2. Mai skated x miles, and Clare skated farther than that. Write an expression for the
distance Clare skated.

The tennis ball's initial height would be 25 feet.

Given is that a tennis ball is dropped from a certain height. Its height in feet is given by {h} = -16t² + 25 represents the time in seconds after launch.

For the initial height of the tennis ball, substitute the value of {t} = 0. We can write -

h{o} = - 16 x 0 x 0 + 25

h{o} = 25

Therefore, the tennis ball's initial height would be 25 feet.

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It will take Rachel 5 months to pay off her debt at her current monthly payment rate.

Interest rate is a percentage that represents the amount of interest charged by a lender to a borrower for the use of money. It is used to calculate the interest that will accrue on a loan or deposit over a specific period of time, and is usually expressed as an annual rate. It is a key component in determining the cost of borrowing money, and affects the amount that must be paid back to the lender, including the principal amount and any additional interest charges.

Rachel's monthly payment of $320 will only cover the interest on her debt and will not significantly reduce the outstanding balance. She would need to pay more each month or find a way to reduce the interest rate in order to pay off her debt in a reasonable amount of time.

To calculate the time it will take for Rachel to pay off her debt, we can use the following formula:

n = ceil(log(P/A) / log(1 + r))

where n is the number of payments, P is the initial balance, A is the monthly payment, and r is the monthly interest rate (expressed as a decimal).

In this case, P = $8,975, A = $320, and r = 17% / 12 = 0.17 / 12 = 0.01417.

So, n = ceil(log($8975 / $320) / log(1 + 0.01417)) = ceil(log(28.09375) / log(1.01417)) = ceil(4.3626) = 5.

It will take Rachel 5 months to pay off her debt at her current monthly payment rate. This means that it will take her just over 4 years to pay off the debt, assuming no additional purchases are made on the card and the interest rate does not change.

As for shopping for a new card, Rachel should consider a card with a lower interest rate. This will allow her to pay off her debt more quickly and save money in interest charges. She may also consider a balance transfer card with an introductory 0% interest rate, which would give her time to pay off the debt without accruing interest. However, she should be aware of any balance transfer fees that may apply. It is best for Rachel to compare options and read the fine print before making a decision.

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The value of y is 4√3

Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.

Also , the ratio of corresponding sides of similar triangles are equal.

There are two triangles that are similar

Therefore;

y /16 = 4/y

y² = 48

y = √48

y = √16 × √ 3

y = 4√3

Therefore, the value of y is 4√3

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The probability of picking a prime number and then picking a prime number is 1/6.

The probability of picking a prime number and then picking a prime number is 0.

There are two prime numbers in the set: 7 and 9. The probability of picking a prime number on the first draw is 2/4 = 1/2.

The probability of picking a prime number on the second draw, without putting the first card back, is 1/3.

The probability of both events happening is 1/2 × 1/3 = 1/6.

Therefore, the answer is 1/6.

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9514 1404 393

Answer:

  186

Step-by-step explanation:

Let b represent the number of boxes in the truck. Then for the weight limit to be met, we require ...

  3512 +16b < 6500

  16b < 2988

  b < 186.75

The maximum number of boxes is 186.

9514 1404 393

Answer:

  yes

Step-by-step explanation:

A horsepower is on the order of 746 watts*, so 2 1/2 times that will be less than 2500. The motor can be used to drive the fan.

_____

* "horsepower" has several different definitions, depending on the application and the units system being used. All are less than 1000 W, so the above conclusion is valid in any case.

9414 1404 393

Answer:

  $1.80, 2.90, 4.00, 10.90

  not proportional

Step-by-step explanation:

For some distance d, we have a charge f(d) that is ...

  \(f(d)=\begin{cases}1.00&0\le d\le0.1\\1.00+0.10\cdot\dfrac{(d-0.1)}{0.10}&0.1<d\end{cases}\)

for d > 0.1, this simplifies to d +0.9.

Then the charges are ...

  \(\begin{array}{cc}\underline{\text{miles}}&\underline{\text{charge}}\\9/10&1.80\\2&2.90\\3\ 1/10&4.00\\10&10.90\end{array}\)

The different relation for the first 1/10 mile indicates ...

  the relationship is not proportional.

Answer:

We cannot agree with Andre because x = 3.

