Three hundred seventeen kids went on a field trip last
Tuesday. There were supposed to be six full buses, but
seven kids were sick that day. How many kids fit on
each bus?
Write an equation

The measure of the unknown angle, m ∠1, is 80°

From the question, we are to determine the measure of the unknown angle in the given diagram.

The unknown angle in the diagram is angle 1.

To determine the measure of angle 1,

First, we will determine the measure of the third (unlabeled) angle in the small triangle. Let the angle be x.

By the alternate interior angles theorem, we can write that

x = 52°

Then,

x + 48° + m ∠1 = 180° (Sum of angles in a triangle)

52° + 48° + m ∠1 = 180°

100° + m ∠1 = 180°

m ∠1 = 180° - 100°

m ∠1 = 80°

Hence, m ∠1 = 80°

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Answer: C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply, explain why?

Given the limit of the function

lim x→[infinity] (4x − ln(x))

Step 1: Substitute x = ∞ into the given function first as shown;

lim x→[infinity] (4x − ln(x))

= (4(∞) − ln(∞))

= ∞ - ∞ (indeterminate)

Step 2: Apply  l’Hospital’s Rule

\(\lim_{n \to \infty} (4x - lnx)\\ \lim_{n \to \infty} \frac{d}{dx}(4x-lnx) \\ \lim_{n \to \infty} (4 - \frac{1}{x}\\\)

Step 3: Substitute the value of x into the resulting function;

\(\\lim_{n \to \infty} (4 - \frac{1}{x})\\= 4 - 1/ \infty\\= 4 - 0\\= 4\)

Hence the limit of the function is 4. And yes, the L'hospital rule was applicable.

The slope of the line is 7/9

It is important to note that the equation of a line is represented as;

y = mx + c

Where;

The formula for calculating the slope of a line is expressed as;

Slope, m = y₂ - y₁/x₂ - x₁

Now, let's substitute the values into the formula from the points given we have;

Slope, m =1 -(-6)/ -3 - (-6)

expand the bracket

Slope, m = 1 + 6/ 3 + 6

add the values

Slope, m = 7/9

Hence, the value is 7/9

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The 1st table represents a linear as well as the quadratic relationship, the 2nd table represents neither and the 3rd table also represents neither relationship.

Hence, the 1st table represents a linear as well as a quadratic relationship, the 2nd table represents neither and the 3rd table also represents neither relationship.

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Answer:

\(x^{2} +x+1\)

Step-by-step explanation:

\(x^{2} +x+1\) is the only prime polynomial because the others can be factored.

\(x^{2} - x -2 \\becomes (x-2)(x+1)\)

\(x^{2} -12x+11\\becomes (x-11)(x-1)\)

\(x^{2} +2x-8\\becomes (x+4)(x-2)\)

In between these four polynomials, x² + x + 1 is the only prime polynomial.

A prime polynomial doesn't have any factor except 1 and itself.

Given,

x² + x + 1 = 1 × (x² + x + 1)

x² – x – 2 = x² - 2x + x - 2 = x(x - 2) + (x - 2) = (x - 2)(x + 1)

x² – 12x + 11 = x² – 11x - x + 11 = x(x – 11) - (x - 11) = (x - 1)(x - 11)

x² + 2x – 8 = x² + 4x – 2x - 8 = x(x+4) - 2(x+4) = (x-2)(x+4)

Therefore, x² + x + 1 is the only prime polynomial here.

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Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

Let's assume that Bryan invested an amount of x dollars in the first account, which earns 11% interest, and (6500 - x) dollars in the second account, which earns 7% interest.

The interest earned from the first account can be calculated as 0.11x, and the interest earned from the second account can be calculated as 0.07(6500 - x).

According to the problem, the total interest earned after one year is $519. So we can set up the equation:

0.11x + 0.07(6500 - x) = 519

Simplifying the equation:

0.11x + 455 - 0.07x = 519

0.04x + 455 = 519

0.04x = 64

x = 64 / 0.04

x = 1600

Therefore, Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

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Answer:

120 cm²

Step-by-step explanation:

Applying,

A = Ph................... Equation 1

Where A = Literal Area of the triangular prism, P = Perimeter of the base, h = height.

