You tie a spherical balloon that is 2 feet in diameter to a
stake in the ground. The string is 15 feet long. The wind
blows and you observe that the top of the balloon is
8 feet over from the stake, as shown in the diagram.
What is the height, b, of the balloon?
Show your work.
15 ft
2 ft
8 ft

The probability of winning on the last attempt is approximately 0.3762 or 37.62%.

The probability of winning a prize in a carnival game is provided as 1/7. This means that in any single attempt, the probability of winning is 1/7 and the probability of losing is 6/7.

Since the outcomes of the carnival games are assumed to be independent from game to game, the probability of losing in each attempt remains the same.

If you have failed to win in the last nine attempts, the probability of losing in each of those attempts is (6/7) multiplied by itself nine times:

Probability of losing in 9 attempts = (6/7)^9

To find the probability of winning on the tenth attempt, we subtract the probability of losing in nine attempts from 1:

Probability of winning on the tenth attempt = 1 - (6/7)^9

Calculating this value, we find:

Probability of winning on the tenth attempt = 1 - (6/7)^9 ≈ 0.3762

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Answer:

The maximum height the projectile reaches is 100 feet

Step-by-step explanation:

Notice that the given equation representing the height of the projectile is a quadratic equation which negative leading coefficient (-16). Such type of equations would have a parabola that branches downwards as its graph.

therefore, what we need to find is the coordinates of the top vertex of that parabola. We can use for such the typical formula for the x-position of the vertex of a parabola with standard equation:

\(f(x)=ax^2+bx+c\)

with x-position of the vertex given by:

\(x_v=\frac{-b}{2a}\)

Then in our case  (\(H(t)=-16t^2+16t+96\))  we have:

Horizontal position of the vertex given by:

\(t_{vertex}=\frac{-16}{2(-16)} =\frac{1}{2}\)

and now we can find the maximum height plugging this value into the height expression:

\(H(t)=-16(\frac{1}{2}) ^2+16\,(\frac{1}{2})+96=-4+8+96=100\,\,ft\)

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

What is matrix ?

A matrix is a rectangular array of numbers or other mathematical objects, typically arranged in rows and columns. Matrices are often denoted using capital letters, such as A, B, and C. Each element of a matrix is identified by its row and column indices,

1) False, If two row interchanges are made in succession, the determinant of the new matrix is the negative of the determinant of the original matrix.

2) False, If the determinant of a matrix is zero, it does not necessarily mean that two rows or two columns are the same or a row or column is zero, it only means that the matrix is singular, i.e. non-invertible and it also can mean that the matrix is linearly dependent.

3) False, The determinant of a matrix is not always equal to the product of the diagonal entries, it is a scalar value calculated through a specific method called matrix expansion which is based on the entries of the matrix and it depends on the size of the matrix.

4) False, The determinant of a matrix is a scalar value, it cannot be equal to another matrix.

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

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Answer:

87.5% are pennies

Step-by-step explanation:

7/8 = 87.5%

Hope this helps!!

To determine the credit card daily interest rate that would make the second option more attractive than the first one, we need to compare the total cost of borrowing for each option.

The second option has an APR of 2% compounded yearly. By calculating the total cost of borrowing for the loan option, we can find the equivalent daily interest rate. If the daily interest rate of the credit card exceeds this calculated rate, the second option would be more attractive.

To find the credit card daily interest rate that would make the second option more attractive, we first calculate the total cost of borrowing for the loan option. Using the formula for compound interest, the total cost can be determined as the principal plus the accumulated interest over 10 years with an APR of 2%. Once the total cost is obtained, we divide it by the number of days in 10 years to find the equivalent daily interest rate.

If the daily interest rate of the credit card exceeds this calculated rate, it means that the cost of borrowing with the credit card would be higher than the second option. Therefore, to make the second option more attractive, the credit card's daily interest rate would need to be lower than the calculated rate from the loan option.

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Answer:40

Step-by-step explanation:

The exponential equation \(14=5^x\) is equivalent to the  given logarithmic equation.

The exponential function that is represented as y=\(m^x\), where:

m=base, m>0

x= exponent

Knowing some of the main logarithm rules.

example: \(log(a*b)= log a + log b\)

example: \(log\frac{a}{b} = log a - log b\)

example: \(log\frac{a^b} = b*log a\)

For solving this question, you should apply the logarithm rules and  rewrite the function as an exponential equation.

\(log_5(x)}-{log_5(25)=7\)

\(\frac{log_5(x)}{log_5(25)} =7\)

\({log_5(x)}=7{log_5(25)}\)

\({log_5(x)}=7{log_5(5^2)}\)

\({log_5(x)}=7*2\)

\({log_5(x)}=14\)

\(x=5^{14^}\)

Therefore, the  exponential function is \(14=5^x\)

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Answer:

1.6 kilometres

Step-by-step explanation:

Well, multiply 3.2cm with 50000 and there's your answer. That's the point of the scale, it gives you a quick and easy way to convert distances on the map to distances in nature.

