(a)
Find the hypotenuse, c, of the triangle.
4
B
12
Figure not drawn to scale

The inequality that represents Rita saving money from the second option is 0.059x < 0.49 + 0.019x

"Information available from the question"

In the question:

1. Pay $0. 49, plus an additional $0. 019 per minute.

2. Pay $0. 059 per minute.

Now, According to the question:

How to determine the inequality that represents the statement?

We have the following parameters that can be used in our computation:

1. Pay $0.49, plus an additional $0.019 per minute.

2. Pay $0.059 per minute.

These statements can be represented as

Option 1: y = 0.49 + 0.019x

Option 2: y = 0.059x

Where y is the total amount and x is the number of minutes

When she saves money, we have

Option 2 < Option 1

Substitute the known values in the above equation, so, we have the following representation

0.059x < 0.49 + 0.019x.

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Answer:

If the probability of getting a two on a biased dice is 0.1, then the probability of not getting a two is 0.9.

To find the expected number of times a two is rolled in 250 rolls:

Expected value = (probability of an event occurring) x (number of trials)

Expected number of twos = 0.1 x 250 = 25

To find the expected number of times a number other than two is rolled in 250 rolls:

Expected number of non-twos = 0.9 x 250 = 225

Therefore, we would expect to roll a two 25 times and a number other than two 225 times in 250 rolls of this biased dice.

Answer:

0.790, or 79%.

Step-by-step explanation:

If the probability of getting a two on a biased dice is 0.1, then the probability of not getting a two is 0.9.

We can use the binomial distribution to calculate the probability of getting a certain number of twos in 250 rolls of the dice. The formula for the binomial distribution is:

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

Where:

P(X = k) is the probability of getting exactly k twos

n is the number of trials (250 rolls)

k is the number of successes (getting a two)

p is the probability of success (0.1)

(1-p) is the probability of failure (0.9)

C(n, k) is the number of ways to choose k successes from n trials (n choose k)

To calculate the probability of getting exactly k twos in 250 rolls, we plug in the values for n, k, p, and (1-p) into the formula:

P(X = k) = C(250, k) * 0.1^k * 0.9^(250-k)

We can use a calculator or a software program to find the probabilities for different values of k. Here are some examples:

The probability of getting no twos (k = 0) is P(X = 0) = C(250, 0) * 0.1^0 * 0.9^250 = 0.057

The probability of getting exactly one two (k = 1) is P(X = 1) = C(250, 1) * 0.1^1 * 0.9^249 = 0.153

The probability of getting at least two twos (k >= 2) is the complement of the probability of getting zero or one two:

P(X >= 2) = 1 - P(X = 0) - P(X = 1)

= 1 - 0.057 - 0.153

= 0.790

Therefore, the probability of getting at least two twos in 250 rolls of the biased dice is approximately 0.790, or 79%.

please leave a star

Answer:

\(\frac{131}{500}\)

Hope this helps!!

Answer:

131/500

Step-by-step explanation:

0.262 = 262/1000

\( = \frac{262 \div 2}{1000 \div 2} \)

= 131/500

The difference quotient for the given function is 9 -2/h.

The difference quotient for the given function can be calculated as:

[f(x+h) - f(x)]/h

= [(3(x+h)² - 2(x+h) + 5) - (3x² - 2x + 5)]/h

= (3x² + 6xh + 3h² - 2x - 2h + 5 - 3x² + 2x - 5)/h

= (6xh + 3h² - 2h)/h

= (6x + 3h -2)/h

Simplifying the expression further, we get:

(6x + 3h -2)/h = 6 + 3h/h -2/h

= 6 + 3 -2/h

= 9-2/h

Therefore, the difference quotient for the given function is 9 -2/h.

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"Your question is incomplete, probably the complete question/missing part is:"

Find the difference quotient [f(x+h)-f(x)]/h, where h≠0, for the function below.

f(x)=3x² -2x+5. Simplify your answer as much as possible.

Answer:

7.17 km

Step-by-step explanation:

Given that:

Distance in kilometers traveled by motorcycle = 3.85 km

Distance in kilometers traveled by horse = 3.32 km

Total distance of journey in kilometers /

3.85 km + 3.32 km

= 7.17 kilometers

Answer:

$1.70

Step-by-step explanation:

To figure out how much each apple costs, divide $1.50 by the quantity of apples (6). The answer to that is $0.25, so multiply it by the two apples to get $0.50.

For the oranges, divide $3 by 5. The answer for that is $0.60. Multiply that by the two oranges to get $1.20.

