LaToya has $149.49 in her checking account. During the week she goes to an ATM and withdraws $40. She is
charged a usage fee of $2.50. The following week she deposits her paycheck of $125.27. She writes two checks,
one for $37.99 and the other for $42.68. What is the current balance in her checking account?

The amount of each Marco's payments for the 2 reclining chairs, a coffee table including with shipping cost is found as $182.

The data for the given question-

Thus, the total cost becomes-

Total cost = 2 x reclining chairs + coffee table + shipping cost

Total cost = 2 x 230 + 350 + 100

Total cost = $910

For the amount of each payment when there are 5 equal payments.

Total cost = 910/5

Total cost = $182

Thus, the amount of each Marco's payments for the 2 reclining chairs, a coffee table including with shipping cost is found as $182.

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As per the binomial distribution, the value of the normal approximation is 0.6573

The term binomial distribution refers the discrete probability distribution that gives only two possible results in an experiment, either success or failure.

Here we have given that n = 95 P = 0.96 and q = 0.04

Now, here we have to check  the binomial distribution to see whether it can be approximated by the normal distribution.

While we looking into the given question we know that the value of n = 95 P = 0.96.

Then as per the binomial distribution formula, the normal distribution is calculated as,

=> P(X=1) = 95C4 * (0.96)⁴ * (1-0.96)⁹⁵⁻⁴

When we simplify this one then we get the value as 0.6573

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The binomial probability of getting exactly 3 sevens in 10 rolls of an 8-sided die is approximately 0.0142 or 1.42%.

Given: Roll an 8-sided die 10 times and to find the probability of getting exactly 3 sevens in those 10 rolls.

Formula: The probability of getting exactly "k" successes in "n" trials of an event with a probability "p" of success in a single trial is given by the binomial probability formula:

P(k successes in n trials) = [tex]C(n , k) * p^k * (1 - p)^{(n - k)}[/tex]

where:

Step1

Calculate the probability of rolling a seven on an 8-sided die (p).

Since there is 1 "success" outcome (rolling a seven) out of 8 possible outcomes (8-sided die),

p = 1/8.

Step 2

Plug the values into the binomial probability formula for getting exactly 3 sevens in 10 rolls:

P(3 sevens in 10 rolls) = [tex]C(10, 3) * (1/8)^3 * (1 - 1/8)^{(10 - 3)}[/tex]

On subtracting gives:

=C(10,  3) * (1/8)^3 * (7/8)^{7}

Plugging the value of C(10,3) = 120 in the above equation:

= 120 * (1/8)^3 * (7/8)^{7}

Step 3:

Calculate the final answer using the formula:

P(3 sevens in 10 rolls) = 120 * (1/512) * (343/512)

≈ 0.0142

Therefore, the binomial probability of getting exactly 3 sevens in 10 rolls of an 8-sided die is approximately 0.0142 or 1.42%.

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Answer:

no c is right answer

Step-by-step explanation:

angle b and e should be supplementary

Answer:

A, B and C

Step-by-step explanation:

Statement A

According to the Alternate Exterior Angles Theorem, when a transversal line intersects two parallel lines, the resulting alternate exterior angles are congruent.

Given ∠c ≅ ∠f, and as ∠c and ∠f are alternate exterior angles, then p ║ q.

Statement B

According to the Corresponding Angles Postulate, when a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.

GIven ∠d ≅ ∠g, and as ∠d and ∠g are corresponding angles, then p ║ q.

Statement C

According to the Same-side Interior Angles Theorem, when two parallel lines are intersected by a transversal, the angles that are interior to the parallel lines and on the same side of the transversal line are supplementary.

Given ∠b and ∠e are supplementary, and as ∠b and ∠e are the interior angles on the same side of the transversal [tex]\ell[/tex], then p ║ q.

Statement D

∠f and ∠g are a linear pair, therefore ∠f and ∠g are supplementary.  However, this does not given enough information to prove p ║ q.

