Expand and simplify
(3x + 4)(2x + 3)

Leo Gandolfi would save $54.34 by paying off the loan when the next payment is due.

What is percentage ?

Percentage can be defined as product of ratio of given value, total value and hundred.

To find out how much Leo Gandolfi saves by paying off the loan early, we need to first calculate how much interest he would pay if he were to continue making payments for the full 6-month term of the loan.

The total interest on the loan for the full 6 months can be calculated as:

Total interest = Total payments - Loan amount

We know the loan amount is $1,800, and the monthly payment is $310.50, so the total payments for the full 6 months would be:

Total payments = Monthly payment x Number of payments

Total payments = $310.50 x 6 = $1,863

Therefore, the total interest paid over the 6-month term of the loan would be:

Total interest = $1,863 - $1,800 = $63

Now, we need to calculate how much interest Leo Gandolfi would pay if he were to pay off the loan after making 4 payments.

The remaining balance on the loan after 4 payments is $612.34, so if Leo were to make one more payment, the remaining balance would be:

Remaining balance = $612.34 - $310.50 = $301.84

To calculate the interest paid on this remaining balance, we need to calculate the interest for one month:

Monthly interest rate = Annual interest rate / 12

Monthly interest rate = 12% / 12 = 1%

Monthly interest = Monthly interest rate x Remaining balance

Monthly interest = 1% x $301.84 = $3.02

Therefore, if Leo were to make one more payment, he would pay $310.50, which includes both the principal and the interest. So, the amount of interest he would pay if he were to pay off the loan after 4 payments is:

Interest paid = Total payment - Remaining balance

Interest paid = $310.50 - $301.84 = $8.66

So, by paying off the loan early, Leo Gandolfi would save:

Savings = Total interest - Interest paid

Savings = $63 - $8.66 = $54.34

Therefore, Leo Gandolfi would save $54.34 by paying off the loan when the next payment is due.

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For the given data, the cutoff point using the upper fence is 791.25 minutes.

To find the cutoff point using the upper fence, we need to first calculate the lower and upper fences.

The lower fence is given by the formula:

Lower fence = Q1 - 1.5 x IQR

where Q1 is the first quartile and IQR is the interquartile range.

The upper fence is given by the formula:

Upper fence = Q3 + 1.5 x IQR

where Q3 is the third quartile and IQR is the interquartile range.

To find these values, we first need to order the data:

307 311 322 321 354 363 377 406 410 425

435 461 464 474 499 505 513 534 548

The first quartile (Q1) is the median of the lower half of the data:

Q1 = (354 + 363) / 2 = 358.5

The third quartile (Q3) is the median of the upper half of the data:

Q3 = (513 + 534) / 2 = 523.5

The interquartile range (IQR) is the difference between the third and first quartiles:

IQR = Q3 - Q1 = 523.5 - 358.5 = 165

Now we can calculate the lower and upper fences:

Lower fence = Q1 - 1.5 x IQR = 358.5 - 1.5 x 165 = 91

Upper fence = Q3 + 1.5 x IQR = 523.5 + 1.5 x 165 = 791.25

Therefore, the cutoff point using the upper fence is 791.25 minutes. Any customer who uses more than 791.25 minutes in a month should be contacted by the phone company as part of the fraud prevention program.

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Susan bought 6 boxes of chocolate cookies, and 2/5(6) = 2.4 or 2 boxes of butter cookies.

Let's call the number of boxes of chocolate cookies that Susan bought "C". Then, she bought 2/5 as many boxes of butter cookies, which is 2/5C.

Let's call the cost of each box of chocolate cookies "x". Then, the cost of each box of butter cookies is x-2, since each box of butter cookies costs $2 less.

We know that the total cost of the chocolate cookies was $84 more than the total cost of the butter cookies. This can be expressed as:

Cx = 2C/5(x-2) + 84

Simplifying this equation, we get:

3/5Cx = 84 + 2/5C(2)

Multiplying both sides by 5/3, we get:

Cx = 140 + 4C/3

We also know that the total cost of all the cookies was $156, which can be expressed as:

Cx(x) + (2/5C)(x-2) = 156

Substituting Cx from the previous equation, we get:

(140 + 4/3C)(C) + (2/5C)(C-2) = 156

Simplifying and solving for C, we get:

C = 6

So Susan bought 6 boxes of chocolate cookies, and 2/5(6) = 2.4 or 2 boxes of butter cookies.

