Logan's birthday party will cost $15 if he invites 5 guests. How many guests can there be, at most, if Logan can afford to spend a total of $30 on his birthday party? Assume the relationship is directly proportional.

The perfect square form the given numbers is 25.

Perfect squares are defined as the number which is the result of the multiplication of another number, likely integers, to itself two times.

For example, 4 = 2 × 2

So 4 is a perfect square of 2.

Here the given numbers are,

20, 21, 24, 25.

We need the perfect squares as the squares of integers.

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

So 25 is a perfect square.

20, 21 and 24 cannot be written as the square of an integer.

Hence the correct number is 25.

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Answer:

2x² + 5x + c = 0

For this quadratic equation to have one double root, the discriminant must equal 0.

5² - 4(2)(c) = 0

25 - 8c = 0

c = 25/8

2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.

2x² + 5x is not a perfect square.

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Answer:

Step-by-step explanation:

on the 250ml ÷ 140 ml = 1L and 78757ml

on the 200 ml ÷ 150 ml = 1L and 333ml

on the 150 ml ÷ 160 ml = 9375ml

on the 100 ml ÷ 170 ml = 58832ml

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The true expression about the account is D.) It is the sum of the initial amount and the additional amount after d days.

The answer is D because it represents the sum of the initial amount and the additional amount after d days. The initial amount is $10 and Owen adds $0.50 to the account each day for a number of days, represented by d.

By subtracting 1 from d, the expression ensures that on the first day (when d=1), only the initial $10 is counted. On each subsequent day, the additional amount of $0.50 is added to the total. Therefore, the expression 10+0.5(d−1) gives the amount of money in Owen's account after d days.

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Answer:

144

Step-by-step explanation:

plug in 5 where you see the x.

that gives us 9(4(5)-4)

multiply the 4 and the 5 first to get 9(20-4)

and by PEMDAS, we solve the parentheses first so now we have 9(16)

so now just multiply 9x16 to get 144

Step-by-step explanation:

9((4×5)-4)

9(20-4)

9(16)

144

The launching of the hot air balloon is from the ocean beach is an illustration of a projectile motion

The function is given as:

\(p(x) =-\frac{2}{2500}x^2 + 0.7x\)

Differentiate

\(p'(x) =-\frac{4}{2500}x + 0.7\)

Set to 0

\(-\frac{4}{2500}x + 0.7 = 0\)

Subtract 0.7 from both sides

\(-\frac{4}{2500}x =- 0.7\)

Multiply through by -2500/4

\(x =437.5\)

Hence, the horizontal distance which a maximum height is attained is 437.5 meters

In (a), we have:

\(x =437.5\)

Substitute \(x =437.5\) in p(x)

\(p(437.5) =-\frac{2}{2500} * 437.5^2 + 0.7 * 437.5\)

Evaluate

\(p(437.5) =153.125\)

Hence, the maximum height above the sea level is 153.125 metres

In (b), the maximum height above the sea level is 153.125 metres

The ratio of the height on land and sea is given as:

Land : Sea = 2 m : 20 m

For the maximum height, we have:

Land : 153.125 m= 2 m : 20 m

Express as fraction

Land / 153.125 m = 2 /20

Multiply both sides by 153.125

Land = 15.3125

Approximate

Land = 15.3

Hence, the maximum height above the ground level is 15.3 meters

We have:

\(p(x) =-\frac{2}{2500}x^2 + 0.7x\)

Substitute 50 for P(x)

\(-\frac{2}{2500}x^2 + 0.7x = 50\)

Using a graphing calculator, we have:

x = 78.465 and 796.535

Hence, the horizontal distances where the balloon 50 m above the ground are 78.465 and 796.535 meters

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Answer:

x + 3 = 5

Step-by-step explanation:

x + 3 = 5 is an example of linear equation.

The confidence intervals for population mean is between (613.56 , 626.44).

A statistic known as the standard deviation, which is derived as the square root of variance, gauges a dataset's dispersion from its mean. By figuring out how far off from the mean each data point is, the standard deviation may be determined as the square root of variance.

