Problem Solving Strategy: Write an
Equation
Write an equation for each problem using the variable -n. Then solve and check the equation.
6) Allan has 84 baseball cards. This is 19 fewer cards than Mike. How many baseball cards does Mike have?
7) Jamie can ride her bike 3 times as fast as Michelle can jog. If Jamie rides her bike at a rate of 12 miles per hour, how fast can Michelle jog?
Problem Solving Strategy: Mental Math

Answer: 110

Step-by-step explanation: If the drama class sold 20 more adult tickets than student tickets to the fall play, and adult tickets cost $8, then the number of adult tickets sold can be calculated by adding 20 to the number of student tickets sold and multiplying by $8. We can set up an equation to represent this relationship, where A represents the number of adult tickets sold and S represents the number of student tickets sold:

A = S + 20

A * 8 = $880

We know that the total amount collected from ticket sales was $880, and we know that adult tickets cost $8, so we can divide $880 by $8 to find the number of adult tickets sold:

A = $880 / $8

A = 110

Therefore, the drama class sold 110 adult tickets to the fall play.

Answer:

3 ln(abs ln(7x)) +C

Step-by-step explanation:

Do not forget to add the absolute value!

The different possibilities

The value of each digit in a number is known as place value. Every digit in a number has a distinct value depending on where it is located. The value of a digit depends on its position in the number, which might result in a number having two comparable digits with distinct values.

Given:

5.4  

Now, filling with different possibilities

Tens       Ones     Tenths     Hundredths

0                5               4                     0

0                5               3                    10

0                5               2                   20

0                 5              1                   30

0                 5              0                   40

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The correct option A) Sunday and Monday, is the days employee 3 does not need to work.

For the stated question-

A medical center's manager wants to schedule employees so that they work 5 days and take 2 days off in a row.

Thus, they are reportedly mandated to have consecutive days off on Saturday and Monday, and there is no better option than A.

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The following are the actions she could take to solve the quadratic equation: 2(x² + 6x + 9) = 18 + 3.

Following is the determination of the quadratic equation's solution;

2x² + 12x - 3 = 0

2x² + 12x = 3

Divide equation by 2.

x² + 6x = 3/2

Add both of the equation's sides after squarely multiplying the x-coefficient by half:

(x + 3)² = 3/2 + 3²

x² + 6x + 9 = 9 + 3/2

2(x² + 6x + 9) = 18 + 3

Thus, in order to calculate the quadratic equation, she could follow these steps: 2(x² + 6x + 9) = 18 + 3.

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The function and the estimated value for the given population of fox are obtained as P(t) = P₀(1 + r)^t and 35346 respectively.

In order to model the population growth first find the value of the growth rate then substitute it into the expression P(t) = P₀(1 + r)^t.

Now, the value of P₀ can be found for t = 0 and thus the function is obtained.

The given problem can be solved as follows,

(a) The population of fox in year 2000 is given as 25800.

And, the growth rate is 4%.

Suppose t = 0 for year 2000.

And for some value of t, the population is P(t).

Now, the following expression for the population can be written as,

P(t) = P₀(1 + r)^t

Where P₀ is the population at the year 2000.

Thus, the expression can be written as,

P(t) = 25800(1 + 4/100)^t

(b) In the year 2008, the value of t is 8.

Substitute t = 8 in the expression of the population to get,

P(t) = 25800(1 + 4/100)^8

⇒ 25800 × 1.37

⇒ 35346

Hence, the function that models the population and the estimated population for year 2008 are given as P(t) = P₀(1 + r)^t and 35346 respectively.

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Answer:

The price of the Penthouse is $2.4 million

Down Payment is $2.1 Million

So the amount that must be financed is $2.4 million - $2.1 million = $0.3 million or $300,000

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

-5 -2=-7

Keep in mind that negative is below zero. by adding eight we have reach 1 point to the right of zero. Thus, explaining tha answer of positive 1.

-7+8=1

Final Answer: 1

The correct proportion used to prove that HJ || KL is [tex]\frac{GK}{HK} = \frac{GL}{LJ}[/tex].

What is the proportion theorem of two similar lines?