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Answer:

∠ CAB = 144°

Step-by-step explanation:

the central angle CAB is twice the measure of ∠ BDC , that is

∠ CAB = 2 × 72° = 144°

The possible lengths for the third side could be: any length between 1 inch and 12 inches (but not equal to either 8 inches or 5 inches) any length greater than 12 inches

What is triangle ?

Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.

Given ,

Lance is drawing a triangle. He draws one side that is 8 inches long and another side Se that is 5 inches long.

The third side of the triangle can be any length that satisfies the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

So, in Lance's triangle, if the first side is 8 inches long and the second side is 5 inches long, then the third side must be less than 8 + 5 = 13 inches.

So, the possible options for the third side are:

6 inches

7 inches

9 inches

10 inches

11 inches

12 inches

13 inches or longer.

Therefore, The possible lengths for the third side could be: any length between 1 inch and 12 inches (but not equal to either 8 inches or 5 inches) any length greater than 12 inches

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Answer:

0.058 hectometers

Step-by-step explanation:

There are 0.058 hectometers in 580 millimeters.

To convert millimeters to hectometers, you need to divide the number of millimeters by 100,000. So, 580 millimeters divided by 100,000 equals 0.0058 hectometers, or 0.058 hectometers when rounded to two decimal places.

Answer:

  15

Step-by-step explanation:

You want the sum of the numbers in the diagram that belong to exactly 3 circles.

We find it easier to eliminate numbers that do not belong to 3 circles. In the attachment, the red lines strike through numbers belonging to 1 circle, the blue lines strike numbers belonging to 2 circles, and the green line strikes the number belonging to 4 circles. (The numbers inside the smallest circle are also in the larger circle surrounding it.)

The numbers that are in 3 circles only are 1, 3, 11. Their sum is 15.

Answer:

Step-by-step explanation:

4.8

i got u brainliest please it helps a lot

We draw the conclusion that perhaps the actual probability of the die falling on the 4th position is between 0.398 and 0.562, with a 90% confidence level. The die appears to be fair since this contains 0.5.

It is predicated on the probability that something might happen. The concept of probability relies mainly on the justification for probability. A coin is tossed, for instance, and the hypothetical likelihood of receiving a head is 1 in 2.

P(A) = f / N determines probability, which quantifies the possibility of an event happening. Probability and odds are related, but probability is necessary for odds to exist. Prior to calculating the likelihood that an event will occur, probability is required.

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What does this problem ask for:

 --> which statement is sufficient to prove that:

     ∠ADB ≅ ∠ABD

Let's separate this image into two triangles: ΔADC and ΔABC

   --> prove that these triangles are congruent

       --> thus proving that: ∠ADB ≅ ∠ABD

Let's consider what evidence we have:

             --> thus: ∠ADC = ∠ABC

The minimum information that we have:

  --> prove that one pair of sides on both triangles are congruent

      --> based on the SSA Triangle Formula

             --> Two triangles that have two sides and one angle that are

                   equal, are therefore congruent

Based on the choices given:

 --> if DA = BA or DA is congruent to BA

  --> then ΔADC = ΔABC

Thus:

--> ∠ADC = ∠ABC

Answer: DA is congruent to BA

The population and the sample is option a population: all of the students in the high school sample: the 10 students selected from the front row

In this scenario, the population refers to the entire group of students that the teacher is interested in studying. The population could be all students in the high school, all high school students within the country, all students in the class, or high school students in New York, depending on the research question.

A sample, on the other hand, is a smaller subset of the population that is actually observed or measured. The teacher selected 10 students from the front row as the sample for her study.

It's important to note that the accuracy of the conclusions drawn from a sample depends on how well the sample represents the population. In this case, the teacher may have concluded that the class did extremely well based on the scores reported by the 10 students in the front row. However, it's possible that the front row students are not representative of the entire class or the entire population, which could lead to inaccurate conclusions.

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We have drawn the graph for the given inequality.

What is inequality?

Inequality is a mathematical statement that compares two values or expressions and shows their relative size. It is represented by the symbols >, <, ≥, or ≤, which respectively mean "greater than", "less than", "greater than or equal to", and "less than or equal to". Inequalities can also include variables and can be used to describe a range of possible values for that variables.

For the given inequality y > -x - 5

we can draw the graph as shown below:

Hence, we have drawn the graph for the given inequality.

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Step-by-step explanation:

first open the bracket

200+320=520

then multiple the answer with 250

thus: 250×520=130,000

130,000

Step-by-step explanation:

first calculate the bracket 200 + 320 =520

than multiply it by 250. 250 x 520 = 130,000

The posterior probability of having cogscitis, given a positive test result from Test 2, is 0.0094 or about 0.94%. This indicates that even though you had a positive Test 2 result, the likelihood that you actually have CNS inflammation is still extremely low less than 1%.

