Abby's credit card statement shows a balance of $135.50 at the beginning of the month. During the month she makes purchases of $63.83. Each month a 1.5% interest charge is added to the statement balance. Abby then makes a payment of $50.00. What is her new balance?

Answer:

d.  2 solutions

Step-by-step explanation:

To find the number of solution present in the equation given, we will follow the steps below:

16X²= 100

Take the square root of both-side

√16X²= √100

4x = ± 10

Divide both-side of the equation by 4

4x/4 = ± 10/4

x =  ± \(\frac{5}{2}\)

x = -\(\frac{5}{2}\)   or    

It has two solutions

The given equation is 16X^2 = 100.

We can solve for X by dividing both sides by 16 and then taking the square root of both sides:

16X^2 = 100

X^2 = 100/16

X^2 = 6.25

Taking the square root of both sides:

X = ±2.5

So, there are 2 solutions to the equation: X = 2.5 and X = -2.5.

Therefore, the answer is (D) 2 solutions.

Answer:y=(-2x+1) (x+1)

Step-by-step explanation:

2x+y=-2x^2 +3x+1

y=-2x^2+x+1

y=-2x^2 -2x+x+1

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

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

The area being measured will not match the Riemann sum. By employing ever smaller forms to divide the area more precisely, this mistake can be minimized. The sum approaches the area as the shapes become ever-smaller.

A specific type of approximation of an integral by a finite sum in mathematics is known as a Riemann sum. It bears the name of the German mathematician Bernhard Riemann from the nineteenth century. Approximating the area of functions or lines on a graph, as well as the length of curves and other approximations, is a highly typical use.

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h(2.5) = 47, and this mean that the height of the football after 2.5 seconds is 47 feet, using the quadratic function h(t) = -16t² + 58t + 2.

In the question, we are given that during a local high school football game, the height of h feet of a football after t seconds can be represented by the quadratic function h(t) = -16t² + 58t + 2.

We are asked to find h(2.5) and explain its meaning.

To find h(2.5), we substitute t = 2.5, in the quadratic function h(t) = -16t² + 58t + 2.

Thus,

h(2.5) = - 16(2.5)² + 58(2.5) + 2,

or, h(2.5) = - 16(6.25) + 145 + 2,

or, h(2.5) = -100 + 147,

or, h(2.5) = 47.

Hence, h(2.5) = 47, and this mean that the height of the football after 2.5 seconds is 47 feet, using the quadratic function h(t) = -16t² + 58t + 2.

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Answer:

There are 400 possible dinners.

Step-by-step explanation:

There are 8 dishes to choose from column A. For each of these 8 dishes, there are 10 dishes to pair with. For each of these 10 dishes, there are 5 dishes to go with from column C.

Therefore, multiply to get \(8\cdot 10\cdot 5=\boxed{400}\) possible dinners.

*Note: Since the order of which you choose is fixed, we do not need to account for rearrangements of the same three dishes.

Recursive algorithm for computing n²: 1. If n equals 0, return 0 (base case), 2. Otherwise, recursively compute (n-1)², 3. Compute n² by using the formula: n² = (n-1)² + 2n - 1.

What is recursive algorithm?

A recursive algorithm is a problem-solving approach where a function calls itself to solve smaller instances of the same problem until a base case is reached.

To prove the correctness of the recursive algorithm for computing n², we will use mathematical induction.

Base case: For n = 0, the algorithm returns 0, which is correct since 0² equals 0.

Inductive step: Assume that the algorithm correctly computes n² for a given nonnegative integer k, i.e., n² = k². Now, we will show that it also computes (k+1)² correctly.

According to the algorithm, (k+1)² is computed by first calculating k² using the recursive step, and then applying the formula n² = (n-1)² + 2n - 1.

Using the assumption, we have k² = (k-1)² + 2k - 1.

Expanding (k-1)², we get k² - 2k + 1 + 2k - 1 = k².

Therefore, (k+1)² = k² + 2(k+1) - 1, which simplifies to (k+1)² = k² + 2k + 1.

This matches the definition of (k+1)², so the algorithm correctly computes (k+1)².

By induction, we have proven that the algorithm correctly computes n² for any nonnegative integer n.