According to this theorem, if you draw a line parallel to one side of a triangle that divides the other sides into two separate points, the line will proportionally divide the other sides. In addition, a line is parallel to the third side if it divides any two triangle sides in the same ratio.

We have,

HJ || KL

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

And in the given triangle,  HJ is parallel to KL, So HJ divided the two sides in proportion, that is

[tex]\frac{GK}{HK} = \frac{GL}{LJ}[/tex]

The correct option is the fourth option.

So, The correct proportion could be used to prove that HJ || KL

[tex]\frac{GK}{HK} = \frac{GL}{LJ}[/tex]

Hence, the correct proportion used to prove that HJ || KL is [tex]\frac{GK}{HK} = \frac{GL}{LJ}[/tex].

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Since the Polynomial has three non zero terms then the type of the polynomial is Trinomial

What are Polynomials?

A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Solution:

Yes the mentioned Ploynomial

7y - 6y² - y^5 is a Polynomial

Since the Polynomial has three non zero terms then the type of the polynomial is Trinomial

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Because the range is supplied as the difference between the side and the total of the sides given, option C, which is 9 cm<x<17 cm, is the right choice.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Here,

The range of possible lengths for the third side,

13-4<x<13+4

9<x<17

The correct option is C that is 9 cm < x < 17 cm because the range is given in difference between the side and sum of sides given.

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Answer:

y = [tex]\frac{3}{4}[/tex] x - 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + b ( m is the slope and c the y- intercept )

given

- 3x + 4y = 4 ( add 3x to both sides )

4y = 3x + 4 ( divide through by 4 )

y = [tex]\frac{3}{4}[/tex] x + 1 ← in slope- intercept form

with slope m = [tex]\frac{3}{4}[/tex]

• Parallel lines have equal slopes , then

y = [tex]\frac{3}{4}[/tex] x + b ← is the partial equation of the parallel line

to find b substitute (4, 0 ) into the partial equation

0 = 3 + b ⇒ b = 0 - 3 = - 3

y = [tex]\frac{3}{4}[/tex] x - 3 ← equation of parallel line

The following assets is not an example of a fixed asset for a manufacturer of road building equipment is " cans of yellow paint for refurbishing equipment warehouse building for storing finished equipment " .

Given :

which of the following assets is not an example of a fixed asset for a manufacturer of road building equipment  group of answer choices employee parking lot production equipment for assembling engines shipping area for finished goods .

What is fixed asset ?

A fixed asset is a long-term tangible property or piece of equipment that a company owns and uses in its operations to generate income.

It is clear that the paints cans cannot a property so it is not an example of fixed assets .

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Answer:

<A ≅ <X

<B ≅ <Y

Method

AAS Congruence Theorem

Step-by-step explanation:

Answer:

2n + 16

Step-by-step explanation:

he adds 8 then doubles the sum

2(n + 8) which is 2n + 16

The end behavior of the polynomial is, rises to the left and falls to the right.

What is end behavior of polynomial?

A polynomial function typically behaves at its end in the same way that its leading term, or the term with the largest exponent, does at its end.

Look at the leading term of the polynomial function to understand its end behavior. Given that the leading term has the highest power, its behavior will dominate the graph because it will grow much more quickly than the other terms as x gets very large or very small.

Consider, the given polynomial g(x) = x^2 (6 - x)

From the graph of the polynomial function we can see that the maximum point of the polynomial is at its vertex.

The vertex of the polynomial is (10, 90).

So this is the maximum value of the function is (10, 90).

Now to find the end behavior of the polynomial.

The degree of the polynomial is 3 and the leading coefficient of the polynomial is, -1.

By using: Odd degree and Negative leading coefficient the graph Rises to the left and falls to the right.

Hence, the end behavior of the polynomial is, rises to the left and falls to the right.

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The exact coordinates of the terminal point (x,y) is = (-2.212185 , 2)  .

In the question ,

it is given that ,

the measure of the angle in the figure is = 2.4 radians ,

From graph ,

we can see that the y - coordinate is = 2 unit , So , y = 2 .

Now , for the x - coordinate ,

we draw a right triangle ABO ,

where the height is 2 units and hypotnuse is = 3 units (radius) ,

the angle 2.4 radian in degree is = 137.51° ,

So , from the trigonometric ratio ,

Cos(θ) = base/hypotnuse ,

Cos(137.51) = x/3 ,

x = 3*Cos(137.51)

x = 3*(-0.737395)

x = -2.212185

Therefore , the exact point (x,y) is = (-2.212185 , 2) .

