Triangle A has a height of 2.5 cm and a base of 1.6 cm. The height and base of triangle B are proportional to the height and base of triangle A. Which of the following could be the height and base of triangle B?​

Using the LCM,  the first customer to receive both a shopping bag and a 25% off coupon is the 45th customer.

To find the first customer who will receive both a free shopping bag and a 25% off coupon, we need to find the least common multiple (LCM) of 15 and 9, since the shopping bags are given every 15th customer and the coupons every 9th customer.

Step 1: Find the prime factors of both numbers.
15 = \(3 * 5\)
9 = \(3^2\)

Step 2: Identify the highest power of each prime factor in both numbers.
3: \(3^2\) (from 9)
5: \(5^1\) (from 15)

Step 3: Multiply the highest powers of each prime factor together to find the LCM.
LCM(15, 9) =\(3^2 * 5^1\) = \(9 * 5\) = 45

So, the first customer who will receive both a free shopping bag and a 25% off coupon is the 45th customer.

Know more about LCM here:

https://brainly.com/question/233244

#SPJ11

It is proved that Cos A = (3+5cosB)/(5+3cosB).

Here it is provided that

tan A/2 = 1/2tan B/2

As we know, trigonometric ratios can be converted into one another,

One such standard conversion is

tanA = √(1-cosA)/√(1+cosA)

Using the above conversion we can write,

\(\sqrt{\frac{1 - cos A}{1 + cos A} } = \frac{1}{2} \sqrt{\frac{1 - cos B}{1 + cos B} }\\\\ (\frac{1 - cos A}{1 + cos A}) = \frac{1}{4} (\frac{1 - cos B}{1 + cos B})\)

4(1-cosA)(1+cosB) = (1-cosB)(1+cosA)

4(1+cosB-cosA-cosAcosB) = (1+cosA -cosB-cosAcosB)

4 + 4cosB - 4cosA - 4cosAcosB = 1 + cosA - cosB - cosAcosB

3 + 5cosB = 3cosAcosB + 5cosA

3 + 5cosB = cosA(3cosB - 5)

cos A = (3+5cosB)/(5+3cosB)

Hence, it is proved that

\(cosA = \frac{3+5cosB}{5+3cosB}\)

To know more about Trigonometric ratios, visit,

https://brainly.com/question/23130410

#SPJ9

An expression is defined as a set of numbers, variables, and mathematical operations. The value of x that will satisfy the given statement "the sum of a number x and 7 is 35" is 28.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Given the statement that the sum of a number x and 7 is 35. Therefore, the given statement "the sum of a number x and 7 is 35" in the form of an expression can be written as,

x + 7 = 35

Subtract 7 from both the sides of the equation,

x +7 - 7 = 35 - 7

x = 28

Hence, the value of x that will satisfy the given statement "the sum of a number x and 7 is 35" is 28.

Learn more about Expression:

https://brainly.com/question/13947055

#SPJ5

Answer: D. < CBA

Step-by-step explanation:

its letter b. 120 degrees

Answer:

B is bigger

Step-by-step explanation:

a) 3^2 / 2^3

3*3 / 2*2*2

9/8

b) 9^4 / 4^6

9*9*9*9/4*4*4*4*4

6561 / 4096

1.601807

important to know the size of the freshman classes in relation to the population size before using z-procedures in this situation, so the answer will be option C

In statistical inference, when using z-procedures such as hypothesis testing or constructing confidence intervals, one of the assumptions is that the samples are independent. In this scenario, knowing that the university had 6000 or more entering freshmen is important to ensure that the sample size is less than 10% of the population size.

The 10% condition is necessary to maintain the independence of samples. When the sample size is small relative to the population size, each sample observation has a greater impact on the population proportion, potentially violating the assumption of independence.

By ensuring that the sample size is less than 10% of the population size, we can reasonably assume that each sample observation is independent of each other. This allows us to use z-procedures and rely on the properties of the normal distribution for inference.

Learn more about statistical inference here:

https://brainly.com/question/31446570

#SPJ11

Answer:

Im pretty sure the answer that is on the picture is right (25.87)

Step-by-step explanation:

Answer:

20 month

Step-by-step explanation:

The unknown here is the number of month required for plans A and B to be the same.
Let x be that month.

for both plans to be equal

19.25x + 200 = 26.75x + 50

19.25x-26.75x = 50-200

-7.5x = -150

x = 20

Answer:

approximately 4.23 cm

Answer:

27y^12

Step-by-step explanation:

you multiply the exponents together

in this case: 4×3=12

and then multiply the base number by 3 as well.