Step-by-step explanation:

Assuming the diagram is a weighing scale which can also be represented as an equation having two sides that is balanced. We can express the situation as follows using equation:

x + 2 = 5

Solve for x

x + 2 - 2 = 5 - 2 (subtraction property of equality)

x = 3

If you plug in the value of x on the diagram given, the scale becomes balance on each side.

Therefore, x = 3. Andre is wrong and we cannot agree with Andre.

Step 1: Pick any two points

The points are represented as (x1,y1), (x2,y2).

where x1= -4, y1= -8, x2= 0, y2= 4

Step 2: Write out the formula of the equation to use

Step 3: Substituting the values and to get the equation

The equation that represents the graph is y= 3x+4.

Option A is the correct answer.

Answer:

C = 290

Step-by-step explanation:

Solve for C

c = 900 - 610

c = 290

Answer:

C   x² - 2x - 1 = 3

Step-by-step explanation:

x² - 2x - 1 = 3

x² - 2x - 4 = 0

a = 1

b = -2

c = -4

x = (-b ±√(b² - 4ac)) / 2a

Answer:

-1+\(\sqrt{x} 5\)

Step-by-step explanation:

Answer:

the area of the rectangle is 35.25 square meters.

Step-by-step explanation:

To find the area of a rectangle, we multiply the length by the width.

First, we need to convert the mixed numbers to improper fractions to make the multiplication easier:

4 and 2/4 = 4 + 2/4 = 16/4 + 2/4 = 18/4

7 and 5/6 = 7 + 5/6 = 42/6 + 5/6 = 47/6

Now we can multiply the length and width:

Area = (18/4) * (47/6)

Area = (9/2) * (47/6) (canceling the common factor of 2 between 18/4 and 6 in 47/6)

Area = (9 * 47) / (2 * 6)

Area = 423/12

Area = 35.25

Therefore, the area of the rectangle is 35.25 square meters.

The capacity or volume of the rectangular water tank is 100000 cm³.

volume of a rectangular water tank = base area × height

where

Therefore,

base area = 1000 cm²

height = 100 cm

Therefore,

capacity(volume) of the water tank = 1000 × 100 = 100000 cm³

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Plot the equation y = 8x on the graph.

The curve is linear and passing through the origin.

Answer: x=12.37 (2 decimal place) and the second box is √153

Step-by-step explanation:

You would have to use pythagoras theorem.

The formula for the short side is x²=c²-b²

The formula with the numbers in it is x²=13²-4²

13²=169

4²=16

x²=169-16

x²=153

To find x on its own you would have to square root 153.

x=12.37 (2 decimal places)

Hope this helps :)

The difference in temperature between Rome and Munich is given as follows:

6ºC.

The difference in temperature between Rome and Munich is given by the subtraction of Rome's temperature by Munich's temperature.

The bar graph in the context of this problem gives the temperature for each town.

From the bar graph given by the image presented at the end of the answer, the temperatures for Rome and Munich are given as follows:

Hence the difference in temperature between Rome and Munich is given as follows:

11 - 5 = 6ºC.

The graph is given by the image presented at the end of the answer.

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Both g(x) = 5 - x² and h(x) = \(5 - e^(6-^x^)\)have the same range as f(x) = -2√(x) - 3 + 8, which is (-∞, 5].

To determine which function has the same range as f(x) = -2√(x) - 3 + 8, we need to first find the range of f(x).

The square root function √(x) takes non-negative values as input and gives non-negative outputs, so the expression -2√(x) will always be non-positive. Therefore, the range of f(x) will be all real numbers less than or equal to -3 + 8, which is 5.

In other words, the range of f(x) is (-∞, 5].

So, we need to find a function whose range is also (-∞, 5]. One possible function is g(x) = 5 - x². We can see that when x is zero, g(x) is at its maximum value of 5, and as we increase or decrease x, g(x) will decrease, eventually approaching negative infinity.

Another possible function is h(x) = 5 - e^(-x). When x is negative infinity, e^(-x) is approaching positive infinity, so h(x) is approaching 0. As we increase x, e^(-x) is approaching zero, so h(x) is approaching 5.

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Answer

The proportion is true.

Explanation

We are asked to check if the proportion is the same

(10/20) = (1/2)

(8/16) = (1/2)

(10/20) = (8/16)

(1/2) = (1/2)

Hope this Helps!!!