The given question is incomplete , the complete question is

The angle below measures 2.4 radians, and the circle centered at the angle's vertex has a radius 3 units long. Determine the exact coordinates of the terminal point (x , y) .

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The final cost of a skateboard after all the discounts and reductions is $53.775.

Given that, during a clearance sale at a sporting goods store, skateboards were marked down 30%. On Saturday, an additional 25% was taken off already reduced prices of skateboards.

We need to find the final price after all discounts had been taken.

What is the discount?

The basic way to calculate a discount is to multiply the original price by the decimal form of the given percentage rate. To calculate the sale price of any item, we need to subtract the discount from the original price.

Given, that the original cost of the skateboard is $119.50.

Now, 30+25=55

So, the total decrease in percentage is 55%.

The final cost of a skateboard=119.50-55% of 119.50

=119.50-0.55 × 119.50

=119.50-65.725

=$53.775

Therefore, the final cost of a skateboard after all the discounts and reductions is $53.775.

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Answer: To answer this question, we need to perform a hypothesis test. The null hypothesis is that the standard deviation of the process is 2 mg or less, and the alternative hypothesis is that the standard deviation of the process is over 2 mg.

To test this hypothesis, we need to calculate the test statistic, which is the z-score. The z-score tells us how many standard deviations a given data point is from the mean. In this case, the z-score is calculated by subtracting the mean of the sample from the hypothesized mean of the population, and dividing that difference by the standard deviation of the sample:

z = (20.2 - 20) / 2.4 = 0.1

Since the z-score is positive, we know that the mean of the sample is greater than the hypothesized mean of the population. However, we need to compare this z-score to the critical value to determine whether it is statistically significant.

The critical value is the z-score that marks the cutoff between the region of acceptance and the region of rejection of the null hypothesis. For a 1% level of significance, the critical value is the z-score that marks the 99th percentile of the normal distribution. Since the normal distribution is symmetrical, this means that the critical value is 2.58 standard deviations from the mean.

Since the z-score we calculated is less than the critical value, we cannot reject the null hypothesis. This means that we cannot assert that the standard deviation of the process is over 2 mg at a 1% level of significance.

The error occur from line 2 to line 3(optionB)

An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent more than 1. The graph of a linear equation forms a straight line.

A linear equation can have one or two variables. For example 5 = y+ 3y is an example of linear equation with one variable and y = 5 +3x is an example of linear equation with two variables.

8x-4= 2(4x+1)-6

8x-4= 8x+2-6

8x-4= 8x-4

Therefore the error is made where the parentheses is been solved, 2 is to multiply both 4x and 1.

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Answer:

Step-by-step explanation:

B

Avoiding discrimination is extremely important because this is an attitude that goes against human dignity and different values.

Some alternatives to overcome discrimination are:

No group should be discriminated against because discrimination promotes negative values and does not allow the correct development of people.

To avoid discrimination you can:

¡Hope this helped!

The correct part is (d) i.e. Fail to reject the null hypothesis.

What is hypothesis testing?

By evaluating whether or not the observed test statistic is more extreme than would be anticipated if the null hypothesis were true, the critical value approach determines whether something is "likely" or "unlikely." This means that the alternative hypothesis is accepted in place of the null hypothesis when the observed test statistic is more extreme than a cutoff number, known as the "critical value." The null hypothesis is not disproved if the test statistic does not deviate significantly from the crucial value.

Here, The critical value is 1.6257 and the sample's test statistic value is 1.3994.

We can see that the sample's test statistic value is not extreme as the critical value, So the null hypothesis should not be rejected.

Hence, It fails to reject the null hypothesis.

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Answer:

2   (the first choice)

Step-by-step explanation:

This is a matrix of size 3 rows and 5 columns  (3 x 5)

Any element of the matrix can be reference by row and column number

C₃₂  refers to the element in the 3rd row, 2nd column which is 2

We need to see how far the figure has moved in translation and directions and angles in rotational transformation.

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.

