Solve For b show your work 3b+2(b-3)=4
Plz show work

(a) The center of the sphere is in the first octant and is tangent to the xz-plane and to the yz-plane. This means that the center of the sphere is at a point of the form (a,b,5) where a,b≥0. The distance from the origin to the center of the sphere is  \(\sqrt{43}\), so we have \(x^{2} +x^{2} +(5-0)^{2} =43\) This gives us \(a^{2} +b^{2} =38\)

The radius of the sphere is the distance from the center of the sphere to the point where the sphere touches the xz-plane. This distance is equal to the length of the hypotenuse of a right triangle with legs of length a and b. Therefore, the radius of the sphere is \(\sqrt{a^{2}+ b^{2} } =\sqrt{38}\)

The equation of the sphere is \((x-a)^{2}+ (y-b)^{2}+ (z-5)^{2} =38\)

(b) The point where the sphere touches the xz-plane is (a,0,5). The distance between the origin and this point is \(\sqrt{a} ^{2}+\sqrt(5-0)^{2} =\sqrt{a^{2} +25}\)

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Answer:-637

Step-by-step explanation:

Answer:

your question makes no sense

Answer:

Distributive property

Step-by-step explanation:

The distributive property is where multiplying the sum of a group of numbers by another number will get you the same number as multiplying the numbers individually, then adding them together.

In this case, this means that adding w + 4 together, then multiplying it by 3, will get you the same number as 3w + 12, which is created by multiplying the numbers individually by 3, then adding them together.

So, this represents the distributive property.

3(w+4)=3w+12 is an example of Distributive property

A distributive property usually conforms to a distributive law where each algebraic expression has an equal variable.

For example;

From the given expression

Others include:

An associative property refers to a rearrangement method used in algebraic terms in which the solution of the variables in the bracket is not affected in the algebraic expression.

i.e.

a+ (b+c) = (a+b) + c

A commutative property determines the multiplication or addition of variables by just altering their order without changing the result.

i.e.  

a + b = b + a

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Given statement 'y is less than -2 ' in inequality notation would be, y < -2

In this question we have been given a statement 'y is less than -2'

We need to write given statement in inequality notation.

We know that, an inequality is a mathematical expression where two non-equal mathematical expressions or numbers are compared.

We know that we use '<' notation for less than.

Consider given statement:

y is less than -2.

⇒ y < -2

Therefore, given statement 'y is less than -2 ' in inequality notation would be, y < -2

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The population of the rabbit in the year 2002 will be 940 rabbits.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now,

The exponential model consisted the expression;

\(y = A r^{t}\)

Where, A is initial population and r is increase rate and t is time.

So, The initial population and increase rate for the given condition are;

\(740 = A . r^{0} \\\\A = 740\)

And,

\(870 = 740 * r^{7}\)

\(r^{7} = \frac{870}{740}\)

\(r^{7} = \frac{87}{74}\)

r = 1.89/1.84

r = 1.02

So, The exponential  model consisted the expression;

\(y = A r^{t}\)

\(y = 740 r^{12}\)

\(y = 740 * (1.02)^1^2\)

\(y = 740 * 1.27\)

\(y = 939.8\)

Therefore,

The population of the rabbit in the year 2002 will be 940 rabbits.

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D 2c + 4c + c

Collect Coefficients of like terms

\((2+4+1)\times c\)

__________________________________________________

Calculate the sum or difference

\(7c\)

__________________________________________________

Determine true/false

\(Determine\ whether\ 7c\ and\ 2c+4c+c\ are equivalent:\)

\(True\)

I hope this helps you

:)

Answer:

the lower limit of first class interval is 15.because ina class intervel the 1st no.is called lower limit so 15.

To determine if all the colors are equally likely, compare the expected probabilities with the observed probabilities. If they are close, then the colors are likely equally likely.

To determine if all the colors in a bag of M&Ms are equally likely based on the probabilities, you need to compare the observed probabilities with the expected probabilities.