But,

P = a+b+c............... Equation 2

Where a, b, c represent the three sides of the triangular base

Therefore,

A = h(a+b+c)............... Equation 3

From the question,

Given: h = 8 cm, a = 4 cm, b = 5 cm, c = 6 cm

Substitute these values into equation 3

A = 8(4+5+6)

A = 8(15)

A = 120 cm²

Answer:

x = 2

Step-by-step explanation:

First, subtract 3 from both sides.

2x + 3 = 7

     - 3    -3

2x       = 4

Then, divide both sides by 2.

2x / 2 = 4 / 2

x = 2

Answer:

the solution for x is x = 2

Step-by-step explanation:

To solve for x, we need to get x by itself on one side of the equation. First, we can subtract 3 from both sides to get:

2x + 3 - 3 = 7 - 3

Simplifying the left side gives us:

2x = 4

Then, we can divide both sides by 2 to get:

2x / 2 = 4 / 2

Simplifying the left side gives us:

x = 2

Answer:

a. c = 5.5n

b. Continuous

c. $33

Step-by-step explanation:

A store sells assorted nuts for $5.50 per pound.

a) Write a function in equation form to represent the total cost (c) of any number of pounds of nuts (n)

For every n, 5.5 is added to c. Thus, c = 5.5n

b) Will the graph of this function be continuous or discrete?

Continuous domains are ones that continue on in between intervals. For example, the height of someone would be continuous, because it could, for example, be between 50 inches and 70 inches. On the other hand, discrete domains are ones that can only be a set of given numbers. An example would be how much food you need to feed to a number of cats (for example, each cat needs to eat 0.5 pounds of food). Because you cannot have half a cat, the domain needs to have whole numbers.

Because you can buy 0.5 or 0.2 (or any amount of nuts), the domain is continuous.

c) What would the total cost be for 6 pounds of nuts?

Using the function from a), we know that the cost is 5.5n, where n is the amount of nuts you buy, in pounds. So, plug in "6"

5.5n = 5.5 * 6 = 33

Cost is $33

I hope this helps! Feel free to ask any questions!

An expression for the area of △KNM is = 1/2 x 2b x a

Given,

In the question:

In triangle KNM ;

The length of the base (MK) = 2b

and, height of the triangle is= a

To write an expression  for the area of △KNM .

Now, According to the question:

We know that :

Area of triangle is = 1/2 x base x height

The length of the base (MK) = 2b

and, height of the triangle is= a

Plug all the values in the area of triangle :

Here, Area of triangle is = 1/2 x 2b x a

Hence, An expression for the area of △KNM is = 1/2 x 2b x a.

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Answer:

False,

Step-by-step explanation:

There is not enough information given.

The given statement - "All the races are 175 miles long" is true.

A function is a relation between a dependent and independent variable.

Mathematically, we can write → y = f(x) = ax + b.

Given is to find whether all races are more than 175 miles or not.

All the races are 175 miles long. The given statement is true.

Therefore, the given statement - "All the races are 175 miles long" is true.

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(1, 3) is not a solution to the system of linear equations and (2,1) is a solution to the system of linear equations.

What are linear equations?

To check if the ordered pair (1, 3) is a solution to the system of linear equations:

2x + y = 5 ...(1)

−3x + 5y = −1 ...(2)

Substitute x = 1 and y = 3 in equations (1) and (2), respectively:

2(1) + 3 = 5 ...(1)

−3(1) + 5(3) = −1 ...(2)

Simplifying these equations:

2 + 3 = 5 (true)

−3 + 15 = −1 (false)

Therefore, (1, 3) is not a solution to the system of linear equations.

