One of two complementary angles is 8 degrees less than the other.
Which of the following systems of equations represents the word problem?

x + y = 90 and x - y = 8
x + y = 90 and 90 - x = 8
x + y = 90 and y = 8x

48.5 out of 50 as a percentage, is 97%.

48.5 out of 50 as a percentage can be calculated by dividing 48.5 by 50 and then multiplying by 100 to get the percentage.

Divide 48.5 by 50: 48.5 / 50 = 0.97

Multiply by 100 to get the percentage: 0.97 * 100 = 97%

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.

Answer:

the answer is actually D

Step-by-step explanation:

got it on edg

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.

If a rectangle is rotated about the line b, then the three-dimensional figure formed is cylinder with a circle base.

One side of the rectangle has lenght of 24 cm. Let the second side has length of x cm. The perimeter of the rectangle is 76 cm, then

24 + x + 24 + x = 76,

2x + 48 = 76,

2x= 76 - 48,

2x= 28,

x = 14 cm.

Then  the three-dimensional figure is a cylinder with a base radius of 14 cm.

Answer: correct choice is D

Answer: •a cylinder with a base radius of 14cm

Step-by-step explanation:

From the given picture it can be seen that the side of rectangle is adjacent to line B is the longer side.

If the rectangle is rotated about line b, then it will create a cylinder such that

the radius of the cylinder= smaller(width) side of the rectangle

The measure of the longer side (length) of rectangle= 24 cm

Perimeter of rectangle=[tex]2[length+width][/tex]

[tex]\\\Rightarrow\ 76=2[24+w]\\\Rightarrow\ 24+w=38\\\Rightarrow\ w=14[/tex]

hence, the measure of smaller side is 14 cm.

Therefore, the base radius =14 cm

((1+0.1994/12)^12)-1 = 21.87% effective rate

it would advertise the APR because it is lower

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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F= kx

 so to get k divide both sides by x

 so k = F/x

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:

 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.

Answer:

They were nomadic and moved from place to place.

Step-by-step explanation:

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.

The solution to the equation 2(x - 4) + 7 = 3 is x = 2, after simplifying and solving for x.

The student has asked which value of x is the solution of the equation 2(x - 4) + 7 = 3. To find the solution, we first simplify and solve for x:

Therefore, the correct solution for x is 2.

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)

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

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.

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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