First, calculate the expected probability for each color by dividing the total number of M&Ms of that color by the total number of M&Ms in the bag. For example, if there are 10 red M&Ms out of 50 total M&Ms, the expected probability for red would be 10/50 = 1/5.

Next, compare the expected probabilities with the observed probabilities. If the observed probabilities are close to the expected probabilities for all the colors, then it suggests that the colors are equally likely. However, if there is a significant difference between the observed and expected probabilities, it indicates that the colors are not equally likely.

For example, if the observed probability for red is 1/10 instead of 1/5, it suggests that red is less likely compared to what would be expected if the colors were equally likely.

In summary, to determine if all the colors are equally likely, compare the expected probabilities with the observed probabilities. If they are close, then the colors are likely equally likely.

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\( \huge \frak \green{question}\)

prove that √p is an irrational number , if p is not a perfect square.

\( \huge \frak \red{answer}\)

Let us assume, to the contrary, that √p is rational. So, we can find coprime integers a and b(b ≠ 0) such that :-

=> √p = a/b

=> √p b = a

=> pb² = a² ….(i) [Squaring both the sides]

=> a² is divisible by p

=> a is divisible by p So, we can write a = pc for some integer c.

Therefore,

a² = p²c² ….[Squaring both the sides]

=> pb² = p²c² ….[From (i)]

=> b² = pc²

=> b² is divisible by p

=> b is divisible by p

=> p divides both a and b.

=> a and b have at least p as a common factor.

But this contradicts the fact that a and b are coprime. This contradiction arises because we have assumed that √p is rational. Therefore, √p is irrational.

_____________________________________

\( \bold \green{i \: hope \: it \: is \: helpful}\)

________________________________

Answer:

9cm, 17 cm, 25cm

Step-by-step explanation:

The answer to the question is 3+x

and the probability of blue balls is 3/3+x

We are required to find out the total number of balls that is the sum of blue and yellow balls

so the total number of balls in the bag​ is 3+x

The concept here used is probability.

Probability is the quantitative relation of rangethe amount|the quantity} of outcomes in  thorough set of equally possible outcomes that manufacture a given event to the whole number of doable outcomes

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

probability of blue balls=blue balls/total balls

=3/3+x

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Hey your question is incomplete, the complete question is

A bag contains 3 blue balls and x yellow balls.Write down the total number of balls in the bag.If a ball is drawn from the bag, write down the probability that it is blue.

Answer:

N= 4

Step-by-step explanation:

y^3 * y^n

_______  = y^6    

   y

First we multiply the 2 y's together to get

y^n+3

____         = Y^6

Y

Then we will multiply y to both sides

y^n+3 = y^7

Get rid of y

n+3 = 7

n=4

Answer:

one

Step-by-step explanation:

Answer:

No solution

Step-by-step explanation:

:)

The distance between diagonally opposite corners of the rectangular brick wall is approximately 6.08 meters (m).

To find the distance between diagonally opposite corners of a rectangular brick wall, we can use Pythagoras' theorem. According to the theorem, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the two sides of the rectangle are the width (6 m) and the height (1 m). Let's consider the width as the base and the height as the height of a right-angled triangle formed within the rectangle.

Using Pythagoras' theorem, we have:

Hypotenuse^2 = Base^2 + Height^2

Hypotenuse^2 = 6^2 + 1^2

Hypotenuse^2 = 36 + 1

Hypotenuse^2 = 37

To find the length of the hypotenuse (distance between diagonally opposite corners), we take the square root of both sides:

Hypotenuse = √37

Calculating the square root of 37 using a calculator or rounding it to one decimal place, we get:

Hypotenuse ≈ 6.08 meters (m) (rounded to 1 decimal place)

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In the late Roman Republic, individuals would typically ensure they had essential items such as a tunic or clothing appropriate for the occasion, footwear, and possibly a small writing implement like a stylus.

During the late Roman Republic period, individuals would prioritize wearing appropriate clothing, such as a tunic, which was a basic garment worn by both men and women. Footwear, such as sandals or shoes, would also be essential to protect the feet while traveling. Carrying money or valuables was crucial for transactions and personal needs, ensuring they had the means to purchase goods or services.