I'll make it even easier for you, I'll convert to kilometers. You have centimeters on map, so take 2 zeros off and you have meters, take 3 more zeros off, and you have kilometers. That makes it 3.2*0.5 which is 1.6 kilometers, or approximately one american imperial mile.

Answer:

Step-by-step explanation:

2.6*50=130 km

Answer:

She should receive $3.56 from paying with a $10 bill

Step-by-step explanation:

The total cost of all her items including sales tax is

$6.44

You have to deduct this total cost from what she paid with.

$10.00 - $6.44 = $3.56

Therefore,

Sara should receive $3.56 from paying with a $10 bill.

Answer: $3.56

Step by step explanation:

1. Figure out how much the eggs cost. (1.69×2=3.38)

2. Add the price of the eggs, bacon, O.J., and sales tax together. (3.38+1.49+1.09+0.48=6.44)

3. Subtract the total ($6.44) by the amount you paid ($10). (10-6.44=3.56)

Answer:

B

Step-by-step explanation:

:0 : )

Answer:

A

Step-by-step explanation:

You can tell it has a negative slope because the line is moving down

hope this helps <3

The variable labeled "level" is discrete.

Based on the information provided, we can conclude that the variable labeled "level" is discrete.

A discrete variable is a type of variable that can only take on specific, separate values and does not have any values in between. In this case, the variable "level" only has whole number values between 1 and 5. This indicates that the variable has distinct categories or levels, and there are no fractional or decimal values allowed.

By observing the data and frequency distribution, we can determine that the variable "level" is discrete because it consists of whole number values within a specific range. This information helps us understand the nature of the variable and how it should be treated in statistical analyses or calculations. Recognizing the type of variable is important for selecting appropriate statistical methods and interpreting the results accurately.

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Answer:

-6x + 19

Step-by-step explanation:

perform multiplication first.

To find the probability of a company having both a website and a section in the newspaper, we can use the formula for conditional probability.

Let's denote the events as follows:
A: A company has a section in the newspaper
B: A company has a website

We are given the following probabilities:
P(A) = 0.43 (Probability of a company having a section in the newspaper)
P(B|A) = 0.84 (Probability of a company having a website given that it has a section in the newspaper)

The probability of both events A and B occurring can be calculated as:
P(A and B) = P(A) * P(B|A)

Substituting in the values we have:
P(A and B) = 0.43 * 0.84
P(A and B) = 0.3612

Therefore, the probability of a company having both a website and a section in the newspaper is 0.3612 or 36.12%.

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Answer:

0, 1, 2, 3

Step-by-step explanation:

-1 < x < 4 means that x has to be an integer (whole number aka no fractions)  between -1 and 4. Note that the < and > means that x cannot be -1 or 4 since it has to be greater than -1, or smaller than 4.

Answer:

4,560 pounds of soil

Step-by-step explanation:

Ok, based on the information given we are assuming that Persephone's garden is in the shape of a square or rectangle and the measurements 8 by 19 are in feet. That being the case we first need to calculate the square footage of the garden and we do this by multiplying the length by the width like so...

8 ft * 19 ft = 152 sq. ft.

Now that we know the square footage, we calculate how much soil is needed. Since the question states that she needs 30 pounds of soil per square foot then we multiply the square footage of the garden by 30.

152 sq. ft. * 30lb =  4,560lb

Finally, we can see that Persephone will need 4,560 pounds of soil for her garden.

Answer:

(x - 10)(x + 8)

Step-by-step explanation:

x² - 2x - 80

Consider the factors of the constant term (- 80) which sum to give the coefficient of the x- term (- 2)

The factors are - 10 and + 8 , since

- 10 × 8 = - 80 and - 10 + 8 = - 2 , then

x² - 2x - 80 = (x - 10)(x + 8)

Hence , equation of the line that is perpendicular to the line y = 6 and passes through the point (-4,-3) is x = -4 which is option (a) .

The line y = 6 could be a horizontal line through the purpose (0,6) on the coordinate axis. A line perpendicular thereto are vertical and thru the coordinate axis. this suggests its equation are x = a wherever a is that the x-coordinate. Since it should experience the purpose (-4,-3) then the equation is x =  -4.

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Alternate Interior angles

x = 25

By careful observation of the diagram, we would see that both angles are at the opposite sides of the transversal. At the same time, they are at the interior of the two parallel lines.

This means that <108 and <4x + 8 are alternate interior angles.