A bigger deviation exists within a data collection if the data points are further from the mean; hence, the higher the standard deviation, the more dispersed the data.

Sample mean = й = 620

Pop std. Deviation =σ = 25

Sample Size = n = 100

Confidence level (C) = 99.0%

So significance level (α) = 1- C = 1.00%

So, α/2 = 0.005

Population is normal so condition for normality is satisfied we will use Z distribution.

Z(α/2) = 2.576

Formula to construct the confidence intervals for population mean (μ)

μ =  й +- Z(α/2)(\(\frac{ σ}{\sqrt{n} }\))

Putting the Values in this Equation, we get

μ= 613.5604 , 626.4396

Hence the confidence intervals for population mean is between (613.56 , 626.44).

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Relative interest refers to the comparison of interest rates between different financial instruments or investment opportunities. It allows individuals or investors to assess and evaluate the attractiveness of various options based on their potential returns.

1. Understand the basic concept: Interest is the cost of borrowing money or the return earned on invested funds. Relative interest involves comparing the interest rates of different financial instruments or investments to determine which one offers a more favorable return.

2. Identify the investment options: Start by identifying the different investment opportunities or financial instruments available. These can include savings accounts, certificates of deposit (CDs), bonds, stocks, or other investment vehicles.

3. Research interest rates: Research and gather information about the current interest rates offered by each investment option. This information can usually be found on financial websites, through financial institutions, or by consulting with a financial advisor.

4. Compare interest rates: Once you have the interest rates for each investment option, compare them side by side. Look for the differences in rates and identify which options offer higher or lower returns.

5. Assess risk and return: Consider the level of risk associated with each investment option. Higher returns often come with higher risk, so it's essential to evaluate the risk-reward tradeoff.

6. Make an informed decision: Based on the comparison of interest rates and the risk-reward assessment, make an informed decision on which investment option aligns with your financial goals and risk tolerance.

Always remember to consider your financial goals, risk tolerance, and consult with a financial advisor if needed.

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The area of the smaller rectangle (KLMN) is 16.

Since rectangles ABCD and KLMN are similar, their corresponding sides are proportional.

Let's assume the length of side AB in rectangle ABCD is x, and the length of side KL in rectangle KLMN is y.

We can set up the proportion:

(x/y) = (20/16)

To find the area of the smaller rectangle, we need to determine the ratio of their areas.

Since the area of a rectangle is given by the product of its length and width, the ratio of the areas will be equal to the square of the ratio of their sides:

(Area of ABCD)/(Area of KLMN) = (x²)/(y²)

We are given that the area of ABCD is 25, so we have:

25/(Area of KLMN) = (x²)/(y²)

To find the area of KLMN, we need to substitute the values of x and y from the proportion:

25/(Area of KLMN) = (20/16)²

Simplifying the right side:

25/(Area of KLMN) = (5/4)²

25/(Area of KLMN) = 25/16

Cross-multiplying:

25 × 16 = 25 × (Area of KLMN)

400 = 25 × (Area of KLMN)

Dividing both sides by 25:

16 = Area of KLMN

Therefore, the area of the smaller rectangle (KLMN) is 16.

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ANSWER: y = (1/2)x - 1.

To find the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1), we need to determine the slope of the tangent line and its y-intercept.

First, let's find the derivative of the function y = √(x - 3) using the power rule:

dy/dx = 1/(2√(x - 3))

Now, we can substitute x = 4 into the derivative to find the slope of the tangent line at that point:

m = dy/dx = 1/(2√(4 - 3)) = 1/2

So, the slope of the tangent line is 1/2.

Next, we can use the point-slope form of a line to find the equation of the tangent line. Given the point (4, 1) and the slope m = 1/2, the equation becomes:

y - y1 = m(x - x1)

Substituting the values (x1, y1) = (4, 1):

y - 1 = (1/2)(x - 4)

Simplifying the equation:

y - 1 = (1/2)x - 2

y = (1/2)x - 1

Therefore, the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1) is y = (1/2)x - 1.