Then, add $0.50 to $1.20 to get a total of $1.70

Answer:

$1.70

Step-by-step explanation:

We know that you can buy 6 apples for $1.50 and 5 oranges for $3.00. So let's look at the cost for one individual apple first.

To find the amount/apple we can divide $1.50 by 6. Here's another way to look at it:

Assume A is cost per apple.

6A = $1.50

6A/6 = $1.50/6

A = $0.25

Now to find the amount for 2 apples, you want to multiply the amount it costs for one apple by 2, because you are multiplying the quantity by 2 as well.

A= $0.25

A *2 = $0.25 * 2

2A = $0.50

So for two apples, it is 50 cents.

We can use a similar process for oranges but with a different price and quantity.

Assume R is cost per orange.

5R = $3.00

5R/5 = $3.00/5

R = $0.60

To find the amount for two oranges we multiply the cost by two.

R = $0.60

R*2 = $0.60*2

2R = $1.20

Finally, we want the total amount for apples AND oranges so we find the sum.

$0.50 + $1.20 = $1.70

The integral ∫10x^p * ln(x) dx converges for all values of p except p = -1.

To determine the values of p for which the integral ∫10x^p * ln(x) dx converges, we need to consider the convergence of the integrand for different values of p. The integral will converge if the integrand is well-behaved and does not exhibit any divergence.

Let's analyze the integrand in two separate cases:

Case 1: p ≠ -1

When p ≠ -1, the integrand is well-defined for all x > 0. We can proceed with evaluating the integral.

∫10x^p * ln(x) dx = [x^(p+1) * ln(x)] / (p+1) + C

To calculate the value of the integral for a specific value of p, we can substitute the limits of integration into the antiderivative expression and evaluate the resulting expression.

Case 2: p = -1

When p = -1, the integrand becomes 10x^(-1) * ln(x), which poses a potential issue at x = 0. To determine if the integral converges for this case, we need to examine the behavior of the integrand near x = 0.

As x approaches 0, the expression ln(x) approaches negative infinity, which would cause the integrand to diverge. Therefore, for p = -1, the integral does not converge.

In summary, the integral ∫10x^p * ln(x) dx converges for all values of p except p = -1.

Please note that when evaluating the definite integral for specific limits of integration, you should substitute the limits into the antiderivative expression and then calculate the difference of the resulting expressions evaluated at the upper and lower limits.

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If the equation y = 760+22t represents the total number of students who graduated from Andrea's school t years after 1998, then the number of students who graduated from Andrea's school each year is 22

The equation is

y = 760 + 22t

Where y is the number of students who graduated from Andrea's school

t is the number of years after 1998

We know

The slope intercept form is

y = mx + b

Where m is the slope of the line

Slope of the line is change in y coordinate with respect to the change in x coordinate.

Here the slope of the line is 22, that is the number of students graduated from Andrea's school each year

Hence, if the equation y = 760+22t represents the total number of students who graduated from Andrea's school t years after 1998, then the number of students who graduated from Andrea's school each year is 22

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Answer:

2/20

Step-by-step explanation:

if you add all of the marbles you will get 20 marbles in total.

The provided table displays the number of hours per week spent playing sports based on gender and grade level. It includes data for grades 3 to 8 and differentiates between boys and girls.

To interpret the table, we observe that each row corresponds to a specific grade level, while the columns represent the gender categories. The numbers within the cells indicate the average hours per week spent playing sports. For example, in grade 3, boys spend 4 hours per week, while girls spend 3 hours per week.

To visually represent this data, a suitable graph would be a grouped bar chart. The x-axis would indicate the grade levels, while the y-axis would represent the number of hours per week. Separate bars would be used for boys and girls, and the height of each bar would correspond to the average number of hours spent playing sports for the respective grade and gender category.

By creating such a chart, we can easily compare the average hours spent playing sports between different grade levels and genders, enabling a visual understanding of the data patterns and potential differences in sports participation.

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Answer:

Slant height = 8 feet.

Step-by-step explanation:

If the perimeter of the square base = 12 then each side of the base = 12/4

= 3  feet and its area = 3*3 = 9 ft^2

The area of one of the triangular sides = 1/2 * 3 * h where h is slant height.

So total surface area = 57 = 9 + 4 * 1.5h

9 + 6h = 57

6h = 48

h = 8 feet.