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The correct value of x will be 9 as it is alternate angles which are equal  so 4x+2=7x-25 for the given set of intersecting lines.

An angle is a figure in Euclidean geometry made up of two rays that share a common endpoint and are referred to as the angle's sides and vertex, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

When a transversal intersects two coplanar lines, alternate interior angles are created. They are located on the transverse sides of the parallel lines, but on the inner side of the parallel lines. At two different locations, the transversal passes through the two lines that are coplanar.

Here,

4x+2=7x-25

3x=27

x=9

The value of x would be 9 and the value of angle is 38°.

Given that the alternate angles are equal, 4x+2=7x-25 for the given set of intersecting lines, the proper value of x will be 9.

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Answer:

Rewriting the expression \((3^\frac{2}{3})^\frac{1}{6}\) with a rational exponent as a radical expression we get \(\mathbf{\sqrt[9]{3} }\)

Step-by-step explanation:

We need to rewrite the expression \((3^\frac{2}{3})^\frac{1}{6}\) with a rational exponent as a radical expression.

The expression given is:

\((3^\frac{2}{3})^\frac{1}{6}\)

First we will simply the expression using exponent rule \((a^m)^n=a^{mn}\)

\((3^\frac{2}{3})^\frac{1}{6}\\=(3^\frac{2}{18})\)

As we know 2 and 18 are both divisible by 2, we can write

\(=(3^\frac{1}{9})\)

Now we know that \(a^\frac{1}{9}=\sqrt[9]{a}\)

Using this we get

\(=\sqrt[9]{3}\)

So, rewriting the expression \((3^\frac{2}{3})^\frac{1}{6}\) with a rational exponent as a radical expression we get \(\mathbf{\sqrt[9]{3} }\)

Answer:

78.4 meters

Step-by-step explanation:

Solving a simple linear equation we can see that the value of b is 7.

Here we have the point (5, b - 7) and we want to find the value of b such that the point lies on the x-axis.

Remember that a point lies on the x-axis only if the y-value is zero, so we need to solve the linear equation:

b - 7 = 0

Adding 7 in both sides we get:

b - 7+ 7 = 0 + 7

b = 7

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Answer:

12 carrots

Step-by-step explanation:

If there is 3 times as much cabbages as there is carrots, and there is 36 cabbages then you would do 36/3 because of the 3 times as much.  The answer would be 12 carrots.

36/3=12

Answer:

4: Matthias

5:8

6: 13 microprocessors

7: No, the poster wouldn't fit

8: 0.2m

9:Yes

10:No

Step-by-step explanation:

for 6:

for 7:

for 8:

for 9:

for 10:

4- Matthias

5-8

6- 13 microprocessors

7- No, the poster wouldn't fit

8- 0.2m

9-Yes

10-No

Step-by-step explanation:

6-   (3 .5)^2  in = 12.25 in^2

      12.25 / 49 / 54= about 13 microprocessors

7-    if you multiply 40*30 you get 1200

      if you multiply 36*36 you get 1296

8-   The edge length of the unit cube is 0.512 which is 0.8m

      the edge length of the new cube is the root of 1 which is 1m

      so you would subtract 1-0.8 and that will give you 0.2 m.

9-    cube root for 729 wouldn't be an integer, so it can't be a perfect               cube or square. 36 would be an exponent expression of 729.

10-     the roots of 1 and -1 are equal, but not the roots of 0, the roots of 0 are 0.

The volume of Darby is given as 76 in'^2

Volume = (4/3)πr³

First, we need to find the radius (r) of the sphere. Since the diameter is given as 21/4, we can find the radius by dividing the diameter by 2:

radius (r) = (21/4) / 2 = 21/8

Now, we can calculate the volume using the formula:

Volume = (4/3)π(21/8)³

Volume = (4/3)π(9261/512) (since (21/8)³ = 9261/512)

Now, we can find the numerical value of the volume:

Volume ≈ (4/3) * 3.14159 * (9261/512)

Volume ≈ 4.18879 * 18.10352

Volume ≈ 75.89438

Rounding the volume to the nearest whole number:

Volume ≈ 76

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The density of the fluid is 1.602cm³

We should know that density involves the content per 1000 the cubical box can contain.