Answer:

first option

Step-by-step explanation:

using the property of logarithms

ln [tex]x^{n}[/tex] = nlnx ( ln is the natural logarithm )

given

[tex]17^{(0.3x+5)}[/tex] = 12

take the ln of both sides

ln [tex]17^{(0.3x+5)}[/tex] = ln 12 , then

(0.3x + 5) ln 17 = ln 12 ( divide both sides by ln 17 )

0.3x + 5 = [tex]\frac{ln12}{ln17}[/tex] ≈ 0.877063 ( subtract 5 from both sides )

0.3x ≈ - 4.12293 ( divide both sides by 0.3 )

x = [tex]\frac{-4.12293}{0.3}[/tex] ≈ - 13.7431 ( to the nearest ten thousandth )

We get the following answers;

(a) The necessary histogram has been created and is supplied below.

(b) According to the data, it is indeed dangerous to drive close to home. Because 23% and 29% of accidents occur within 1 to 5 miles of home, respectively.

Step 1: in 2001, progressive insurance asked customers who had been involved in auto accidents how far they were from home when the accident happened. the data are summarized in the table.

Step 2:

Table :

Miles from home          % of accidents      Cumulative

Less than 1                               23                        23

1 to 5                                         29                        52

6 to 10                                       17                         69

11 to 15                                       8                          77

16 to 20                                     6                         83

over 20                                     17                        100

(a) the required histogram is made and attached below.

(b) Yes, the data indicates that driving near home is particularly dangerous. Because, less than , 1 to 5 miles from home 23%, 29% of accidents.

Hence we get the required answers.

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Answer:

1) -10x + 5

2) 5p - 26

3) -5y + 6

third side,  AB= 14.318 Units  and  tanB = 0.461

given:

BC=13 units

AC=6 units

solution:

using pythagoras theorem, we get

AB² = BC² + AC²

AB² = 13² + 6²

AB² = 169 + 36

AB² = 205

AB = 14.318 units

tanB = side opposite/side adjacent

tanB = AC/BC

tanB = 6/13

tanB = 0.461

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Using Pythagoras theorem, Third side,  AB= 14.318 Units  and tanB = 0.461

The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a2 + b2, are equal to the squares on the legs.

given:

BC=13 units

AC=6 units

solution:

using pythagoras theorem, we get

AB² = BC² + AC²

AB² = 13² + 6²

AB² = 169 + 36

AB² = 205

AB = 14.318 units

tanB = side opposite/side adjacent

tanB = AC/BC

tanB = 6/13

tanB = 0.461

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The statements best describe probability as the relative likelihood that an event will occur. It is a number between 0 and 1 inclusive.

Probability

A mathematical tool used to examine unpredictability is probability. It discusses the likelihood that an event will occur. For instance, you might not get two heads and two tails if you flip a fair coin four times. But if you flip the same coin 4,000 times, you'll get results that are almost evenly split between heads and tails. The theoretically predicted chance of heads in any given toss is 12, or.5. There is a predictable pattern of results when there are numerous repetitions, even though the results of a few repetitions are unknown. One of the authors tossed a coin 2,000 times after reading about the English statistician Karl Pearson, who threw a coin 24,000 times and got 12,012 heads. The outcome was 996 heads. The expected chance of 5 is quite near to being reached by the fraction of 9962,000, which is equivalent to 498.

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Least time required to reach the point Q as per the distance and the speed rate is equal to 2 hours.

As given in the question,

Nearest point on the coast is 2 miles far away

rate of the row = 1mile per hour

Walk at the rate of 3 miles per hour

Let 'x' hours be the least time to reach point Q.

Time = distance / speed

Time taken to reach the point Q = [√ 1 + ( 3 - x)² ]/ 3

Time taken to reach the coast = (√ 4 + x² ) / 1

Total  time taken 't' = (√ 4 + x² ) / 1 + [√ 1 + ( 3 - x)² ]/ 3

To find least time dt/dx = 0

t  = (√ 4 + x² ) / 1 + [√ 1 + ( 3 - x)² ]/ 3

⇒dt/dx = [ x / √ 4 + x² ] + ( 3 - x) / √( 10 -6x + x² )

⇒x / √ 4 + x² = ( x - 3) / √( 10 -6x + x² )

Squaring both the side we get,

x² / (4 + x²) = ( x - 3)² / ( 10 -6x + x² )

⇒3x² -24x +36 =0

⇒ x² -8x + 12 = 0

⇒ x = 2 or 6 hours

Therefore , the least time taken to reach the point Q is equal to 2 hours.