Answer: 529.3 downloads

Explanation:

Standard version size = 2.1 MB

High quality version = 4.7 MB

The high-quality version was downloaded twice as often as the standard version

H = 2 S

The total size downloaded for the two versions = 3335 MB

H + S = 3335

We have the system:

H = 2 S (a)

H + S = 3335 (b)

Put A into B

(2S ) + S = 3335

3S = 3335

S= 3335/3

S= 1,111.67 MB

Divide the total MB of standard versions by the size of each standard version.

1,111.67 / 2.1 = 529.3 downloads

Answer:

a

2

−

b

2

=

(

a

+

b

)

(

a

−

b

)

where

a

=

2

and

b

=

x

.

2

(

2

+

x

)

(

2

−

x

)

Step-by-step explanation:

Answer:

12-13 weeks

Step-by-step explanation:

1 week of work is $85

$1400 - $340 = $1060

$1060 / $85 = 12.47

round it up and its 13 (or not then its 12)

normally you would round down, but i think it would make more sense to round up in this situation

To rewrite the linear system as a matrix equation, we can let y = [y1, y2, y3] and A be the coefficient matrix:

y' = Ay
where
A = [1 1 2; 1 0 1; 2 1 3]

To compute the eigenvalues of A, we can use the formula:
det(A - λI) = 0
where det represents the determinant and I is the identity matrix.

So, we have:
|1-λ 1 2|     |1 1-λ 2|     |1 1 1-λ|
|1 0-λ 1|  =  |1 0 1|  =  |1-λ 0 1|
|2 1 3-λ|     |2 1 3|     |2 1 3-λ|

Expanding the determinants, we get:
(1-λ)[(0-λ)(3-λ)-1]-1[(1)(3-λ)-2(1)]+2[(1)(1)-2(1-λ)]
= (λ-3)(λ-1)(λ-2) = 0

Therefore, the eigenvalues of A are 3, 1, and 2.

Refer for more,

https://brainly.com/question/13987127#

#SPJ11

The capacity of fish tank in quarts is 246.

Therefore the answer is 246.

A pint is a unit of volume in the US customary system of measurement and is equal to 16 fluid ounces. A quart is also a unit of volume in the US customary system of measurement and is equal to 32 fluid ounces or 2 pints.

There are 2 pints in 1 quart, so to convert from pints to quarts, we need to divide by 2.

The capacity of the fish tank in pints is 492.

Therefore, the capacity of the fish tank in quarts is

= 492 pints / 2 pints per quart

= 246 quarts

So, the capacity of the tank in quarts is 246 quarts.

To know more on pints quarts conversion

https://brainly.com/question/17732315

#SPJ4

Answer:

A

Step-by-step explanation:

The value of Mean is 137.2 and the value of Median is 206.5 .

The result of dividing the sum of a set of values by the total number of values in the set is the mean. When a set of numbers is sorted from smallest to greatest, the median is the middle number in the group. The value in a set of values that is repeated the most often is the set's mode.

The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.

Given ,

Mean = 127+136+150+119+150+141 divide by six 6

= 823/6 = approx. 137.2

Median = for the median, you will arrange the numbers in other. from smaller to the bigger number.

119,127,136,141,150, 150. so 136 & 141 is the middle number.

so you will add the middle number and divide by 2.

that is 136+141/2 = 206.5

Therefore  the value of Mean is 137.2 and the value of Median is 206.5.

To learn more about mean and median refer to:

https://brainly.com/question/14532771

#SPJ4

Answer:

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

the order of letter should resemble the same shape

Answer:

3. Parallel lines have the same slope but different y-intercepts, so they never intercept each other.

Step-by-step explanation:

A kind of evolution through artificial selection is the practice of choosing creatures with desired features over several generations.

The mix of alleles found in an organism is known as its genotype. A phenotype is also the culmination of all the organism's discernible traits. In artificial selection, people choose animals or plants with favored phenotypic features for reproduction.

Since the phenotype is impacted by the genotype, the process of artificial selection alters allele frequencies throughout generations, resulting in the evolution of desirable features in offspring.

In conclusion, a kind of evolution through artificial selection is the practice of selecting creatures with desired qualities over several generations.

To learn more about artificial selection

https://brainly.com/question/14480958

#SPJ4

Answer:

Step-by-step explanation:

Solving systems of equations gives the points of intersection when the equations are graphed.