To check if the ordered pair (2,1) is a solution to the system of linear equations:

2x + y = 5 ...(1)

−3x + 5y = −1 ...(2)

Substitute x = 2 and y = 1 in equations (1) and (2), respectively:

2(2) + 1 = 5 ...(1)

−3(2) + 5(1) = −1 ...(2)

Simplifying these equations:

4 + 1 = 5 (true)

−6 + 5 = −1 (true)

Therefore, (2,1) is a solution to the system of linear equations.

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Answer: an improper fraction

Step-by-step explanation:  An improper fraction is a fraction that is larger than 1 7/3 is larger than one because 7, the numerator is larger than the denominator so 7/3 is an improper fraction

Step-by-step explanation:

Answer

The price of 6 DVDs, including sales tax = $62.87

Sales tax = $2.99

Required:

The cost of one DVD.

Explanation:

Step 1: Price of 6 DVDs excluding sales tax.

The price of 6 DVDs excluding sales tax = $62.87 - $2.99 = $59.88

Step 2: Use the Unitary Method:

According to the question,

6 DVDs price = $59.88

1 DVD price excluding sales tax = $ 59.88/6

The rate that is equivalent to the rate at which John drove to San Antonio is 60 miles per hour

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

John drove from here to San Antonio which is 180 miles away in 3 hours.

This means that

Distance = 180 miles

Time = 3 hours

Using the above as a guide, we have the following:

Speed = Distance/Time

Substitute the known values in the above equation, so, we have the following representation

Speed = 180/3

Evaluate

Speed = 60

Hence. the rate that is equivalent to the rate at which John drove to San Antonio is 60 miles per hour

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A.  {(–1, 2), (0, 3), (1, 4), (2, 5)} → Non-linear function.

B. {(–3, 9), (–2, 4), (3, 9), (4, 16)} → Non-linear function.

C. y = –14x + 9 → Linear function

D.  y = x  → Linear function

A linear function has a straight line as its graph. A linear function has the form shown below.

a + bx = y = f (x).

A linear function consists of one independent variable and one dependent variable. The independent and dependent variables are x and y, respectively.

When the absolute value of the input value of the function is connected to more than 1 output value, then the function is linear else it is a non-linear function.

From the given choices;

A.  {(–1, 2), (0, 3), (1, 4), (2, 5)}

Here, the absolute value of 1 is connected to more than one point, so non-linear function.

B. {(–3, 9), (–2, 4), (3, 9), (4, 16)}

Here, the absolute value of 3 is connected to more than one point, so non-linear function.

C. y = –14x + 9 is equivalent to the slope-intercept form of linear function y = ax + b.

D.  y = x is a linear function.

Therefore, B and D are linear functions.

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The congruence theorem required for each figure are

1. AAS

2. ASA

3. ASA

4. ASA

5. ASA

6. ASA

ASA (Angle-Side-Angle) congruence theorem states that if two triangles have two angles and the included side in common, then they are congruent.

That is to say, if two angles and the included side of one triangle are congruent to the corresponding two angles and included side of another triangle, then the two triangles are congruent.

AAS (Angle-Angle-Side) congruence theorem states that if two angles and a non-included side of one triangle are congruent to the corresponding angles and non-included side of another triangle, then the two triangles are congruent.

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Subtract the width from the length.

8.5 - 5.95 = 2.55 yards

Answer:

hshshshshshshshsiqkZjfdudiodjfhfbbxdudijdd

The daily percentage rate (DPR) for the given Annual Percentage Rate (APR) on credit card is 17.8% is equal to 0.048%.

Given the Annual Percentage Rate (APR) on credit card is 17.8%.

Now, we need to find the daily percentage rate (DPR) for the given yearly percentage on credit card.

To find your current annual percentage rate, look at your monthly statements. To determine the daily percentage rate (DPR), divide the annual percentage rate (APR) by 365 (the number of days in a year).

So, given APR = 17.8%

Now, daily percentage rate will be:

⇒ Daily percentage rate = Annual Percentage Rate ÷ 365

⇒ DPR = APR / 365

⇒ DPR = 17.8% ÷ 365

⇒ DPR = 0.048%

Therefore, daily percentage rate (DPR) is equal to 0.048%.