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0.3% is the percentage rate of increase  in exponential function.

What exactly makes a function exponential?

A mathematical function using the following formula is an exponential function: f (x) = an x. where an is a constant known as the function's base and x is a variable.

                   The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base.

We have,

y = 50( 1.3)ˣ

The equation represents exponential growth because the growth factor is greater than 1.

The general form equation is

y(x)= a(1-r)^x such that r is the growth percent.

   1 + r = 1.3

     r = 0.3 ⇒  0.3%

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The area of a rectangle with the sides of x+7 and 3x-4 is 3x² + 17x - 28.

Any shape's area can be calculated by counting how many unit squares will fit inside of it. A square with a side of 1 unit is referred to as a unit square in this context. Therefore, the quantity of unit squares that make up a rectangle's perimeter is its area. Alternately, the area of the rectangle is the area contained within the boundary of this shape. The unit-length tiles in your home are a good illustration of a rectangle form. By counting the number of tiles, you can quickly determine how much space the floor takes up. This will also enable you to calculate the rectangle floor's area.

Given

Sides = x+7 and 3x-4

Area of rectangle

Length ×Breadth

(x + 7) (3x - 4)

Multiplying,

x(3x - 4) + 7(3x - 4)

3x² - 4x + 21x - 28

3x² + 17x - 28

The area of a rectangle with the sides of x+7 and 3x-4 is 3x² + 17x - 28.

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Answer: i think 15/8 but, im not sure

Step-by-step explanation:

Answer: 72

Step-by-step explanation

Let's just look at the denominators for this problem.

8 and 18

8 can go into 24, 3 times but 18 does not multiply into 24

18 can go into 36, 2 times but 8 does not multiply into 36

Therefore 72 is the least common denominator.

8 times 9 = 72

18 times 4 = 72

72 is the least common denominator.

An expression which describe the given sequence is, an = -2 + n.

Arithmetic sequence states that a sequence where the difference between each successive pair of terms is the same.

an = -2 + n is an expression which describe the given sequence

The general rule for the arithmetic sequence is given by,

 an = a + (n - 1)d  ......[1]

where, denotes the initial word.

the common difference

there are n terms;

The given order is -1, 0, 1, 2,.....

This is a frequent difference arithmetic sequence.

Since,0-(-1) = 1

1-0 =1

2-1 = 1 ....

Here, a1 = -1

When you replace [1] with the value of d = 1, you get, a1 = -1

an = -1 + (n -1)(1)

an = -2 + n

Consequently, the following expression describes the given sequence: an = -2+n.

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The equations that represent given problem is

P + S = 384 and 2.50P + 1.25S = 696.25.

What is an equation?

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Given that the cost of 1 slice pizza is $2.50.

The cost of 1 bottle can of soda is $1.25.

In total sell for a day is 384.

Assume that you sell P slice of pizza and S number of soda bottle.

Thus your total sell is P + S.

Therefore, P + S = 384.

The cost 1 slice pizza is $2.50

Then the cost P slice of pizza is $2.50P.

The unit rate of soda bottle is  $1.25.

Then the cost S bottles of soda is $1.25S.

Therefore the total sell for that day is 2.50P + 1.25S

2.50P + 1.25S = 696.25

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The equation of the parabola is y = -1/4 x² + 3/2 x - 17/4. Where the vertex of the equation is at (3, -2) and the focus is at (3, -2 2/16) that opens downwards.

The equation of the parabola with vertex at (h, k) is

y = a(x - h)² + k

The focus of the parabola is represented by (h, k + 1/4 a).

It is given that, the vertex of the parabola is (h, k) = (3, -2)

And the focus of the parabola is (h, k + 1/4 a) = (3, -2 1/16)

From the focus point, we can calculate the value of 'a'.

