Joe has 4 less than 7 times as many shirts as Mark. Together, Joe and Mark have 140 shirts. How many shirts does Joe have? How many shirts docs Mark have?​

Answer:

-1/2

Step-by-step explanation:

Step-by-step explanation:

3a²-7a−6

Factor the expression by grouping. First, the expression needs to be rewritten as 3a

2

+pa+qa−6. To find p and q, set up a system to be solved.

p+q=−7

pq=3(−6)=−18

Since pq is negative, p and q have the opposite signs. Since p+q is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product −18.

1,−18

2,−9

3,−6

Calculate the sum for each pair.

1−18=−17

2−9=−7

3−6=−3

The solution is the pair that gives sum −7.

p=−9

q=2

Rewrite 3a

2−7a−6 as (3a

2−9a)+(2a−6).

(3a 2−9a)+(2a−6)

Factor out 3a in the first and 2 in the second group.

3a(a−3)+2(a−3)

Factor out common term a−3 by using distributive property.

(a−3)(3a+2)

Answer:

\(\purple{ \boxed{ \bold{ { \bigg(9a - \frac{21}{2} \bigg)}^{2} - \bigg(\frac{33}{2} \bigg)^{2} }}}\)

Step-by-step explanation:

\(3a^2- 7a- 6 \\ \\ \implies \: take \: 3 \: as \: common \\ = 3 \bigg \{ {a}^{2} - \frac{7}{3} a - 2 \bigg \} \\ \\ = 3 \bigg \{{a}^{2} - 2 \times \frac{7}{6} a + \bigg( \frac{7}{6} \bigg)^{2} - \bigg( \frac{7}{6} \bigg)^{2} - 2 \bigg \} \\ \\ = 3 \bigg \{ { \bigg(a - \frac{7}{6} \bigg)}^{2} - \frac{49}{36} - 2 \bigg \} \\ \\ = 3 \bigg \{ { \bigg(a - \frac{7}{6} \bigg)}^{2} - \bigg(\frac{49 + 72}{36} \bigg) \bigg \} \\ \\ = 3 \bigg \{ { \bigg(a - \frac{7}{6} \bigg)}^{2} - \bigg(\frac{121}{36} \bigg) \bigg \} \\ \\ = 3 \bigg \{ { \bigg(a - \frac{7}{6} \bigg)}^{2} - \bigg(\frac{11}{6} \bigg)^{2} \bigg \} \\ \\ = { \boxed{ \bold{3 { \bigg(a - \frac{7}{6} \bigg)}^{2} - 3\bigg(\frac{11}{6} \bigg)^{2} }}} \\ \\ = { \boxed{ \bold{ { \bigg(9a - \frac{9\times 7}{6} \bigg)}^{2} - \bigg(\frac{9\times 11}{6} \bigg)^{2} }}}\\ \\ = \purple{ \boxed{ \bold{ { \bigg(9a - \frac{21}{2} \bigg)}^{2} - \bigg(\frac{33}{2} \bigg)^{2} }}}\)

Answer:

> there you go

Step-by-step explanation:

Answer:

>

Step-by-step explanation:

The distributions of the numbers X and Y of resulting heads and tails [(pλ)^k / k! e^(-pλ)] [(1-p)^λ / (1-p+ p/k+1)]  and [(pλ)^m / m! e^(-pλ)] [(1-p)^λ / (1-p+ p/m+1)]. Here,  X and Y are independent.

Let X be the number of heads and Y be the number of tails. Then we have:

X + Y = N

We want to find the distributions of X and Y. Let's start with X:

P(X = k) = P(X = k | N = n)P(N = n)

where P(X = k | N = n) is the probability of getting k heads given that the number of flips is n. This is simply a binomial distribution with parameters n and p:

P(X = k | N = n) = (n choose k) p^k (1-p)^(n-k)

where (n choose k) is the binomial coefficient.

The probability of N being equal to n is given by the Poisson distribution:

P(N = n) = e^(-λ) λ^n / n!

