z^2+3z+2}{z(z+3)}[/tex]

Hence,

z≠ -1,0 and -3.

Since, otherwise the denominator will be equal to zero and hence the product will not be defined.

Now, we know that:

[tex]z^2+3z+2=z^2+2z+z+2\\\\z^2+3z+2=z(z+2)+1(z+2)\\\\z^2+3z+2=(z+1)(z+2)[/tex]

Hence,

[tex]\dfrac{z^2}{z+1}\times \dfrac{z^2+3z+2}{z^2+3z}=\dfrac{z^2}{z+1}\times \dfrac{(z+1)(z+2)}{z(z+3)}\\\\=\dfrac{z(z+2)}{z+3}[/tex]

( since z and (z+1) term is cancelled as it was same in numerator and denominator)

Hence, the product is:

[tex]\dfrac{z(z+2)}{z+3}[/tex] such that: z≠ -1,0 and -3.

To find the height of the lighthouse, set up a proportion using the lengths of the shadows and solve for h. The height of the lighthouse is 12 meters.

To find the height of the lighthouse, we can set up a proportion based on the lengths of the shadows. Let h be the height of the lighthouse. The proportion is:

(h / 36) = (1.5 / 4.5)

Now, we can cross multiply and solve for h:

h = (1.5 / 4.5) * 36

h = 12 meters

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The smallest positive integer with exactly 14 positive divisors is 24. The number is found by considering its prime factorization and adding 1 to each exponent, then multiplying the results together. Another prime factor raised to the power of 5 can be included to have exactly 14 divisors.

The smallest positive integer with exactly 14 positive divisors is 24.

To find this, we need to consider the prime factorization of the number. Let's express 24 as a product of prime factors: 24 = 2^3 * 3^1.

The number of divisors is found by adding 1 to each exponent in the prime factorization and multiplying them together: (3+1)(1+1) = 4 * 2 = 8. However, we need exactly 14 divisors, so we can multiply 24 by another prime factor raised to the power of 5: 24 * 5^4 = 24 * 625 = 15,000.

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The smallest positive integer with exactly 14 positive divisors is 192. We derived this by using the prime factorization method and finding suitable combinations to get exactly 14 divisors.

To find the smallest positive integer with exactly 14 positive divisors, we need to understand the number of divisors formula. For an integer n = p1e* p2e² * ... * p^ke^k, the number of divisors is given by (e1 + 1)(e² + 1) ... (e^k + 1).

To have exactly 14 divisors, we need (e1 + 1)(e² + 1) ... (e^k + 1) = 14. The factorizations of 14 are 14 = 14 * 1, 7 * 2, or 2 * 7. Let's use the smallest primes to minimize our number:

14 = 14 * 1: This means n = p113. Using the smallest prime number, we have n = 213 = 8192, which is too large.

14 = 7 * 2: This means n = p16 * p21. Using the smallest primes, we get n = 26 * 3 = 64 * 3 = 192.

14 = 2 * 7: This means n = p11 * p26. Using the smallest primes, we get n = 2 * 36 = 2 * 729 = 1458.

Comparing these solutions, the smallest positive integer is n = 192, which has exactly 14 positive divisors.

Answer:

The data set for two weeks that shows the number of cars parked in the restaurant parking lot during the lunch hour each day is given as:

8   7   14   10   13   27   11    10   14   7   12    9   14   9

The statements that hold true according to the data is:

Based on the data set, the true statement is: C. There is one outlier that indicates an unusually large number of cars were in the parking lot that day.

An outlier can be defined as a data value that is either unusually small or large when compared to the overall pattern of the numerical values in a data set.

This ultimately implies that, an outlier lies outside most of the other values in a particular data set, and as such makes them different from the other numerical values.

In this scenario, there is only one outlier in this data set, which is 27 and it simply indicates an unusually large number of cars were in the parking lot that day.

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The actual height of the building is 54 meters.

The actual height of the building is calculated by multiplying the scale drawing height by the scale factor.

Given that the scale is 1:600, this means that 1 centimeter on the drawing represents 600 centimeters in reality.

Therefore, to find the actual height of the building, one would multiply the height of the building on the scale drawing (9 cm) by the scale factor (600).

Using the scale, the actual height H of the building can be determined as follows:

[tex]\[ H = \text{scale drawing height} \times \text{scale factor} \] \[ H = 9 \, \text{cm} \times 600 \] \[ H = 5400 \, \text{cm} \][/tex]

To convert centimeters to meters, since there are 100 centimeters in a meter, we divide by 100:

[tex]\[ H = \frac{5400 \, \text{cm}}{100} \] \[ H = 54 \, \text{m} \][/tex]

Thus, the actual height of the building is 54 meters.