Volume of the cubical box is V=S³

The length of the box is given as 5cm

Substitute in the formula to get Volume=5³

Volume=125

The pressures are summed to get

594+1133

Total pressure = 1727

Subtract the volume of the cubibic box

= 1727-125

=1602

Divide by 1000

Density = volume/1000

Density=1.602cm³

In conclusion, the density of the fluid is 1.602cm³

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Answer:

A five units right and three units up

Step-by-step explanation:

take coordinate C for example and count how many spaces you need to go either right or left and then up and down for the two triangles to be in the same place

The dimensions of the rectangle will be 16 inches long and 7 inches wide,

Let W be the rectangle's width and L its length.

The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be

Area of the rectangle = L × W square units

The length of a rectangular poster is 2 more inches than two times its width. The area of the poster is 112 square inches. Then the equations are given as,

LW = 112           ...1

L = 2W + 2       ...2

From equations 1 and 2, then we have

(2W + 2)W = 112

2W² + 2W - 112 = 0

W² + W - 56 = 0

W² + 8W - 7W - 56 = 0

W(W + 8) - 7(W + 7) = 0

(W + 8)(W - 7) = 0

W = 7, -8

Neglect - 8 because of negative signs. Then the length is given as,

L = 2 x 7 + 2

L = 14 + 2

L = 16

The dimensions of the rectangle will be 16 inches long and 7 inches wide,

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Answer:

8 4 7 5 2

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

i believe its A the rest dont make that much sense

Answer: yes

Step-by-step explanation:

x=3, y=8. You need to plug in -1 into x and -8 into y because it’s (x,y)

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The covered employee worked for 9 hours of overtime pay for the month.

In this problem, a covered employee who is paid monthly works 38, 42, 35 and 47 hours during 4 consecutive weeks. We need to find out how many hours of overtime pay is he required to receive for the month.

Let us consider, if the employee works for 38 hours, then it is considered to be regular hours.

If the employee works for more than 40 hours, then it is considered to be overtime hours.

Week 1 : Regular hours = 38, Overtime hours = 0

Week 2 : Regular hours = 42, Overtime hours = 2

Week 3 : Regular hours = 35, Overtime hours = 0

Week 4 : Regular hours = 40, Overtime hours = 7

Total regular hours = 38 + 42 + 35 + 40 = 155

Total overtime hours = 0 + 2 + 0 + 7 = 9

Thus, the covered employee worked for 9 hours of overtime pay for the month.

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Hence if purchasing power parity holds true the price hockey puck in the USA IS 65.70.

Purchasing power parity is the measurement of expenses in distinctive nations that uses the expenses of particular goods to compare absolutely the buying power of the nation's currencies, and, to a degree, their people's residing requirements.

The purchasing power parity conversion issue is the number of units of a rustic's foreign money required to shop for equal amounts of goods and services within the domestic market as the U.S. greenback might purchase within the united states of America. This conversion element is for GDP.

Purchasing power parity (PPP) is essential as it permits economists to examine unique economies, mostly the financial productivity and the standard of dwelling among international locations. It seeks to equalize currencies to decide the fee of a basket of products.

Price of hockey pucks in the US

= 1/1.2937 Canadian dollars

Price of hockey pucks in Canada = 85 Canadian dollars,

= 1.2937 Canadian dollars then  85 Canadian dollars,

We will use cross multiplication

= 1× 85/1.2937= 65.70

Hence if PPT holds true the price hockey puck in the USA is 65.70

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Answer:

$0.02

Step-by-step explanation:

20/1,000 = 0.02

1350000 because 20x15 and 30x15

Answer:135000 ft^2

Step-by-step explanation:

Answer: 3

Step-by-step explanation:

6y, 4y, and 2a

Answer: 0 = 23

Almost positiveee :))

Step-by-step explanation:

If you are buying 5 pounds of candy corn, to make the average cost of the mixture $0.95 per pound, you need to buy 6.67 pounds of licorice.

This is a weighted average problem.

Let:

p = cost of product A

x = number of product A

q = cost of product B

y = number of product B

Then,

cost of mixture of A and B = (p.x + q.y) / (x + y)

Let A = candy corn, B = licorice

Parameters given:

p = $0.75 per pound

x = 5 pound

q = $1.10 per pound

cost of the mixture =$0.95 per pound

Hence,

0.95 = (0.75 . 5 + 1.1 . y) / (5 + y)

4.75 +0.95 y = 3.75 + 1.1 y

0.15 y = 1

y = 6.67 pound

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Answer:

819

Step-by-step explanation:

Answer:

1. Mean : 85.6

2. Median : 90

3. Mode : 95

4. Range : 35

Step-by-step explanation:

1. For Mean, you add up all the terms and divide the resulting sum by the number of terms. In this case there were 9 terms that added up to 770, and when you divided that result by 9, the answer was 85.555 repeating. Since the question asks to round to the nearest tenth 85.6 represents the correct mean or average of the class.

2. To find the median, line up all the numbers in order from least to greatest. Like so :

60,75,75,90,90,95,95,95,95

In order to find the median, find the middle term. Since there are 9 terms, the middle term will be the fifth one. In this case, the answer was 90.

3. Mode represents the number that appears the most in a data set. Look at the 9 terms and find the one that appears the most. In this case it is 90.

4. Lastly, to find the range, subtract the lowest value in the data set from the highest one. 95 is the highest and 60 is the lowest. Do \(95-60\) and you will get an answer of 35.

Hope this helps!

Answer:

Mean: 85.6

Median: 90

Mode: 95

Range: 35

Step-by-step explanation:

Mean: Add up all the value and divide by the number of values you have.

75 + 95 + 90 + 95 + 60 + 95 + 75 + 95 + 90 = 770

770 / 9 = 85.6

Median: Rearrange in increasing order + look at middle number

60, 75, 75, 90, 90, 95, 95, 95, 95

Mode: Number that shows up the most.

95 shows up 4 times.

Range: Maximum - Minimum.

95 - 60 = 35.

Answer:

Approximately 0.1894 or 18.94% of the population is less than 10.0.

Step-by-step explanation:

On use the z-score formula and the standard normal distribution.

a. To compute the z-value associated with 14.3, we use the formula:z = (x - μ) / σWhere:

x = 14.3 (the value)

μ = 12.2 (mean)

σ = 2.5 (standard deviation)

Substituting the values:

z = (14.3 - 12.2) / 2.5

z = 2.1 / 2.5

z ≈ 0.84

Therefore, the z-value associated with 14.3 is approximately 0.84.

b. To obtain the proportion of the population between 12.2 and 14.3, we need to get the area under the standard normal distribution curve between the corresponding z-scores.

Using a standard normal distribution table or a calculator, we can find the area associated with each z-score.The z-value for 12.2 can be calculated using the same formula as in part a:

z1 = (12.2 - 12.2) / 2.5

z1 = 0 / 2.5

z1 = 0

The z-value for 14.3 is already known from part a: z2 ≈ 0.84.

Now, we obtain the proportion by subtracting the area associated with z1 from the area associated with z2:

Proportion = Area(z1 < z < z2)

Using a standard normal distribution table or a calculator, we obtain:

Area(z < 0) ≈ 0.5000 (from the table)

Area(z < 0.84) ≈ 0.7995 (from the table)

Proportion = 0.7995 - 0.5000

Proportion ≈ 0.2995

Therefore, approximately 0.2995 or 29.95% of the population is between 12.2 and 14.3.

c. To obtain the proportion of the population less than 10.0, we need to get the area under the standard normal distribution curve to the left of the corresponding z-score.Using the z-score formula:z = (x - μ) / σ

Where:

x = 10.0 (the value)

μ = 12.2 (mean)

σ = 2.5 (standard deviation)

Substituting the values:

z = (10.0 - 12.2) / 2.5

z = -2.2 / 2.5

z ≈ -0.88

Now, we obtain the proportion by looking up the area associated with z ≈ -0.88 using a standard normal distribution table or a calculator:

Area(z < -0.88) ≈ 0.1894 (from the table)

Therefore, approximately 0.1894 or 18.94% of the population is less than 10.0.

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