susan bought a 1 kilogram bag of grape. on the way home, she ate 125 grams of the grapes. how many grams of grapes does susan have left?

To find the tax revenue in 1995 and 2006 for a city with an annual increase of 3.5%, we use the formula for exponential growth. The revenue in 1995 is calculated to be $296,923, and for 2006, it is calculated to be $438,995.

The tax revenue that a small city receives increases by 3.5% per year. To calculate the tax revenue for the years 1995 and 2006, we can use the formula for exponential growth: Final Amount = Initial Amount * (1 + Growth Rate)Number of Years.

For 1995, which is 5 years after 1990, the calculation would be:
Revenue in 1995 = $250,000 * (1 + 0.035)5
Revenue in 1995 = $250,000 * (1.035)5
Revenue in 1995 = $250,000 * 1.18769
Revenue in 1995 = $296,923

Similarly, for 2006, which is 16 years after 1990, the calculation would be:
Revenue in 2006 = $250,000 * (1 + 0.035)16
Revenue in 2006 = $250,000 * (1.035)16
Revenue in 2006 = $250,000 * 1.75598
Revenue in 2006 = $438,995

Final answer:

The value of z where 0.9642 of the area lies between -z and z is found by looking up the area 0.4821 (half of 0.9642) in a Z-table or using the invNorm function with 0.4821 on a normal distribution calculator. This will provide the z-score to be rounded to two decimal places.

Explanation:

You are looking for the value of z such that 0.9642 of the area under the normal distribution curve lies between −z and z. To find this, you'll need to use the properties of the standard normal distribution, commonly represented by a Z-table.

For a symmetrical distribution, half of the area you are interested in would be to the left of 0 and half to the right. Since 0.9642 is the total area between −z and z, we need to find the z-score that corresponds to half of this area from the mean to one end. Specifically, you're looking for the z-score where the area to the left is 0.4821 (0.9642 divided by 2).

Using a Z-table or an inverse normal function on a calculator, you can find the z-score that corresponds to an area of 0.4821. If you're using a Z-table, look up the closest area in the body of the table and find the corresponding Z-score. If you're calculating it (such as with the invNorm function on a calculator like the TI-83 or 84), input the left-tail area. The answer should be rounded to two decimal places.

The calculation would be something similar to invNorm(0.4821, 0, 1), where 0 and 1 are the mean and standard deviation of the standard normal distribution, respectively.

If z represents the variable of the standard normal distribution curve N(0,1), which is symmetrical about z=0, then we look for

P(z)-P(-z)=0.9642=1-2P(-z) => P(-z)=(1-0.9642)/2=0.0179

=>

-z=-2.099192

=> z=2.099192

Check:

P(2.099192)-P(-2.099192)=0.9642

The Symmetric Property of Congruence states that If angle A is equivalent to angle B then the angle B will also be equivalent to angle A .

In the problem it is given that ∠LMN ≅ ∠NSP

So, as per the Symmetric Property of Congruence ∠NSP ≅ ∠LMP

The Symmetric Property of Congruence allows you to say that if ∠LMN ≅ ∠NSP, then ∠NSP ≅ ∠LMN.

Hope this helps..!!

Thank you :)

The correct completion of the statement using the Symmetric Property of Congruence is: If [tex]\( \angle LMN \cong \angle NSP \)[/tex], then [tex]\( \angle NSP \cong \angle LMN \)[/tex].

The Symmetric Property of Congruence states that if two angles are congruent, then the second angle is also congruent to the first. In other words, the order in which the angles are listed does not affect the congruence. Therefore, if [tex]\( \angle LMN \)[/tex] is congruent to [tex]\( \angle NSP \)[/tex], it follows that[tex]\( \angle NSP \)[/tex] is congruent to [tex]\( \angle LMN \)[/tex]. This property is a fundamental aspect of geometry that allows us to reverse the order of the angles in a congruence statement without changing the meaning of the statement.

To calculate the sales tax on the second item, we determined the sales tax rate from the first item and applied it to the second item's cost, resulting in $7.99 sales tax on the second item.