The completed table with regards to terms of an expression are presented as follows;

     Condition      \({}\)              (6·x + 3) + (5·x - 4)            (-4·y - 16) - 8·y + 10 + 2·y

         Exactly 3 terms          N/A     \({}\)                              N/A

         Exactly 5 terms          N/A         \({}\)                          N/A

Includes a zero pair             No \({}\)                                   No

Uses distributive property   No                                    No

Includes a negative factor   No                                    

Has no like terms                False                                False

Condition       \(8 - \dfrac{1}{2} \cdot \left(4 \cdot x - \dfrac{1}{2} + 12\cdot x -\dfrac{1}{4} \right)\)  0.25·(8·m - 12) - 0.5·(-4·m + 2)

Exactly 3 terms       No                         \({}\)                    No

Exactly 5 terms       Yes                          \({}\)   \({}\)              No

Includes a zero pair No    \({}\)                         \({}\)              Yes

Uses the distributive property Yes            \({}\)             Yes

Includes a negative factor      Yes           \({}\)                Yes

Has no like terms                    No          \({}\)                  No

A mathematical expression is a collection of variables and numbers along with mathematical operators which are all properly arranged.

The details of the conditions in the question are as follows;

Terms of an expression

A term is a subunit of an algebraic expression which are joined together by operators such as addition or subtraction

Zero pair

A zero pair are two numbers that when added together have a zero result

Distributive property

The distributive property of multiplication states that the multiplication of a number or variable by an addend is equivalent to the sum of the multiplication of the number or variable and each member of the addend

Negative factor

A negative factor is a factor that has a negative sign prefix

Like terms

Like terms are terms consisting of identical variables with the same  powers of the variable

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Therefore, the principal is $654.50 when rate of interest is 10% and time period is 16 months.

Percent is a way of expressing a number as a fraction of 100. It is denoted by the symbol "%". Percentages are commonly used to express ratios, proportions, and rates. They are used in many areas of everyday life, such as in finance, business, and statistics.

Here,

The Interest Formula is:

I = P * R * T

where I is the interest earned, P is the principal (initial amount of money), R is the interest rate, and T is the time period.

We can rearrange the formula to solve for P:

P = I / (R * T)

Substituting the given values, we have:

P = 1047.20 / (0.10 * 16)

= $654.50

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Answer:

Answer is D. \(\frac{121}{49}a^8b^2\)

Step-by-step explanation:

We expand the powers.

\(\frac{11}{7}^2*(a^4)^2*(b)^2\\\frac{11}{7}*\frac{11}{7}*(a^4)(a^4)*(b*b)\\\frac{121}{49}*(a^8)*(b^2)\)

when doing variable power you add them together.

a^4*a^4=a^(4+4) , b^1*b^1=b^(1+1)

Answer:

Depends

Step-by-step explanation:

This question is a very advanced question, but this depends on the grape that the raisin was previously.

Answer:

The vertical asymptotes are x=3 and x=-3. The horizontal asymptote is y=20.

Step-by-step explanation:

The given function is

Equate the denominator equal to 0, to find the vertical asymptotes.

Add 9 on both sides.

Taking square root on both sides.

Therefore the vertical asymptotes are x=3 and x=-3.

The given function can be written as

Degree of numerator and denominator are same.If degree of numerator and denominator are same, then horizontal asymptote is

Therefore the horizontal asymptote is y=20.

Step-by-step explanation:

Hope this helps:)

8cos(2x)=4 for the smallest three positive  the smallest three positive solutions are approximately 0.52, 3.67, and 6.83.

To solve the equation 8cos(2x) = 4, we can start by dividing both sides of the equation by 8:

cos(2x) = 4/8

cos(2x) = 1/2

Now, we need to find the values of 2x that satisfy the equation.

Using the inverse cosine function, we can find the solutions for 2x:

2x = ±arccos(1/2)

We know that the cosine function has a period of 2π, so we can add 2πn (where n is an integer) to the solutions to find additional solutions.

Now, let's calculate the solutions for 2x:

2x = arccos(1/2)

2x = π/3 + 2πn

2x = -arccos(1/2)

2x = -π/3 + 2πn

To find the solutions for x, we divide both sides by 2:

x = (π/3 + 2πn) / 2

x = π/6 + πn

x = (-π/3 + 2πn) / 2

x = -π/6 + πn

Now, let's find the smallest three positive solutions by substituting n = 0, 1, and 2:

For n = 0:

x = π/6 ≈ 0.52

For n = 1:

x = π/6 + π = 7π/6 ≈ 3.67

For n = 2:

x = π/6 + 2π = 13π/6 ≈ 6.83

Therefore, the smallest three positive solutions are approximately 0.52, 3.67, and 6.83.