The answer is 3.

Answer:

  11.4

Step-by-step explanation:

You want the distance between C(-5, 5) and D(4, -2).

The distance formula is ...

  d = √((x2 -x1)² +(y2 -y1)²)

For the given points, the distance is computed to be ...

  d = √((4 -(-5))² +(-2 -5)²) = √(81 +49) = √130

  d ≈ 11.4

The length of CD is about 11.4 units.

__

Additional comment

The distance formula is an application of the Pythagorean theorem. It computes the hypotenuse of a right triangle whose legs are the differences in x- and y-coordinates.

Answer:

x=0

Step by step explanation:

cos (a+b) = cos(a) cos(b) -sin (a) sin (b)

Same identity forms in question.

L.H.S -cos (x+60)

Now write it in the form of sin .

sin [90-(60+x)]

Equal to RHS

R.H.S - 30

90-(60+x)=30

30-x=30

x=0

#SPJ1

The answer to the equation cos195°cos285° is -1/4.

An equation is a mathematical statement that asserts the equality of two expressions. Equations are used to describe relationships between different quantities and can be used to solve for unknown values. Equations are typically written as symbols, but can also be written in words. Simple equations might involve addition, subtraction, multiplication, and division, while more complex equations may involve exponents, logarithms, and trigonometric functions. Equations can be used to model and understand real-world phenomena, such as calculating projectile motion, or predicting the behavior of a chemical reaction.

This is derived from the trigonometric identity cos{60°−x}cosx – sin(60°−x)sinx. This identity states that the cosine of the sum of two angles is equal to the product of the cosines of each angle minus the product of the sines of each angle.

By substituting the angles 195° and 285° into the identity, we get cos{60°−195°}cos195° – sin(60°−195°)sinx. When we use the values of the angles, we get cos{-135°}cos195° – sin(135°)sinx. We can then simplify this to -1/4cos195° – 0sinx. As the sine of the angle is 0, this simplifies to –1/4cos195°. As the cosine of 195° is -1/4, the answer to the equation cos195°cos285° is -1/4.

To know more about equation click-

https://brainly.com/question/2972832

#SPJ1

Answer:

3 OR 8  hope this helps!

Step-by-step explanation:

The probability of drawing a red 7 and black face card is P ( A ) = 1/221

Given data ,

Let the probability of drawing a red 7 and black face card be P ( A )

Now , the compound probability is given by\

The number of red 7 cards = ( red of diamonds 7 + red of hearts 7 )

Probability of drawing a red 7 = 2/52

Now , the card is not replaced , so the total number of remaining cards = 51

And , number of black face cards = 6

Probability of drawing a black face card = 6/51

So , P ( A ) = 2/52 ( 6/51 )

P ( A ) = 12 / 2652

On simplifying , we get

P ( A ) = 1/221

Hence , the probability is P ( A ) = 1/221

To learn more about probability click :

https://brainly.com/question/17089724

#SPJ1

Answer:

5 sqrt(3) =x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp / adj

tan 30 = x/15

15 tan 30 = x

15 ( sqrt(3)/3) = x

5 sqrt(3) =x

Answer:

Step-by-step explanation:

base = X

hypotenuse = √5

cos 45° = base / hypotenuse

1/√2 = X / √5

X = √5 / √2

X = 1.58

Answer:

Part A: \(\frac{3}{5}\)

Part B: \(\frac{1}{2}\)

Step-by-step explanation:

We know that Alinn flipped a coin 20 times, and that 12 of those times resulted in heads. The other 8 times resulted in tails.

Part A wants us to find the experimental probability of the coin landing on heads. Experimental probability is the probability determined based on the experiments performed.

Part B wants us to find the theoretical probability of the coin landing on heads. Theoretical probability is determined based on the number of favorable outcomes over the number of possible outcomes.

Experimental probability is determined as # of times something occurred experimentally / total number of times.  

Since 12 of the 20 times that Alinn flipped the coin resulted in heads, this means that the experimental probability of Alinn flipping heads is \(\frac{12}{20}\), which simplifies down to \(\frac{3}{5}\).

Theoretical probability, as stated above, is the number of favorable outcomes / possible outcomes.

Our favorable outcome is flipping heads, and on a coin, there are two sides that a coin can land on: heads and tails. This means that there are two possible outcomes, and only one of them is favorable.

This means that our theoretical probability is \(\frac{1}{2}\).