To find the sales tax on the second item, we use the information provided about the first item to determine the rate of sales tax and then apply this rate to the second item. If the first item costs $147 with a sales tax of $14, we can find the sales tax rate by dividing the sales tax by the cost of the item before tax:

Sales tax rate = Sales tax / Price before tax

= $14 / $147

= 0.0952 or 9.52%

Once we have the sales tax rate, we can calculate the sales tax on the second item, which costs $84 before tax:

Amount of sales tax = Price × Rate of sales tax

= $84 × 0.0952

= $7.99 (rounded to the nearest cent)

Therefore, the sales tax on the second item is $7.99.

The numberofpennies() function calculates the total number of pennies by converting dollars to pennies and adding any additional pennies. It multiplies the number of dollars by 100 and adds the extra pennies to find the total.

Function to Calculate Total Number of Pennies

The function numberofpennies() is used to calculate the total number of pennies for a given amount of dollars and optionally, additional pennies. To do this, it converts the dollars into pennies and then adds the additional pennies if they are provided.

Example Function in Python

Here is an example of how one might write the numberofpennies() function in Python:

In this example, the function takes two arguments: dollars, which is a mandatory argument representing the number of dollars, and extra_pennies, which is an optional argument representing additional pennies. The function then returns the total number of pennies by multiplying the number of dollars by 100 and then adding the extra pennies if any.

Part A:

As given,

Base of the triangle = 8x + 2 units

Height of the triangle = 4x − 5 units

Formula to find area of a triangle = [tex]\frac{base * height}{2}[/tex]

= 0.5bh

we have been given base and height, so the area becomes,

area = [tex]\frac{(8x+2)(4x-5)}{2}[/tex]

area = 0.5(8x+2)(4x-5)

= 0.5(32x²-32x-10)

= 16x²-16-5

after factoring it, we get

area = (4x-5)(4x+1) units.

Part B:

It is a degree 2 polynomial as the polynomial has one variable that is x, and the largest exponent of that variable is 2.

Part C:

Part A demonstrates the closure property of polynomials because after multiplying two polynomials we get another polynomial.

Answer:

.56 (C)

Step-by-step explanation:

The simplified answer is y = 1000(1.03)x.

Answer:

3/2

Step-by-step explanation:

To find the slope of the line that contains the points A(3, 2) and B(7, 8), we can use the formula for slope:

slope = (change in y) / (change in x)

Let's calculate the values:

Change in y = 8 - 2 = 6

Change in x = 7 - 3 = 4

Now, we can find the slope:

slope = 6 / 4 = 3/2

Therefore, the slope of the line that contains the points A(3, 2) and B(7, 8) is 3/2.

Answer:

C. 11 is the correct answer

Step-by-step explanation:

The table representing the probabilities of player's batting average is,

                        Left-Handed pitchers         Right-Handed pitchers

Bats Left                    0.285                                      0.175

Bats Right                   0.215                                      0.250

So, when the players bats left 100 times,

The probability of hits he gets when faced by left-handed pitchers = 0.285 × 100 = 28.5

The probability of hits he gets when faced by right-handed pitchers = 0.175 × 100 = 17.5

Thus, the difference in the hits = 28.5 - 17.5 = 11

Hence, the player will get 11 more hits t when he faces left-handed pitchers as opposed to right-handed pitchers.

Answer:

What is the question?yea

Step-by-step explanation:

Answer:

0.1172

Step-by-step explanation:

The formula for the probability in a binomial distribution (n trials, r successes) is

[tex]\binom{n}{r}(p)^r(1-p)^{n-r}[/tex] where p is the probability of success.

For flipping a coin, the probability of success, p, is 0.5.

The number of trials, n, is 10.  The number of successes, r, is 7.  This gives us

[tex]\binom{10}{7}(0.5)^7(1-0.5)^{10-7}\\\\\binom{10}{7}(0.5)^7(0.5)^3=0.1171875 \approx 0.1172[/tex]

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