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Answer:

answer is 1

Step-by-step explanation:

Answer:

18 square centimeters

Step-by-step explanation:

To find the area of a rectangle follow the formula, A=lw. Where A is the area, l is the length, and w is the width. So to find the area plug the dimensions into the formula. This would be A=6 x 3, which equals 18. Therefore the answer is 18 centimeters squared.

Answer:

9 cm

Step-by-step explanation:

Area is length x width

3 cm x 3 cm = 9 cm

But if you are doing the problem from the picture it is

A = 6 cm x 3 cm

= 18 cm

Answer:

B) 3b. 10b

Step-by-step explanation:

B) 3b. 10b = (3x10)(bxb) = 30b²

Answer:

the answer is negative 135

Answer:

it hit the ground at 6 sec

Step-by-step explanation:

The taxpayer who would most likely benefit from an installment sale is Allan, who sold a business use car at a net gain that was less than the amount of depreciation.

An installment sale is a transaction in which the sales price is received over a period of time that spans more than one tax year. Installment sales may have tax advantages, which is why taxpayers should consider them.

The taxable profit in an installment sale is not calculated using the entire sales price. Instead, it is calculated by applying the gross profit percentage to each installment's payments received during the year. In general, if an installment sale meets the definition, the taxpayer reports income from the sale as the payments are received, rather than in the year of sale.

However, in some situations, taxpayers might choose to report the entire profit from an installment sale in the year of sale. In such instances, an election to do so must be made.

The difference between the sales price and the adjusted cost basis of the asset is known as the gain. The gain is reduced by selling expenditures to arrive at the net gain. Net gain occurs when the sales price of a commodity is higher than its cost of acquisition and other fees or expenses related to its purchase and sale.

Depreciation is a term used in accounting and finance to describe the systematic decrease in the value of an asset over time due to wear and tear. It is an expense that lowers a company's net income and lowers the value of an asset on the balance sheet.

Hence, Allan, who sold a business use car at a net gain that was less than the amount of depreciation, will most likely benefit from an installment sale.

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The cost per square inch is $0.16 per square inches ( nearest hundredth)

Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

The area of a circular pie = πr²

= 3.14 × (10/2)² since r = d/2

= 3.14 × 5²

= 78.5 square inches

apple pies are sold for a cost of $12.85

Therefore the cost per square inches

= 12.85/78.5

= $0.16(nearest hundredth) per square inches

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Answer:

x=9.3

Step-by-step explanation:

use SohCahToa

in this case u use cos

cos(41°)=7/x

x=7/cos(41)

x=9.275090953

x=9.3

The angle of elevation of the ladder is obtained using trigonometric ratios which is 62.18°.

What is trigonometric ratio?

Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios.

The ladder is leaning 15ft against the side of a house.

The value for hypotenuse is given as 15 ft.

The bottom of the ladder is 7ft away from the side of the house.

The value for base is given as 7 ft.

Apply the trigonometric ratio to find the angle -

cos θ = Base / Hypotenuse

Substitute the values in the equation -

cos θ = 7 / 15

θ = cos^-1 (7/15)

θ = 62.18°

Therefore, the angle value is obtained as 62.18°.

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The perimeter first figure that is made of a square and equilateral triangle is 52 cm.

What exactly are squares?

A square is a two-dimensional planar shape with four equal sides and four 90-degree angles. The features of a rectangle are similar to those of a square, but the distinction is that a rectangle has just its opposing sides equal.

A square's most significant qualities are

The diagonal of a square is divided into two isosceles triangles.

Square area=(side)²

Square perimeter=4*side

Now,

For first figure given that

sides of square are 14 cm in length

and length of side of equilateral triangle are=5 cm

but for finding perimeter of the figure only 3 sides of square and 2 sides of triangle are needed.

So, perimeter=3*14+2*5

=42+10

=52 cm

hence,

         The perimeter first figure 52 cm.

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By usinf Divison method and Prime Factorization, the factors of the polynomial are x=1,2,2

A polynomial is an expression made up of variables, constants, and exponents that is combined using mathematical operations such as addition, subtraction, multiplication, and division.

cubic polynomial = x³ - 5x² + 8x - 4

suppose  x = 1 ,

x - 1 = 0

So, one of the factor = (x - 1)

Now,

By Division method

x³ - 5x² + 8x - 4 = Dividend

 x - 1 = Divisor

x² - 4x + 4 = Quotient

Now for x² - 4x + 4

x² - 2x- 2x + 4

(x-2)(x-2)

x=2,2

so, factors are x=1,2,2

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Answer:

x > − 2

Step-by-step explanation:

If your motive was to solve for x thats your answer, if not good luck!