Answer:

y = (1/2)x - 1/2

Step-by-step explanation:

Step 1: Find the derivative of the function

The derivative of a function gives the slope of the tangent line to the curve at any point. To find the derivative of the given function y = sqrt(x - 3), we can use the power rule of differentiation which states that:

d/dx (x^n) = nx^(n-1)

Applying this rule to our function, we get:

dy/dx = d/dx sqrt(x - 3)

To differentiate the square root function, we can use the chain rule of differentiation which states that:

d/dx f(g(x)) = f'(g(x)) * g'(x)

Applying this rule to our function, we have:

g(x) = x - 3

f(g) = sqrt(g)

So,

dy/dx = d/dx sqrt(x - 3) = f'(g(x)) * g'(x) = 1/(2*sqrt(g(x))) * 1

Substituting g(x) = x - 3, we get:

dy/dx = 1/(2*sqrt(x - 3))

So, the derivative of y with respect to x is 1/(2*sqrt(x - 3)).

Step 2: Evaluate the derivative at the given point

To find the slope of the tangent line at the point (4, 1), we need to substitute x = 4 into the derivative expression:

dy/dx = 1/(2*sqrt(4 - 3)) = 1/2

So, the slope of the tangent line at the point (4, 1) is 1/2.

Step 3: Use point-slope form to write the equation of the tangent line

Now that we know the slope of the tangent line at the point (4, 1), we can use point-slope form to write the equation of the tangent line. The point-slope form of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is the point on the line and m is the slope of the line.

Substituting the values x1 = 4, y1 = 1, and m = 1/2, we get:

y - 1 = (1/2)*(x - 4)

Simplifying this equation, we get:

y = (1/2)x - 1/2

So, the equation of the tangent line to the curve y = sqrt(x - 3) at the point (4, 1) is y = (1/2)x - 1/2.

Hope this helps!

Answer:

The value of x(perpendicular) is 17.80

Step-by-step explanation:

Given triangle is a right angled triangle as one of the angles is 90°

Also according to the reference angle 54°,

Hypotenuse = H = 22

Perpendicular = P = x

We can use the trigonometric ratio of sine as it involves both known value perpendicular and hypotenuse.

So,

\(sin\ 54 = \frac{P}{H}\\sin\ 54 = \frac{x}{22}\\0.8090 = \frac{x}{22}\\x = 0.8090*22\\x = 17.798\)

Rounding off to nearest hundredth

x = 17.80

Hence,

The value of x(perpendicular) is 17.80

The sum of the eigenvalues of A is equal to the trace of A, and we have proved the desired result.

Let A be an n x n square matrix with eigenvalues λ1, λ2, ..., λn.

The trace of A is defined as the sum of the diagonal elements of A, i.e.,

tr(A) = a11 + a22 + ... + ann

where aij is the element of A in the ith row and jth column.

Now, consider the characteristic equation of A, which is given by

det(A - λI) = 0

where I is the n x n identity matrix.

Expanding the determinant, we get

(-1)^n λ^n + (-1)^(n-1) tr(A) λ^(n-1) + ... + det(A) = 0

By Vieta's formulas, the sum of the roots of this polynomial equation is equal to the negative of the coefficient of the (n-1)th power of λ divided by the coefficient of the nth power of λ.

Thus, the sum of the eigenvalues of A is given by

λ1 + λ2 + ... + λn = -(-1)^(n-1) tr(A)/(-1)^n

= tr(A)

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the answer is 3p

hope it helps!

Answer: 3p

Step-by-step explanation:

5 − 3 + =

3

Answer:

314.16

Step-by-step explanation:

Area= Pi x radius squared

Answer:

i think the answer is 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

thats it

Answer:

2

Step-by-step explanation:

The he expected value of the raffle is $2.50

What is the expected value of a raffle ticket?

The expected value is the sum of the winnings multiplied by their probabilities of persons participating

One person out of 400 would win $300, we have 1/400*$300

2 persons would win $200 each out of 400, we have 2/400*$200

3 persons would win $100, we have 3/400*$100

expected value=( 1/400*$300)+(2/400*$200)+(3/400*$100)

expected value=$2.50

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Answer:

The expected value of the raffle is -$1.50.