(h, k + 1/4 a) = (3, -2 1/16)

⇒ k + 1/4 a = -2 1/16 = -33/16

⇒ -2 + 1/4 a = -33/16

⇒ 1/4 a = -33/16 + 2

⇒ 1/4 a = -1/16

⇒ a = -1/16 × 4

∴ a = -1/4

Since a is negative the parabola is downwards.

Now, the equation of the parabola is

y = a(x - h)² + k

On substituting the values, we get

y = -1/4(x - 3)² - 2

  = -1/4(x² - 6x + 9) - 2

  = -1/4 x² + 3/2 x -9/4 - 2

  = -1/4 x² + 3/2 x - 17/4

Therefore, the equation of the parabola is y = -1/4 x² + 3/2 x - 17/4.

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The length of EF in line segment DF is 15.

A line segment's boundaries are two separate places on the same line. Another way to describe a line segment is as a piece of the line that joins two points.

Given that,

Length of line segment DF = 19.

Also, E is any point on line segment,

And DE = 4.

To find the length of EF,

Since, E lies on line segment DF,

Implies that,

DE + EF = DF

4 + EF = 19

EF = 15

The required length of EF is 15.

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Answer: The coefficient of the term with t^3 and q^14 in the expansion of (3t - q)^17 is 816 / 3.

Step-by-step explanation: The coefficient of the term with a certain power of t and a certain power of q in the expansion of a binomial raised to a power can be found using the binomial formula. The formula is given by:

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(a + b)^n = sum_{k=0}^n choose(n, k) * a^(n-k) * b^k

In this case, we have a = 3t, b = -q, and n = 17. We want to find the coefficient of the term with t^3 and q^14, which means we need to find the coefficient of the term with a^(n-k) = t^3 and b^k = q^14. Plugging these values into the formula, we get:

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(3t - q)^17 = sum_{k=0}^17 choose(17, k) * 3^(17-k) * (-1)^k * t^(17-k) * q^k

To find the coefficient of the term with t^3 and q^14, we need to find the value of choose(17, k) for k = 3. The binomial coefficient choose(n, k) is equal to the number of ways to choose k items from a set of n items. It can be calculated using the formula:

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choose(n, k) = n! / (k! * (n-k)!)

where n! is the factorial of n, which is the product of all positive integers less than or equal to n. For example, 5! = 5 * 4 * 3 * 2 * 1 = 120.

In our case, we have n = 17 and k = 3, so the coefficient we are looking for is:

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choose(17, 3) = 17! / (3! * (17-3)!) = 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 / (3 * 2 * 1 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) = 17 * 16 / 3 = 816 / 3

Therefore, the coefficient of the term with t^3 and q^14 in the expansion of (3t - q)^17 is 816 / 3.

The equation of the line would be y = x/3 + 1/2.

Option (B) is correct.

What is the slope-intercept form of the line?

The slope-intercept equation is used to find the general equation of a straight line using its slope and the point where it intersects the y-axis. The slope intercept form equation is given as, y = mx + b.

As we can see in the graph the line cuts the y-axis at y = 1/2

so the y-intercept of the line would be c = 1/2.

And when x=4, y = 2

So we can prepare the equation as y = x/3 + 1/2.

Hence, the equation of the line would be y = x/3 + 1/2.

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The equation of the line would be y = x/3 + 1/2.

Option (B) is correct.

What is the slope-intercept form of the line?

The slope-intercept equation is used to find the general equation of a straight line using its slope and the point where it intersects the y-axis. The slope intercept form equation is given as, y = mx + b.

As we can see in the graph the line cuts the y-axis at y = 1/2

so the y-intercept of the line would be c = 1/2.

And when x=4, y = 2

So we can prepare the equation as y = x/3 + 1/2.

Hence, the equation of the line would be y = x/3 + 1/2.

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The mean time of the entire operation is given by 31 seconds and standard deviation is approximately 4.47 seconds

mean time (μ₁) = 11 seconds

mean chassis time (μ₂) = 20 seconds

a)Total time taken = μ₁ + μ₂ = 11 +20 = 31  seconds

Now we will find the standard deviation:

standard deviation = √ (2²+4²) = √ 20 ≈ 4.47 seconds

b) The probability that the entire process will take less time:

Total time taken = 31 seconds

Less time taken will be 2 seconds for the entire time

P(T<30) = 30 - 31 / 4.47  = - 0.22

Now from the normal distribution table we get the p-value as :

p-value = 0.4129

Hence the required probability is 41.29 % .