Given is a triangle ABC,

In translation transformation, the original image is congruent to the transformed one hence, we need to see  how far the shape has moved to the left or right and how many it has moved up or down.

In rotational transformation, the original figure is not necessarily congruent to the image hence, we need to see direction (clockwise CW or counterclockwise CCW) angle in degrees and Center point of rotation (turn about what point)

Hence, we need to see how far the figure has moved in translation and directions and angles in rotational transformation.

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Answer:

-9

Step-by-step explanation:

[tex]f(-2)=2(-2)=-4 \\ \\ g(-2)=|-2-3|=5;\\ \\ (f-g)(2)=-4-5=-9[/tex]

a) The function in vertex form is; y = -16(x - 3.5)² + 198

b) The maximum height if the arrow is; 198 feet

c) The time that it takes the arrow to hit the ground is; 16 seconds

We are given the function as;

y = -16t² + 112t + 2.

where;

y is the height (in feet) of an arrow

t is the time in seconds after it is shot from a bow

This is the equation of a vertical parabola open downward

The vertex is a maximum

The general form of a  quadratic equation in vertex form is;

y = a(x - h)² + k²

where (h, k) is the vertex coordinate

a) y = -16t² + 112t + 2

This is in standard form and using completing the square, we can write in vertex form as;

y = -16(x - 3.5)² + 198

b) The vertex is the point (3.5, 198)

The maximum height of the arrow represents the y-coordinate of the vertex of the function

Thus, the maximum height of the arrow is 198 feet

c) We know that when the arrow hits the ground, the value of y is equal to zero. Thus, at y= 0, we have;

-16(x - 3.5)² + 198 = 0

Rearranging gives;

(x - 3.5)² = (198/16)

(x - 3.5) = ±√(198/16)

(x - 3.5) = ±12.375

x = 12.375 + 3.5

x = 15.875 ≈ 16 seconds which is the time it will take to hit the ground.

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Answer:

y(0.1) = 0.05, y(0.2) = 0.09

Modified Euler's method is a numerical method used to solve ordinary differential equations (ODEs). It is a variation of Euler's method that is more accurate than the original, but still relatively simple to implement. It works by taking a single iteration of the Euler method, then using the midpoint between the current and previous points to calculate the next point in the sequence. This is done in order to reduce the error.

Solution

We have, y(0) = 0

dy/dt = 1 – y

h = 0.1

Using modified Euler's method,

y(0.1) = y(0) + (1/2) h (f(t0, y0) + f(t0 + h, y0 + hf(t0, y0)))

= 0 + (1/2) (0.1) [(1 - 0) + (1 - 0 + 0.1)]

= 0.05

Similarly,

y(0.2) = 0.1 + (1/2) (0.1) [(1 - 0.05) + (1 - 0.1 + 0.1)]

= 0.0975

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The required step to be taken is to factor the trinomial in the derivation.

The general form of a quadratic equation is given as ax^2 + bx + c = 0.

Here, a ≠ 0 and b and c are integers.

The degree of a quadratic equation is 2.

It can be factorized by completing square method.

The given problem can be solved as follows,

The derivation made by Jimmy is given as,

ax² + bx + c = 0

=> x² + (b/a)x + c/a = 0

=>  x² + (b/a)x =  -c/a

=> x² + (b/a)x + (b/2a)² = -c/a + (b/2a)²

Now, in order to solve the equation the trinomial on the LHS can be factored as follows,

(x + b/2a)² = -c/a + (b/2a)²

Hence, the next step taken by jimmy should be to factorize the trinomial on LHS.

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Answer:

Step-by-step explanation:

There are several ways to write an equation for the money collected as a function of the number of t-shirts sold. One possible equation is $y = x \cdot p$, where $p$ is the price of each t-shirt. This equation says that the total amount of money collected is equal to the number of t-shirts sold multiplied by the price of each t-shirt.Another possible equation is $y = p \cdot (x - c)$, where $c$ is the cost of producing each t-shirt. This equation says that the total amount of money collected is equal to the price of each t-shirt multiplied by the number of t-shirts sold minus the cost of producing each t-shirt.These are just two examples of how to write an equation for the money collected as a function of the number of t-shirts sold. The exact equation will depend on the specific details of the situation.