Step-by-step explanation:

Answer:

Step-by-step explanation:

perimeter of semicircle = 1/2 π d

                                       = 1/2 π (6)

                                       = 9.425 x 4 semicircles

                                       = 37.7

Answer:

(72)²=72×72=5,184

.................

Answer:

5 units

Step-by-step explanation:

its hard to tell but i think it dilated 5 units

We want to find the scale factor at which QRST is dilated to form Q'R'S'T'

We will find that the scale factor is 2.

In a general dilation, we will see that all the measures change in the same way, by the scale factor.

This means that:

QR*k = Q'R'

RS*k = R'S'

And so on, where k is the scale factor.

Then we can just find one of the equivalent measures in both trapezoids and find the value of k.

For example, we have:

Q'R' = 8

QR = 4

Replacing these on the above equation we get:

4*k = 8

k = 8/4 = 2

k = 2

The scale factor of dilation is 2.

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Both planes have the same normal vector:

\(6x-y-z=6\implies\mathbf n=\langle6,-1,-1\rangle\)

The plane we want must contain the point (4, -3, -1), so its equation would be

\(\mathbf n\cdot\langle x-4,y+3,z+1\rangle=0\)

\(\implies 6(x-4)-(y+3)-(z+1)=0\)

\(\implies\boxed{6x-y-z=28}\)

The solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.

The similar symbol (=) is used in arithmetic equations to signify equality between two statements. It is shown that it is possible to compare various numerical factors by applying mathematical algorithms, which have served as expressions of reality. For instance, the equal sign divides the number 12 or even the solution y + 6 = 12 into two separate variables many characters are on either side of this symbol can be calculated. Conflicting meanings for symbols are quite prevalent.

Part A:

Given:

To find an equation,

Where x is number of monthly minutes.

and y is total monthly of splint plan.

So, equation is:

\(\rightarrow \text{y} =\text{mx} +\text{b}\)

For the first case:

\(\rightarrow\bold{173 = 380x + b}\)

Second case:

\(\rightarrow\bold{249= 570x + b}\)

Solve for x:

\(\rightarrow{173 - 380\text{x}=249- 570\text{x}\)

\(\rightarrow{-207=-321\)

\(\rightarrow \text{x} =\dfrac{321}{207}\)

\(\rightarrow \text{x} =\dfrac{107}{69}\)

\(\rightarrow \text{x} \thickapprox1.55\)

For value of b

\(\rightarrow 173 = 380(1.55) + \text{b}\)

\(\rightarrow 173 - 589 = \text{b}\)

\(\rightarrow -416 = \text{b}\)

Part B:

\(\rightarrow \text{y} = 942(1.55) - 416\)

\(\rightarrow \text{y} = 1460.1 - 416\)

\(\rightarrow \text{y} \thickapprox1044\)

Therefore, the solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.

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\(w^2 - 6w + 4\) is a polynomial that represents how much more profit is earned by selling w apple trees than w pear trees.

The profit earned by selling w pear trees is 2w + 10

To find the difference in profit, we need to subtract the profit earned by selling w pear trees from the profit earned by selling w apple trees:

\((w^2 - 4w + 14) - (2w + 10)\)

Simplifying the expression:

\(w^2 - 6w + 4\)

Therefore, the polynomial that represents how much more profit is earned by selling w apple trees than w pear trees is \(w^2 - 6w + 4\).

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Answer:21 cm.

Step-by-step explanation:

Para encontrar la longitud del lado de un cuadrado con un área de 441 cm², podemos usar la fórmula del área de un cuadrado.

El área de un cuadrado se calcula elevando al cuadrado la longitud de uno de sus lados, es decir, A = L², donde A es el área y L es la longitud del lado.

Dado que el área del cuadrado es 441 cm², podemos escribir la ecuación:

441 = L²

Para encontrar L, podemos tomar la raíz cuadrada de ambos lados de la ecuación:

√441 = √L²

21 = L

Por lo tanto, la longitud del lado de un cuadrado con un área de 441 cm² es de 21 cm.

The answer is 0.471 radians.

FORMULA:

Just do 27° × π/180 = 0.4712rad but then cut off the two.