Here BD is perpendicular bisector

So

\(\\ \tt\hookrightarrow UV=74+74=148\)

Apply Pythagorean theorem

\(\\ \tt\hookrightarrow BD^2=UD^2-UB^2=UD^2-VD^2\)

\(\\ \tt\hookrightarrow TC^2=TD^2-CD^2\)

\(\\ \tt\hookrightarrow TC^2=78^2-30^2\)

\(\\ \tt\hookrightarrow TC^2=6084-900=5184\)

\(\\ \tt\hookrightarrow TC=72\)

Answer:

UV = 148

VD = 78

TC = 72

Step-by-step explanation:

BD is the perpendicular bisector of side UV.

Therefore, ΔUDV is an isosceles triangle.

This implies that UD = VD and BV = UB so UV = 2 x BV

ΔUDC is a right triangle.

Given CD = 30 and UD = 78,

and using Pythagoras' Theorem, we can calculate UC:

UC = √(UD² - CD²)

⇒ UC = √(78² - 30²)

⇒ UC = 72

CD is the perpendicular bisector of side UT.

Therefore, ΔUDT is an isosceles triangle, so UC = TC

Since UC = 72, then TC = 72

The degree of the polynomial,

2x³y²z+x²z is 3.

Degree of the polynomial is highest occurring power .

so , 3 is highest power so the degree of polynomial is 3.

A polynomial's degree is the largest exponential power in the polynomial equation. To determine the degree of any polynomial, just variables are evaluated; coefficients are ignored. The degree of a polynomial for an nth degree polynomial function with real coefficients and x as the variable with the largest power n, where n accepts whole integer values

A polynomial's degree is the maximum power of a variable in the polynomial equation. Only terms with variables are considered for determining the degree of a polynomial function. The degree of a polynomial is determined by the variable term with the largest exponential power in the polynomial.

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A line segment that measures 92 millimeters in length can be drawn using scale.

Given that,

A line segment has to be drawn which has a measure of length 92 millimeters.

We know that,

10 millimeters = 1 centimeter

1 millimeter = 1/10 centimeters

92 millimeters = 92/10 = 9.2 centimeters

So it is enough to draw a line segment of length 9.2 centimeters.

In the scale, between a centimeter, there are 9 small lines which indicates the millimeters.

In between 9 and 10, there are 9 lines which indicates, 9.1, 9.2, 9.3, ....., 9.9 and after that is 10 cm.

So draw a line segment starting from 0 to 9.2.

Hence the line segment is drawn with scale.

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Answer:

A. 64/125

B. 124/125.

Step-by-step explanation:

A).  As the events ( germinate or not germinate) are independent we multiply the probabilities.

Prob(All seeds germinate) = 4/5*4/5*4/5 =  64/125.

B). Probability of at least one germinating =  1 - probability that none germinate

Probability of  1 seed not germinating = 1 -45 = 1/5.

So Prob(at least one germinating)

= 1 - (1/5 * 1/5 * 1/5)

= 1 - 1/125

= 124/125.

The probability that all 3 seeds will germinate is 64/125 and the probability that at least one of the seeds will germinate is 124/125.

The probability of an event occurring is defined by probability.

Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.

(A)

The probability of all seeds will germinate will be the product of individual probability since all events are independent.

4/5 × 4/5 × 4/5 =  64/125.

B)

Probability of at least one germinating =  1 - the probability that none germinate

The probability of  1 seed not germinating will be given as,

1 -4/5 = 1/5

Thus, the probability of all three seeds not germinating = 1/5 ×  1/5 ×  1/5

Thus, the probability that at least 1 of the seeds will germinate.

⇒ 1 - (1/5 × 1/5 × 1/5)

⇒ 1 - 1/125

⇒ 124/125

Hence "The probability that all 3 seeds will germinate is 64/125 and the probability that at least one of the seeds will germinate is 124/125".

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Answer:

6.5% of 6000$=6000$x6.5/100=390$

amount of interest = 390$x2=780$

Compound Interest

n=1, 2

Po=6000$

Pn=Po(1+r)^n

Pn=6000$1+6.5%)^n

Pn=6000$(1.065)^n

P1=6000$(1.065)^1=6390$

P2=6000$(1.065)^2=6805.35