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Answer:

hey man

Step-by-step explanation:

hope this answer helped

click that link below

thanks

The last row of the table will show the total interest paid, which is approximately $243.11.

The correct option is C.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

To calculate the total interest paid,

we need to first find out how many months it will take to pay off the entire balance.

We can use the following formula to calculate the number of months:

N = -log(1-(r×b/p))/log(1+r)

where N is the number of months, r is the monthly interest rate (which is the annual percentage rate divided by 12), b is the balance, and p is the payment.

In this case,

r = 0.1799/12 = 0.01499 (monthly interest rate), b = $1,800, and p = $125.

Plugging these values into the formula, we get:

N = -log(1-(0.01499 × 1800/125))/log(1+0.01499) ≈ 16.24

So it will take about 16.24 months to pay off the entire balance.

Using a spreadsheet, we can create a table with the following columns:

Month: 1 to 16

Balance: starting with $1,800 and decreasing by $125 each month

Interest: calculated as the monthly interest rate times the balance

Payment: $125

Total Interest: calculated as the sum of the interest for all previous months

The last row of the table will show the total interest paid, which is approximately $243.11.

Therefore, the value is (C) $243.11.

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Answer: Option C is correct $243.11

Step-by-step explanation: I got it right On the test!!!

(f/g)(-5) is equal to 1/4, and the value -1 is not in the domain of f/g.

To find (f/g)(-5), we need to substitute -5 into the functions f(x) and g(x) and then divide f(-5) by g(-5).

Given:

f(x) = (4+x)(6+x)

g(x) = 1+x

Substituting -5 into the functions:

f(-5) = (4+(-5))(6+(-5)) = (-1)(1) = -1

g(-5) = 1+(-5) = -4

Now, we can calculate (f/g)(-5):

(f/g)(-5) = f(-5) / g(-5) = -1 / -4 = 1/4

Therefore, (f/g)(-5) equals 1/4.

Now let's determine the values that are not in the domain of f/g. The values that are not in the domain of f/g are the values that make the denominator g(x) equal to zero. In this case, the denominator is g(x) = 1+x.

To find the values that make the denominator zero, we solve the equation:

1 + x = 0

Subtracting 1 from both sides, we get:

x = -1

So, the value x = -1 is not in the domain of f/g because it would make the denominator equal to zero.

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Answer:

the correct answer is 193

Step-by-step explanation:

25×1-0=25

25×2-1=49

49×2-1=97

97×2-1=193

Answer:

$104

Step-by-step explanation:

The computation of the best point estimate for the mean monthly water bill is shown below:

Given that

The mean monthly water bill is $104

and, the number of residents is 44

based on the above information

The best point estimate would be equivalent to the mean monthly water bill i.e. $104

hence, the same would be considered

The word that describes the slope of the line representing the data in the table is "negative."

To determine the slope of the line representing the data in the table, we need to examine the relationship between the number of cards sold and the remaining amount of money needed.

Looking at the given data, we observe that as the number of cards sold increases, the remaining amount of money needed decreases. This indicates an inverse relationship between the two variables.

The slope of a line represents the rate of change between two variables. In this case, the slope is negative because the line decreases as we move from left to right.

Therefore, the word that describes the slope of the line representing the data in the table is "negative."

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Answer:

(-1,5)

Step-by-step explanation:

Just took it. Edg 2020. Hope this helps :)

Answer:

its A  (-1,5)

Step-by-step explanation:

The disadvantage of piece rate pay is that the cost of producing higher quantities of a product can be a reduction in the quality of the items produced.

Piece rate is any type of job in which a worker is paid a set amount for each unit produced or action performed, regardless of time. Some employees may be paid on a piece rate or on a commission basis.

Employees are paid on a piece rate, and commission payments are based on results rather than an hourly or weekly pay rate. This means that the employee's weekly pay will vary depending on how much work they do. One of the drawbacks of piece rate pay is that the cost of producing larger quantities of a product may result in a decrease in the quality of the items produced.

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