The population or sample standard deviation and the standard error of a statistic are not the same thing, but they are related. The standard error of the sample mean is the standard deviation of the set of means computed by drawing an infinite number of repeated samples from the population and computing a mean for each sample.

The mean's standard error is estimated by dividing the sample standard deviation by the square root of the sample size, which matches the population standard deviation divided by the square root of the sample size.

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Answer:

42

Step-by-step explanation:

If 2/7 left that means that 5/7 are still there.

5/7x = 30  Multiple both sides by 7/5

x = [tex]\frac{30}{1}[/tex] x [tex]\frac{7}{5}[/tex]

x = 42

The quantity that is multiplied by pi in the formula for the area of a circle is the square of the radius

From the question, we have the following parameters that can be used in our computation:

Area of a circle

The formula for the area of a circle is represented as

A = πr²

Express the formula as a product

So, we have the following representation

A = π * r²

In the above formula, we can see that the square of r is multiplied by pi

Hence, the required quantity is the square of the radius of the circle

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Answer:

Amy has to pay $600 every month for rent.

Step-by-step explanation:

To take 1/4 of a number is to multiply 1/4 and said number.

So you can do 0.25*number

or number/4.

For this problem, the number is 2400 because Amy is going to pay 1/4 of 2400 for rent.

[tex]rent = 2400/4\\rent = 600[/tex]

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Answer: 75%

Step-by-step explanation:



93 is 75 percent of 124.

Explained in the picture attached...

Hope that helps...

Answer: P/2 - L = W

Step-by-step explanation:

P = 2L + 2W. We are isolating W. Subtract 2L from both sides to isolate the term first
P - 2L = 2W. Divide by 2 on both sides to isolate W.
P/2 - L = W

Answer:

(3,0)

have a nice day.(I needed 20 charecters so yeah i needed to say this)

Answer:

(3,0)

Step-by-step explanation:

The first number in the ordered pair tells us how far we are from the orgina (0,0) (the middle of the graph).  We are 3 units to the right.  The second number in the ordered pair tells us how far up or down from (0,0) we are.  You do not go up for down so that number should be zero.

Sales of one store is $274762500 and sales of other store is $275237500.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Given

In a recent year, the total sales at Restaurant A were $475,000 more than at Restaurant B. Total sales at the two stores were $550,000,000.

Let sales of one store be x

Equation,

475000 + x + x = 550,000,000

2x = 550,000,000 - 475000

2x = 549525000

x = 274762500

Sales of one store = $274762500

Sales of other store

= $274762500 + $475000

= $275237500

Sales of one store is $274762500 and Sales of other store is $275237500.

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The angle A is an obtuse angle of the regular polygon.

What is an angle?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, 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.

The interior angle of a polygon is [(n-2)180°]/n.

Where n is the number of sides of the polygon.

The number of sides of the polygon is 8.

The measure of the interior of the polygon is [(8-2)180°]/8

= 135°

The obtuse angle is an angle that more than 90°.

Therefore angle is an obtuse angle.

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Answer:

final answer would be $6,550

Step-by-step explanation:

To calculate the state income tax owed on a $50,000 per year salary, we can use the progressive tax rate provided in the question. We can divide the salary into three ranges, corresponding to the three tax rates:

Income Range: $0 - $10,000

Progressive Tax Rate: 3%

Tax Owed: $0 - $10,000 * 3% = $0 - $300

Income Range: $10,001 - $50,000

Progressive Tax Rate: 5%

Tax Owed: $10,001 - $50,000 * 5% = $500 - $2,500

Income Range: $50,001 - $100,000

Progressive Tax Rate: 5.5%

Tax Owed: $50,001 - $100,000 * 5.5% = $2,750 - $5,500

Thus, the total state income tax owed on a $50,000 per year salary would be $300 + $2,500 + $2,750 = $6,550. This amount should be rounded to the nearest whole dollar amount, so the final answer would be $6,550.