Therefore, we have:

P(X = k) = ∑ P(X = k | N = n)P(N = n)

   = ∑ (n choose k) p^k (1-p)^(n-k) e^(-λ) λ^n / n!

   = e^(-λ) / k! ∑ (n choose k) p^k (1-p)^(n-k) λ^n

   = e^(-λ) / k! (pλ + (1-p)λ)^k ∑ ((pλ + (1-p)λ)/λ)^n / (k+1)^n

   = e^(-λ) / k! (pλ + (1-p)λ)^k e^(pλ+(1-p)λ) / (k+1)

   = [(pλ)^k / k! e^(-pλ)] [(1-p)^λ / (1-p+ p/k+1)]

The first factor in the last expression is the Poisson distribution with parameter pλ, which means that X has a Poisson distribution with parameter pλ.

Similarly,  Y has a Poisson distribution with parameter (1-p)λ is  [(pλ)^m / m! e^(-pλ)] [(1-p)^λ / (1-p+ p/m+1)]

Now we need to show that X and Y are independent. To do this, we need to show that for any values k and m:

P(X = k and Y = m) = P(X = k) P(Y = m)

Using the expressions we found earlier for P(X = k) and P(Y = m), we have:

P(X = k and Y = m) = e^(-λ) / k! [(pλ)^k e^(-pλ)] [(1-p)^m λ^m e^(-(1-p)λ)]

P(X = k) P(Y = m) = e^(-λ) / k! [(pλ)^k e^(-pλ)] [(1-p)^λ / (1-p+ p/m+1)] e^(-λ) / m! [(1-pλ)^m e^(pλ)]

Notice that the two expressions are the product of two factors, one depending on k only, and the other depending on m only. Therefore, the joint distribution of X and Y factorizes into the product of their marginal distributions, which means that X and Y are independent.

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The total mass of a 2m rod whose linear density function is f(x)=1+0.5sin(x)kg/m for 0≤x≤2 is is 1.5 + 0.5cos(2) kg.

To find the total mass of the 2m rod with the given linear density function f(x) = 1 + 0.5sin(x) kg/m for 0 ≤ x ≤ 2, we need to integrate the linear density function over the given interval:

m = ∫f(x)dx from 0 to 2
m = ∫(1 + 0.5sin(x))dx from 0 to 2
m = [x + 0.5cos(x)] from 0 to 2
m = [2 + 0.5cos(2)] - [0 + 0.5cos(0)]
m = 2 + 0.5cos(2) - 0.5
m = 1.5 + 0.5cos(2) kg

Therefore, the total mass of the 2m rod with the given linear density function is 1.5 + 0.5cos(2) kg.

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Answer: x = -3

Explanation did the test

Answer:

its 8

Step-by-step explanation:

<3

Answer:

5/8

Step-by-step explanation:

15/3=5 and 24/3=8

Answer:

5/8

Step-by-step explanation:

divide both by 3

The area of the part with tulips is 23 m²

Since the garden is rectangular, we will use the formula for the area of a rectangle.

The area of a rectangle is given by:

A = L * W

where L and W are length and width of the rectangle

The area of the part with tulips can be determined by subtracting the area of the two roses parts from the area of the whole garden. That is:

area of the part with tulips = (7 * 5) - (3 * 2) - (3 * 2)

area of the part with tulips = 35 - 6 - 6

area of the part with tulips = 23 m²

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Complete Question

Check attached image

the number that can exactly 19 is 38

Answer:

18.5 about

Step-by-step explanation:

2\(\pi\)r

2\(\pi\)3

= about 18.5

Answer:

circumference=2πr

2× 22/7×3=18.85

Answer:

z = -1

Step-by-step explanation:

Answer: See explanation

Step-by-step explanation:

a. Let the money in m savings account be represented by x.

If I doubled the money in my savings account, I would have $150.62. This means that:

(2 × x) = $150.62

2x = $150.62

Divide both side by x

2x/2 = $150.62/2

x = $75.31

The amount in the savings account is $75.31

b. Let the hourly wage be represented by x.

Three times the hourly wage plus $7.65 in tips equals $27.90. This will be:

(3 × x) + 7.65 = 27.90

3x + 7.65 = 27.90

3x = 27.90 - 7.65

3x = 20.25

x = 20.25/3

x = 6.75

The hourly wage is $6.75

Your answer will be 9.

I hope this helped, have a wonderful day! Bye.

Answer:

surface area y is equal to 7cm.

Charlie

Here, we want to check if polynomials is closed under subtraction or not

To check this, we proceed either ways, if the answer is same, then it is closed. If otherwise, then it is not

We have;

As we can see, both results are not equal

If subtraction was closed under polynomials, then the results of both should have been equal. This means Charlie is correct.

Solution

The rule of the diamond problem is given below

I will label the question as follow

Basically, we need to find a and a + b

From the above info

The diamond problem solution is

Answer:

95°

Step-by-step explanation:

Here we have angles of 30° and 55°, so the remaining angle is:

Answer:

angleLMK and angleQPR

Answer:

-1/4 is the slope.

Step-by-step explanation:

To find the slope of the given points, we can use the formula:

y2-y1/x2-x1

So, in this case, subtract 5 and 7, and subtract 9 and 1.

5-7=-2

9-1=8

-2/8

Now, simplify.

-1/4 is the slope.

factor the right side of the formula A = 2πrx² + 2πrh, we can factor out 2πr from both terms:A = 2πr(x² + h)

What is cylinder?

A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases of the same size and shape, and a curved lateral surface connecting the bases.

To factor the right side of the formula A = 2πrx² + 2πrh, we can use the distributive property of multiplication. We can factor out the common factor of 2πr from both terms in the expression, leaving us with 2πr times the sum of x² and h. This gives us the factored form A = 2πr(x² + h). This expression represents the surface area of a cylinder in terms of its radius (r) and height (h).

Factoring the right side of the formula in this way can simplify calculations and help us better understand the relationship between the variables in the formula.

Therefore, to factor the right side of the formula A = 2πrx² + 2πrh, we can factor out 2πr from both terms:A = 2πr(x² + h)

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I got you, bro

Answer:

(x+4)(x+18)

Explanation

Let's factor x2+22x+72

x2+22x+72

The middle number is 22 and the last number is 72.

Factoring means we want something like

(x+_)(x+_)

Which numbers go in the blanks?

We need two numbers that...

Add together to get 22

Multiply together to get 72

Can you think of the two numbers?

Try 4 and 18:

4+18 = 22

4*18 = 72

Fill in the blanks in

(x+_)(x+_)

with 4 and 18 to get...

(x+4)(x+18)

Answer:

(x+4)(x+18)

Answer:

(x+4)(x+18)

Step-by-step explanation:

Using the factorisation method :

We need 2 numbers that multiply to give +72 and add to give +22 :

To find these numbers we write out all the factors of 72 :

1, 72

2 , 36

3 , 24

4 , 18    ----> These must be the numbers as 4+18 = 22

Now we split +22x into +4x and +18x :

x² + 4x + 18x + 72

Factor the first 2 terms together and the last two terms :

x(x+4) + 18(x+4)

Keep 1 bracket and terms outside the brackets collect them into one:

(x+4)(x+18)

This is our final answer

Hope this helped and have a good day

Answer:

63 centimeters

Step-by-step explanation:

What we know:

A cricle has a diameter of 20 cm.

To find circumference, use πd or 2πr.

3.14(10 * 2)

3.14(20)

62.8 cm, which rounds to 63 cm.

The exact values of the sine, cosine, and tangent of the angle 255° are -1/√2, 1/√2, and -1, respectively.

To find the exact values of the sine, cosine, and tangent of the angle 255°, we can use the identity that relates the trigonometric functions of an angle to the trigonometric functions of its complement.

By expressing 255° as the sum of 300° and -45°, we can determine the exact values of the trigonometric functions for the given angle.

We know that the sine, cosine, and tangent of an angle are periodic functions, repeating every 360 degrees. To find the exact values of the trigonometric functions for 255°, we can express it as the sum of 300° and -45°, where 300° is a multiple of 360°.

Since the sine, cosine, and tangent functions are odd or even functions, we can use the values of the trigonometric functions for 45° to determine the values for -45°.

For 45°:

sin(45°) = cos(45°) = 1/√2

tan(45°) = 1

Since cosine is an even function, cos(-45°) = cos(45°) = 1/√2.

Since sine is an odd function, sin(-45°) = -sin(45°) = -1/√2.

Using the definition of tangent as the ratio of sine to cosine, tan(-45°) = sin(-45°) / cos(-45°) = (-1/√2) / (1/√2) = -1.

Therefore, for the angle 255°:

sin(255°) = -1/√2

cos(255°) = 1/√2

tan(255°) = -1

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Answer:

\(\frac{y^{2}}{2x}\)

Step-by-step explanation:

a) simplify

\(\frac{y^{2} }{2x}\)

Answer:

ez y² /2x

Step-by-step explanation:

If a typical somatic cell has 64 chromosomes, each gamete of that organism is expected to have 32 chromosomes.

In sexually reproducing organisms, somatic cells are the cells that make up the body and contain a full set of chromosomes, which includes both sets of homologous chromosomes. Gametes, on the other hand, are the reproductive cells (sperm and egg) that contain half the number of chromosomes as somatic cells.

During the process of gamete formation, called meiosis, the number of chromosomes is halved. This reduction occurs in two stages: meiosis I and meiosis II. In meiosis I, the homologous chromosomes pair up and undergo crossing over, resulting in the shuffling of genetic material. Then, the homologous chromosomes separate, reducing the chromosome number by half. In meiosis II, similar to mitosis, the sister chromatids of each chromosome separate, resulting in the formation of four haploid daughter cells, which are the gametes.

Since a typical somatic cell has 64 chromosomes, the gametes produced through meiosis will have half that number, which is 32 chromosomes. These gametes, with 32 chromosomes, will combine during fertilization to restore the full set of chromosomes in the offspring, creating a diploid zygote with 64 chromosomes.

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The net profit margin for this shirt is 55%.

What is net profit?

Net profit is the amount of money your business earns after deducting all operating, interest and tax expenses over a period of time. To arrive at this value, you need to know the company's gross profit. If the value of net profit is negative, it is called net loss.

Net profit is another important parameter that determines the financial health of your business. It shows whether the company can earn more than it spends. Net profit helps you decide when and how to expand your business and when to cut costs.

It is important for a business owner to know the difference between profit and profitability. Profit is an absolute number equal to revenues minus expenses. Profitability, on the other hand, is a relative number (percentage) that equals the ratio of profit to revenue.

Profitability is a measure of efficiency and is useful in determining the success or failure of a business.

Given,

Revenue = $12

Cost of goods sold = $3

Operating expenses = 20% of revenue = 20/100 x $12 = $2.4

We know,

Net Profit = Revenue - Cost of goods sold - Operating expenses

\(Net \: Profit = 12 - 3 - 2.4\)

Hence, Net Profit = $6.6

Again,

Net Profit Margin = (Net Profit / Revenue) x 100%

Net Profit Margin \(= ( \frac{6.6}{ 12}) \times 100\%\)

SO, Net Profit Margin = 55%

Therefore, the net profit margin for this shirt is 55%.

So, it is clear that choice A is correct.

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Answer:

11x-8

Step-by-step explanation:

1. Simplify 13 x 2 to 26

2. simplify 12 x 2 to 24

3. simplify 24-2x + 6 to 2x + 30

4. remove the parentheses 26 + 9x - 4 + 2x - 30

5. collect the terms

( 26 - 4 - 30) + ( 9x + 2x)