Additionally, individuals might carry a small writing implement, such as a stylus, for taking notes, marking important information, or engaging in correspondence. These items would have been considered essential for individuals in the late Roman Republic when leaving their homes.

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Answer:

f(x) = (-3/4)x^2 + 3

Step-by-step explanation:

First, look at the vertex to see if it intersects the y-axis. It does, which is good, because it makes your job a lot easier by making your equation to fill out y = ax + b. Your b is the y value of your vertex, which in this case is 3. Then, your a is the amount you're multiplying plain old x^2 by to get your values (before adding 3). Because the graph is pointing down, you know right away that it's going to be negative. Also, going to the left or right by 2 (the points you are given) from the vertex gives you a result of going down 3. Normally this would mean you move up by 4 (again, from the vertex), so what do you need to multiply 4 by to get -3? -3/4, so that's your a. This makes your equation (y OR) f(x) = (-3/4)x^2 + 3

I hope I didn't make any mistakes reading your graph! I had a bit of difficulty with it unfortunately.

There is no tangent of the angle in this scenario.

In a right angled triangle, the cosine of an angle is equal to the adjacent side divided by the hypotenuse.

Therefore, if cos θ = ⅘ in a right angled triangle, we can label the adjacent side as 8 (since cosine is adjacent over hypotenuse and we know cosine and hypotenuse) and the hypotenuse as 5 (since we know cosine and hypotenuse and can solve for the adjacent side using Pythagorean theorem).

Now, to find the tangent of the angle, we need to divide the opposite side by the adjacent side. We do not know the value of the opposite side, but we can use the Pythagorean theorem to find it.

Let's label the opposite side as x. Using Pythagorean theorem, we get:

(8)^2 + x^2 = (5)^2

64 + x^2 = 25

x^2 = -39

This is impossible because the square of a real number cannot be negative. Therefore, there is no tangent of the angle in this scenario.

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Answer:

Step-by-step explanation:

Remark

-2 looks pretty good.

y = 1/2 (-2) + 3

y = - 1 + 3

y = 2

y = absolute value (x)

y = abs(-2)

y = 2

The absolute value is always the positive possible answer.

Answer:

(5,0) (0,1)

Step-by-step explanation:

Your monthly allowance and your friend's monthly allowance is $45 and $36 respectively.

From the given tape diagram, the ratio of your monthly allowance to your friend's monthly allowance is 5:4.

What is the ratio?

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Here, 5+4=9

Now, your monthly allowance = 5/9 × 81

= 45

So, your friend's monthly allowance = 81-45 = 36

Therefore, your monthly allowance and your friend's monthly allowance is $45 and $436 respectively.

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To solve the initial value problem (IVP) (e⁽²ʸ⁾ - y)cos(a)y' = sin(2x) with y(0) = 0, we can separate variables and then integrate both sides.

Here are the step-by-step solutions:

Step 1: Separate variables

Rearrange the equation to separate the variables y and x:

(e⁽²ʸ⁾ - y)cos(a)dy = sin(2x)dx

Step 2: Integrate both sides

Integrate both sides of the equation with respect to their respective variables:

∫(e⁽²ʸ⁾ - y)cos(a)dy = ∫sin(2x)dx

Step 3: Evaluate the integrals

Integrate each term separately:

∫e⁽²ʸ⁾cos(a)dy - ∫ycos(a)dy = ∫sin(2x)dx

Step 4: Evaluate the integrals on the left side

For the first integral, we can use u-substitution:

Let u = 2y, then du = 2dy

∫e⁽²ʸ⁾cos(a)dy = (1/2)∫eᵘᵈᵘ = (1/2)eᵘ + C1 = (1/2)e⁽²ʸ⁾ + C1

For the second integral, we integrate y with respect to y:

∫ycos(a)dy = (1/2)y²cos(a) + C2

Step 5: Simplify the equation

Substitute the evaluated integrals back into the equation:

(1/2)e⁽²ʸ⁾ + C1 - (1/2)y²cos(a) - C2 = ∫sin(2x)dx

Step 6: Evaluate the integral on the right side

Integrate sin(2x) with respect to x:

∫sin(2x)dx = -(1/2)cos(2x) + C3

Step 7: Combine constants

Combine the constants C1, C2, and C3 into a single constant C:

(1/2)e⁽²ʸ⁾ - (1/2)y²cos(a) + C = -(1/2)cos(2x) + C

Step 8: Solve for y

Rearrange the equation to solve for y:

(1/2)e⁽²ʸ⁾ - (1/2)y²cos(a) = -(1/2)cos(2x) + C

Step 9: Apply the initial condition

Use the initial condition y(0) = 0 to solve for the constant C:

(1/2)e⁰ - (1/2)(0)²cos(a) = -(1/2)cos(2(0)) + C

1/2 - 0 + C = -1/2 + C

1/2 = -1/2 + C

C = 1

Step 10: Final solution

Substitute the value of C back into the equation:

(1/2)e⁽²ʸ⁾ - (1/2)y²cos(a) = -(1/2)cos(2x) + 1

This is the solution to the initial value problem (IVP). The interval of convergence will depend on the range of validity of the functions involved, but without specific restrictions or constraints, the solution is valid for all real values of x and y.

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Answer:

she had $77 to her name

Step-by-step explanation:

Add the cost up from the cd & dvd then add the total from that and the 55

Answer:

She should've had 77 dollars before

Step-by-step explanation:

55 plus 12 = 67

67 plus 10 = 77

Steps to convert decimal into fraction

Write 4.005 as  

4.005

-----------

1

Multiply both numerator and denominator by 10 for every number after the decimal point

4.005 × 1000

---------------------

1 × 1000

=  

4005

-----------

1000

Reducing the fraction gives

801

--------

200

a) The null hypothesis, H0: p1 - p2 = 0, states that there is no real change in opinion among U.S. adults from May to June. The alternative hypothesis, Ha: p1 - p2 ≠ 0, states that there is a real change in opinion among U.S. adults from May to June.

(b) Under the null hypothesis, the difference in the percentages is expected to be 0%. The estimated standard error for this difference can be calculated as sqrt((p1(1-p1)/n1)+(p2(1-p2)/n2)), where p1 and p2 are the sample proportions for May and June, respectively, and n1 and n2 are the sample sizes for May and June, respectively.

(c) The two-sample z test statistic can be calculated as (p1-p2)/SE, where p1 and p2 are the sample proportions for May and June, respectively, and SE is the estimated standard error for the difference in proportions.

(d) The p-value can be calculated as the area under the normal distribution curve to the left of the negative of the absolute value of the z test statistic plus the area under the normal distribution curve to the right of the absolute value of the z test statistic.

(e) Our conclusion depends on the significance level chosen and the p-value obtained. If the significance level is chosen to be 0.05 and the p-value obtained is less than 0.05, then we reject the null hypothesis and conclude that there is evidence for a real change in opinion among U.S. adults from May to June.

If the p-value obtained is greater than or equal to 0.05, then we do not reject the null hypothesis and conclude that there is not enough evidence to support a real change in opinion among U.S. adults from May to June.

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Answer:

3000

300

3000/300 = 10

Hannah has 10 times greater value of 3 than Greg.

Take 3000 from Hannah and DIVIDE the 300 from Greg. You will get 10 and that is the multiplier or "greater times" amount.

Answer:

Answer in picture with working

Step-by-step explanation:

Answer:

\(p^4\) or \(x^4\) because you wrote \(.... -10x^2+9\) instead of p

Step-by-step explanation:

I'm going to assume (p2-9)(p2-1) is actually \((p^2-9)(p^2-1)\)

so if I expand it then,

\(p^4-p^2-9p^2+9=p^4-10p^2+9\)

So the missing part(blank)

is \(p^4\) or is it \(x^4\)