Since the two lines intersecting the transversal are parallel, the alternate interior angles are equal

That is,

4x + 8 = 108

4x = 108 - 8

4x = 100

x = 100/4

x = 25

Answer:

f(t) = -.03t + 0.45

Step-by-step explanation:

Answer:

DE is 12

Step-by-step explanation:

all the side lengths of the first triangle are multiplied by 3 to get to the larger one so 4×3=12

The value of the variable 'x' will be 8, 8.1, 9, and 13.

Given that:

Inequality, - x ≤ - 8

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Simplify the inequality, then we have

- x ≤ - 8

x ≥ 8

The value of 'x' is greater than or equal to 8.

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Answer:

12

Step-by-step explanation:

2*126=252

252/21=12

Answer:  180(n-2)

You use the distribution rule to factor

The distribution rule is a(b+c) = a*b+a*c

Answer:

B.

Step-by-step explanation:

x^4

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\((x)(x)(x)(x)\\\\=x^{1+1+1+1} ~~~ ;[x^a \cdot x^b = x^{a+b}]\\\\=x^4\)

In order to determine whether this graph shows a proportional relationship, you should determine if the ratios of the two variables plotted on the graph have a constant of proportionality.

In Mathematics, the graph of a proportional relationship between two variables is always characterized by a straight line with its data points passing through the origin (0, 0).

Mathematically, a proportional relationship can be modeled by the following linear equation:

y = kx

Where:

In conclusion, the ratio of the two variables plotted on the graph of a proportional relationship is always constant.

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The parametric form can be written as -

\(x = x_2 \left[ \begin{array}{c} -3 \\ 1 \\ 0 \\ 0 \\ \end{array} \right] + x_3 \left[ \begin{array}{c} 0 \\ 0 \\ 1 \\ 0 \\ \end{array} \right] + x_4 \left[ \begin{array}{c} 4 \\ 0 \\ 0 \\ 1 \\ \end{array} \right]\)

A matrix equation of the form \($A\overrightarrow x=0\) is called homogeneous matrix equation.

A matrix equation of the form  \($A\overrightarrow x=\overrightarrow b\) is called non - homogeneous matrix equation.

Given is to find the solution in parametric vector form.

If there are {m} free variables in the homogeneous equation, the solution set can be expressed as the span of {m} vectors :

\($\overrightarrow x=s_{1} \overrightarrow v_{1} + s_{2} \overrightarrow v_{2}+......+s_{m} \overrightarrow v_{m}\)

We have a matrix where {A} is the row equivalent to that matrix -

\(\begin{bmatrix} 1&3&0&-4 \\ 2&6&0&-8 \end{bmatrix}\)

Given matrix can be written in Augmented form as -

\(\left[ \begin{array}{cccc|c} 1&3&0&-4 & 0\\2&6&0&-8&0\\ \end{array} \right]\)

Row Reduced Echelon Form can be obtained using the following steps -

{ 1 } - Interchanging the rows R{1} and R{2}.

\(\left[ \begin{array}{cccc|c} 2&6&0&-8&0 \\ 1&3&0 &-4 & 0 \\ \end{array} \right]\)

{ 2 } - Applying the operation R{2} -> 2R{2} - R{1}, to make the second 0.

\(\left[ \begin{array}{cccc|c} 2&6&0&-8&0\\1&3&0&-4&0 \\ \end{array} \right] \;\;\;\;\;\;R_2 \rightarrow 2R_2 - R_1\)

\(\left[ \begin{array}{cccc|c} 2 & 6 & 0 & -8 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ \end{array} \right]\)

{ 3 } - Using R{1} -> R{1}/2

\(\left[ \begin{array}{cccc|c} 2&6&0&-8&0\\0&0&0&0&0\\ \end{array} \right]  \;\;R_1 \rightarrow \dfrac{1}{2} R_1\)

{ 4 } - Following equation can be deducted as

\(x_1 + 3x_2 - 4x_4 =0\)

{ 5 } - We can write the parametric form as -

\(x = x_2 \left[ \begin{array}{c} -3 \\ 1 \\ 0 \\ 0 \\ \end{array} \right] + x_3 \left[ \begin{array}{c} 0 \\ 0 \\ 1 \\ 0 \\ \end{array} \right] + x_4 \left[ \begin{array}{c} 4 \\ 0 \\ 0 \\ 1 \\ \end{array} \right]\)

Therefore, the parametric form can be written as -

\(x = x_2 \left[ \begin{array}{c} -3 \\ 1 \\ 0 \\ 0 \\ \end{array} \right] + x_3 \left[ \begin{array}{c} 0 \\ 0 \\ 1 \\ 0 \\ \end{array} \right] + x_4 \left[ \begin{array}{c} 4 \\ 0 \\ 0 \\ 1 \\ \end{array} \right]\)

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