With your positive test result from Test 2, we must apply Bayes' theorem to get Doctor B's posterior probability that you have cogscitis, which is:

P(A|B) = P(B|A) * P(A) / P(B)

The following probabilities are known:

P(A) = 0.001 (the population prevalence and previous likelihood of getting cogscitis)

P(B|A) = 0.95 (the possibility of receiving a positive Test 2 result while having cogscitis)

P(B|not A) = 0.10 (the possibility of receiving a positive test result from Test 2 even if you do not have  cogscitis)

The law of total probability, which asserts the following, can be used to determine the marginal probability of a positive test result (P(B)):

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

where:

P(not A) = 1 - P(A) = 0.999 (the multiplier of the previous probability of contracting cogscitis)

Substituting the values, we get:

P(B) = 0.95 * 0.001 + 0.10 * 0.999 = 0.1008

The posterior probability of developing cogscitis can now be determined, given a positive test result from Test 2:

P(A|B) = P(B|A) * P(A) / P(B)

= 0.95 * 0.001 / 0.1008

= 0.0094

Therefore, the posterior probability of having cogscitis, given a positive test result from Test 2, is 0.0094 or about 0.94%. This indicates that even though you had a positive Test 2 result, the likelihood that you actually have CNS inflammation is still extremely low less than 1%.

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Answer:

40

Step-by-step explanation:

To determine the number of rolls, take the number of packs and multiply by the number of rolls per pack.

10 *4 = 40

40 rolls total.

Answer:

40 rolls

Step-by-step explanation:

10 packs * 4 rolls per pack

Answer:

26 oz

Step-by-step explanation:

4 lb x 16 oz/lb = 64 oz

64 oz - (2 lb)(16 oz/lb) - 6 oz = 26 oz are left

The value of a is obtained as follows:

a = 5.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

When two lines are perpendicular, the multiplication of their slopes is of -1.

Then the equation to obtain the value of a is given as follows:

0.5(1 - a) x 0.5 = -1.

0.25(1 - a) = -1

1 - a = -4

a = 1 + 4

a = 5.

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Answer: The equation 20x³-25x²+4x-5 can be factored by finding its roots, which are the values of x that make the equation equal to zero.

To find the roots, you can use one of the following methods:

Rational Root Theorem

Synthetic Division

Factor Theorem

Binomial Expansion

I would recommend using the Rational Root Theorem, which states that if a polynomial has a rational root, then it can be expressed as a product of linear factors with rational coefficients.

First, list out the possible rational roots of the equation: ±1, ±2, ±5, ±1/2, ±1/5.

Next, test each root by dividing the equation by (x-root), using synthetic division. If the remainder is zero, then the root is a factor of the equation. Repeat this process until you have found all of the roots.

Finally, factor the equation by grouping the roots into pairs and multiplying each pair to obtain a quadratic factor. Factor each quadratic and simplify the expression.

It is important to note that this is a rather advanced topic in algebra and finding the roots of polynomials can be quite challenging. If you need further assistance, I recommend seeking help from a tutor or textbook on algebra.

Step-by-step explanation:

The next two days when Alicia would be allowed to eat junk foods are Thursday and Tuesday.

The first day after Saturday when Alicia would have junk food can be determined by counting the fifth day after Saturday.

Sunday - first day

Monday - second day

Tuesday - third day

Wednesday - fourth day

Thursday - fifth day

The next day after Thursday when Alicia would have junk food is the fifth day after Thursday.

Friday - first day

Saturday - second day

Sunday - third day

Monday - fourth day

Tuesday - fifth day

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PLEASE GIVE BRAINLIEST!

have a good day ;)

Answer:

2500,500,100, 20, 4, 0.8

Step-by-step explanation:

dividing by 5 every term.

2500/ 5 = 500

500/ 5 = 100

100/ 5 = 20

20/5 = 4

4/5 = 0.8

When the dimension of height is doubled, the volume of the cone also gets doubled.

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies. Volume is measured in cubic units like m3, cm3, in3, etc. The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Various forms have various volumes. We have studied the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry. We will discover how to find the volume for each of these shapes.

Volume of a cone is given by,

V = πr²h/3

Where,

V = Volume,

r = radius of the base,

h = height of the cone.