Answer:

135m²

Step-by-step explanation:

Perimeter = 2(l + w)

l = w + 6

Substituting for l, gives;

2(w+6+w)

48 = 2w + 12 +2w

48 = 4w + 12

48 - 12 = 4w

36 = 4w

w = 9

Since w = 9, then l = w +6

l = 9 + 6

l = 15

Area = l * w

Area = 15 * 9

Area = 135m²

Let's analyse both scenarios: for the first pick, you have 5 cards in total, of which 2 are red. So, you have a chance of 2/5 of picking a red card.

Now, assume you picked a red card with the first pick. The new scenario will be different, now there are only 4 cards in total (since you didn't replace the first picked card), of which only 1 is red. This means that you have a chanche of 1/4 of picking a red card.

Once you figured the probabilities of both events, if you want to compute the probability of the two events happening one after the other, you simply have to multiply them, so you have

[tex] \cfrac{2}{5} \cdot \cfrac{1}{4} = \cfrac{2}{20} = \cfrac{1}{10} [/tex]

Answer:

1/10 is the answer.

Step-by-step explanation:

To find the measures of complementary angles A and B with a known difference of 20 degrees, we set up a system of equations and solved them to find that angle A measures 55 degrees and angle B measures 35 degrees.

The problem involves finding the measures of two complementary angles, angle A and angle B, with a known difference in their measures. By definition, complementary angles are two angles whose sum is 90 degrees. Given the difference of 20 degrees between the angles, we can set up a system of equations to solve for their measures.

Let's denote the measure of angle A as a and angle B as b. Therefore, we have the two equations based on the problem statement:

a + b = 90 (because they are complementary)

a - b = 20 (the difference in their measures)

To find the values of a and b, we can add the two equations:

a + b = 90
a - b = 20

By adding them together, we get:

2a = 110

Dividing both sides by 2, we find a:

a = 55

To find b, we substitute a back into one of the original equations:

55 + b = 90

Subtracting 55 from both sides gives us b:

b = 35

Therefore, angle A measures 55 degrees and angle B measures 35 degrees.

The Simplest form of the expression 1/4+4(1/2−3/4)^2  is 1/2

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.

Using PEMDAS

1/4+4(1/2−3/4)^2

Subtract inside parenthesis

(1/2−3/4) = -1/4

Now, Square                        

1/4+4(-1/4)^2

1/4+4(1/16)

Then Multiply 4 and (1/16)

1/4+(1/4)

Now Adding;

2/4 = 1/2

Hence, The Simplest form of the expression 1/4+4(1/2−3/4)^2  is 1/2

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The correct answers are actually : 2x+2 these are correct bc i just took the test.

Hope this helps.

The graph of f(x) after transforming into the graph of g(x) by a vertical compression of 1/3 and a translation of 2 units up is g(x) = 2x + 2.

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

The graph of f(x) = 6x

Vertical compression = 1/3.

Translation = 2 units up.

If there is a vertical compression of 1/3 on the graph f(x).

The graph of f(x) = 6x transformed as g(x) = 1/3 x 6x = 2x

Now,

If the graph g(x) 2x has a translation of 2 units up we get,

g(x) = 2x + 2

g(x) = 2(x + 1)

Thus,

The graph of f(x) after transforming into the graph of g(x) by a vertical compression of 1/3 and a translation of 2 units up is g(x) = 2x + 2.

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Answer:

The weight of baby at the end of 8 month is 18.125 lb.

Step-by-step explanation:

Given information:

The weight of baby at birth = 7.25 lb

At the end of 8 months, the baby weighed [tex]2\frac{1}{2}[/tex] times its birth weight.

We need to find the weight of baby at the end of 8 month.

[tex]2\frac{1}{2}=\frac{4+1}{2}=\frac{5}{2}[/tex]

The weight of baby at the end of 8 month is 5/2 times of its initial weight.

[tex]\text{Total weight}=7.25\times \frac{5}{2}[/tex]

[tex]\text{Total weight}=18.125[/tex]

Therefore the weight of baby at the end of 8 month is 18.125 lb.

Answer:

C) 8

Step-by-step explanation:

Let's solve for:

[tex]a^2 -64=0\\\\a>0[/tex]

Add 64 to both sides:

[tex]a^2-64+64=0+64\\\\a^2=64[/tex]

Take the square root of both sides

[tex]\sqrt{a^2} = \sqrt{64} \\\\a=\pm 8[/tex]

Therefore, we got two solutions:

[tex]a=8\\\\or\\\\a=-8[/tex]

However, since:

[tex]a>0[/tex]

The only solution is:

[tex]a=8[/tex]

We are given the formula for volume V:

V = 3.14 r^2 h

where r is radius and h is height

The standard height and radius is both 20 cm each, therefore we can write it as:

V = 3.14 (20)^2 (20)

It is stated that the radius can be modified, for every 1 cm change in tanks radius, the height must increase by 5 cm, therefore:

V = 3.14 (20 – x)^2 (20 + 5x)

or in general form:

V = 3.14 (r – x)^2 (h + 5x)