Let, height at first be x, then volume would be,

V1 = πr²x/3

As the height is doubled, so height = 2x, then volume would be,

V2= πr²(2x)/3

We observe that:

V2 = 2(πr²x/3)

V2 = 2V1

Therefore, when the height is doubled, the volume of the cone also gets doubled.

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Answer:

600 calories

Step-by-step explanation:

The problem asks us to use the given trend line to find how many calories are burned after 40 minutes. The trend line is the slope of the graph that is given, so all that we have to do is find 40 minutes on the x axis, and then find the point on the slope in the given graph that has an x value of 40, and this point ends up being (40, 600). This means that in 40 minutes, 600 calories are burned.

The expression that represents all the possible widths of the rectangle is given as follows:

0 < x < 5.

The area of a rectangle of length l and width w is given by the multiplication of these dimensions, as follows:

A = lw.

For this problem, the length is 5 meters more than five times the width, hence:

l = 5 + 5w.

Hence the area is given as follows:

A = w(5 + 5w)

A = 5w² + 5w.

The area is less than 100m², hence the inequality is given as follows:

5w² + 5w < 100

5w² + 5w - 100 < 0.

w² + w - 20 < 0.

(w + 5)(w - 4) < 0.

Hence the solutions are:

The width cannot be negative, hence the interval is:

0 < x < 5.

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The quadratic trinomial of the given expressions are z² + 4 + 4z, 16 + n² - 8n, m² + 100 + 20m respectively.

A trinomial is an algebraic expression that has three terms. An algebraic expression consists of variables and constants of one or more terms.

A polynomial is an algebraic expression that has one or more terms and is written as [tex]a_0x^n + a_1x^{ n - 1} + a_2x^{n-2} + ...+ a_n x^0[/tex] in the standard form. Where [tex]a_0, a_1, a_2, ....,a_n[/tex] are constants and n is a natural number.

A quadratic trinomial is a type of algebraic expression with variables and constants. It is expressed in the form ax² + bx + c, where x is the variable and a, b and c are non-zero real numbers. A quadratic trinomial also describes the discriminant D where it defines the quantity of an expression and it is written as D = b² - 4ac.

Given:

(-z - 2)²

⇒ [-(z + 2)]²

⇒ (z)² + (2)² + 2(z)(2)

⇒ z² + 4 + 4z

(4 - n)²

⇒ (4)² + (n)² - 2(4)(n)

⇒ 16 + n² - 8n

(-m - 10)²

[-(m + 10)]²

⇒ (m)² + (10)² + 2(m)(10)

⇒ m² + 100 + 20m

So, the expressions are converted into quadratic trinomial.

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Answer:

The third option

Step-by-step explanation:

The third option, {1, 4, 7, 10, ...} is an arithmetic sequence because you add 3 to get from 1 to 4, and then you add 3 to get to 7, and then you add another 3 to get to 10.

If administrators at International University are curious how students' GAs after their first year compare to their high school GPs. The correct answer is: C. We cannot assume independence between the high school GPAs in the sample.

The GPAs of the students in the sample at the end of their first year at the university are likely to be correlated with their high school GPAs, as students with higher high school GPAs are likely to perform better in university as well.

Thus, the high school GPAs of the students in the sample are not independent of each other, and using the formula for the standard deviation of the sample would not be appropriate in this situation.

Therefore the correct option is C.

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The correct question is:

Administrators at International University are curious how students' GPAs after their fist year compare to their high school GPAs. They plan on taking an SRS of 80 of the 900 freshmen to look up their high school GPAs. They plan to look at the difference between the mean high school and the mean university GPA for students in the sample at the end of their first year. Why is it not appropriate to use the formula for the standard deviation of

The samples are not independent of each other.

We cannot assume independence between the university GPAs in the sample.

We cannot assume independence between the high school GPAs in the sample.

The samples are independent of each other.

Answer: A

Step-by-step explanation:

The sample is sampling the high school GPA and college GPA of the same students meaning the samples are not independent.

The value of the unknown side length, BC, in given diagram is 28.3 ft

From the question, we are to determine the value of the unknown side length in the given diagram

By similar triangles theorem, we can write that

AX/XY = AB/BC

From the given information,

AX = 12ft

XY = 17 ft

AB = AX + XB

= 12 ft + 8 ft

= 20 ft

BC = ?

Then, we can write that

12/17 = 20/BC

Cross multiply

12 × BC = 17 × 20

12 × BC = 340

BC = 340/12

BC = 28.3

Hence, the value of BC is 28.3 ft

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answers are on the picture

Step-by-step explanation: