Yaritza finds some nickels and pennies in her change purse. How many coins does she have if she has 140 nickels and 130 pennies? How many coins does she have if she has nn nickels and pp pennies?

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Describe the first experiment

Two slips were drawn simultaneously, this means that the outcome of the first slip drawn will be multiplied by the outcome of the second slip drawn. The probability will follow the "and rule of probability".

STEP 2: Describe the second experiment

Since one slip is drawn and then put back into the box before a second slip is drawn, this is a PROBABILITY WITH REPLACEMENT. The outcome of the first event will not affect the outcome of the second event since the paper slips are replaced hence not reduced.

STEP 3: Describe the third experiment

Since one slip is drawn and not put back into the box before a second slip is drawn, this is a PROBABILITY WITHOUT REPLACEMENT. The outcome of the first event will affect the outcome of the second event since the paper slips reduce.

Difference between b and c is that b is with replacement and the total outcomes does not change while c is without replacement and the total outcomes change(reduce) after the first slip is drawn.

If the half-life is 15 hours and there are 18 g, it means that after 15 hours,

18/2 grams would decay, leaving behind 18/2 grams

This means that 9 grams would be left.

After another 15 hours (making a total of 30 hours), 9/2 grams would decay leaving behind 9/2 grams (i.e 4.5 grams.

After another 15 hours (making a total of 45 hours), 4.5/2 grams would decay leaving behind 4.5/2 grams. Hence 2.25 grams are left

After another 15 hours (making a total of 60 hours), 2.25/2 grams would decay leaving behind 2.25/2 grams.

Hence after 60 hours, only 1.125 grams would be left

(vi) The cube of a two digit number may have seven or more digits. (vii) The cube of a single digit number may be a single digit number. Q. The number of zeroes at the end of a perfect square is always odd.

I hope it will be helpful for you.

Answer:

The answer is the third one.

Step-by-step explanation:

They show the points plotted correctly.

All the values are;

1) f (-4) = 16

2) f (1) = 1

3) f (5) = 10

4) f (7) = 14

5) f (9) = 50

What is substitution method?

Find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The function is;

f (x) = { 4 - 3x ; if x ≤ 1

     = { 2x  ; if x > 1

     = { 5x + 5 ; if x ≥ 9

Now, Find all the values as;

Since - 4 is belong in x ≤ 1, so we get;

f (x) = 4 - 3x

f (-4) = 4 - 3 × -4

f (-4) = 4 + 12

f (-4) = 16

And, Number 1 is belong in x ≤ 1, so we get;

f (x) = 4 - 3x

f (1) = 4 - 3 × 1

f (1) = 4 - 3

f (1) = 1

And, Number 5 is belong in x > 1, so we get;

f (x) = 2x

f (5) = 2 × 5

f (5) = 10

And, Number 7 is belong in x > 1, so we get;

f (x) = 2x

f (7) = 2 × 7

f (7) = 14

And, Number 9 is belong in x ≥ 9, so we get;

f (x) = 5x + 5

f (9) = 5 × 9 + 5

f (9) = 50

Thus, All the values are;

1) f (-4) = 16

2) f (1) = 1

3) f (5) = 10

4) f (7) = 14

5) f (9) = 50

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Solution:

The question will be represented below as

To figure out the horizontal component (x), we will use the trigonometric ratio below

By substituting the values, we will have

Step 2:

To figure out the vertical component (y), we will use the trigonometric ratio below

By substituting the values, we will have

Hence,

The horizontal component is = 63.1 km/h

The vertical component is = 90.1 km/h

If we consider a, b and c all positive constants and b > 1, a exponential growth in general is represented by a function like:

In otherwise, a exponential decay can be represent by:

Now we can check whose functions are similar to one of these:

h(x) = 3x + 1.3 is a linear function, therefore, this is neither exponential growth or decay;

f = 3*(4.2^x) is an exponential growth;

y = (5/6)*(7^x) is an exponential growth;

T = 0.6*(1.3^x) is an exponential growth;

W(x) = (1/8)*[(3/5)^x] is an exponential decay, since in this case we have 3/5 < 1.

K = 4.2*(0.28^x) is an exponential deacay by the same argument.

The proportional relationship graph that represents the table of values given would look like the graph shown below.

A proportional relationship graph always passes through the point of origin, (0, 0). The slope of the graph of a proportional relationship is also called the constant of proportionality, k, which can be calculated by using the coordinates of any point on the line, (x, y).

Constant of proportionality, k = y/x.

The equation for a proportional relationship is given as y = kx.

Given the table of values above which represents a proportional relationship, the graph of the table of values will go through the points below:

(0, 0)

(14, 7)

(6, 3)

(26, 13)

Therefore, the graph of the proportional relationship would look like the graph attached below which passes through:

B. (0, 0) and continues through the point (14, 7).

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The ladder leaning on the house formed a right angled triangle

Using an illustration from the diagram given:

To get the height the house makes with the ladder, we will apply pythagoras' theorem:

Hypotenuse² = opposite² + adjacent²

Given the following table of values, k'(-1) is 3.

The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's core tool is the derivative. finding a function's derivative, or rate of change, in mathematics. Differentiation is the process of determining a function's derivative. The derivative is the rate at which x changes in relation to y when x and y are two variables.

Given Data

k(x) = -3h(x) + [tex]\frac{4x^{4} }{g(x)}[/tex]

k(x) = -3h'(x) + 4 [tex]\frac{4x^{3}g(x)-x^{4}g'(x) }{gx^{2} }[/tex]

k'(-1) = -3h'(-1) + 4 [tex]\frac{4g(-1)-g'(-1)}{g(-1^{2}) }[/tex]

k'(-1) = -3(-1) + 4(0)

k(-1) = 3 + 0

k'(-1) = 3

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Answer:

506.40

Step-by-step explanation:

.

Graph the inequality by finding the boundary line, then shading the appropriate area.

y < −x −3

ANSWER

EXPLANATION

We want to find the number of different combinations of colors possible if both spinners are spun at once.

To do this, we have to find the product of the number of colors on each spinner.

That is:

The answer is option B.

Answer:

To solve this problem you will have to use PEMDAS (parenthesis, exponents, multiplication, division, addition, and subtraction).

Lauren can add $30 each month to her savings account

Income made by Lauren from part-time job = $185

Money sent to Lauren by her parents = $120

Total income of Lauren  = Money from job+ money received from parents = 120+185 = $305

Let her total expenses be x

Substituting the values in the formula we get:

Sum of Lauren's paycheck + Money she gets from her parents = Total expenses+ 11% more than her total expenses

185 + 120 = x+11% of x

305=x+11/100*x

305 = 1.11x

x=274.77 or 275

Money she can add in her savings account each month = Total money received - Expenses = 305 - 275 = $30

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Step 1

From the question;

We are required to find how many months it will take him to read 90 books

Step 2

We will use the ratio below to solve the problem.

Answer; It will take Bobby 9months to read 90 booj

Here, we are given a quadratic equation graph and we are tasked with getting the equation of the quadratic equation from the graph

The first thing we need to note here is the shape of the parabola.

This in the sense that if the parabola opens up or faces down

On the graph we can see that the parabola faces the positive x-direction

Generally, the equation of a quadratic graph is usually in the form below;

So by identifying the values of a,b and c, we can get the complete equation of the graph

The above form is called the standard form while the form we have in the options is referred to as the vertex form

The vertex form can be written as;

Now, looking at the graph, we can see that the graph crosses the y-axis at the point y = 6

At this point, the value of x is 0

The vertex (h,k) represents the center point of the parabola

In the case of this question, the point is (-2,2)

so h =-2 and k is 2

What is left is to get a

we can obtain this from the value of y = 6 and x = 0

Thus;

6 = a(0-(-2))^2 + 2

6 = a(2)^2 + 2

6 = 4a + 2

4a = 6-2

4a = 4

a = 4/4 =1

So the equation in the vertex form is f(x) = (x + 2)^2 + 2

ANSWER

The solution is: -3 < p < 3.8

EXPLANATION

When we have an absolute value inequality, to "eliminate" the absolute value we have to write the following:

To solve this we have to add 4 everywhere in the inequality:

And divide everything by 10:

To graph we have to draw a line from -3 to 3.8, with empty circles at the ends - because those values are not included in the solution.

The expression equivalent to 3(−4.5b − 2.1) − (6b + 0.6) is -19.5b - 6.9.

Given expression:

3(−4.5b − 2.1) − (6b + 0.6)

To simplify the expression open the brackets and multiply the terms,

-13.5b − 6.3 − 6b - 0.6

Now, combine the like terms together and add them,placing a negative sign in front of the terms

-13.5b − 6b - 0.6 - 6.3

-19.5b - 6.9

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Write a mathematical expression for the following statement: x is at least 19

this means that x > 19

in set builder notation: (19,∞)

Here is the meaning of each statement:

The percentage of households that have the internet in 2007 is 61.7%

The percentage of households that have the internet in 1984 is k%.

The percentage of households that have the internet in 2017 is greater than the percentage of households that have the internet in 2000.

The sum of the percentage of households that have the internet in 1997 and 2001 is approximately equal to the percentage of households that have the internet in 2009.

Percentage is the fraction of an amount expressed as a number out of 100. In order to change a number to percentage, multiply the number by 100. The sign that represent percentage is %.

A function is an expression or rule that defines the relationship between the independent variable and the dependent variable. A function could be a linear function or an exponential function.

In this question,

x = is the number of years after 1980

and the independent variable is the percentage of households that use the internet after 1980.

H(27) = 61.7

1980 + 27 = 2007

This means that 61.7% households use the internet 27 years after 1980 or 61.7% households use the internet in 2007

H(4) = k

1980 + 4 = 1984

This means that k% households use the internet 4 years after 1980 or k% households use the internet in 194

H(37) > H(30)

This means that the percentage of households that use the internet 37 years after 1980 is greater than the percentage of households that use the internet 30 years after 1980

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Given:

Initial amount (Base) = 15, 757

Rate of increase = 3.5% or 0.035 in decimal form

Find: new price and the price increase

Solution:

To be able to get the new price, we need to solve for the price increase first. To do that, we need to know what is 3.5% of the old price 15, 757. To calculate that, we will multiply 0.035 by 15,757.

3.5% of 15, 757 is 551.50. This is the price increase of the car next year.

Hence, by next year, the new price will now be 15,757 + 551.50 = 16, 308.50.

For the constant speed, it take 5 minutes 3 seconds after you depart JBLM will you be the closest to Mt. Rainier.

Speed:

Speed means a rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered.

Given,

You're flying from Joint Base Lewis-McChord (JBLM) to an undisclosed location 165 km south and 152 km east. Mt. Rainier is located approximately 56 km east and 40 km south of JBLM.

Here we need to find the time taken after you depart JBLM will you be the closest to Mt. Rainier for the constant speed of 800 km/hr.

Let us consider +x direction is east, and the -y direction is south.

We know that, JBLM is at the origin (0, 0). All distance units are presented in kilometers.

While we consider that, you are flying on line

165x + 152y = 0

We know that the slope of the line

ax + by = c

is given by -a/b, which suggests we can form the equation of a perpendicular line by swapping x and y coefficients and negating one of them.

Then, we get the equation as,

152x - 165y = c

That is perpendicular to the flight path.

Now we need to find c so that this is true at the coordinates of Mt. Rainier.

The perpendicular line through (56, -40) is

152x - 165y - (152(56) - 165(-40)) = 0

When we expand it then we get,

152x - 165y - (8512 + 6600 ) = 0

152x - 165y - 15112 = 0

We know that the distance in km from JBLM (0, 0) to this line is given by

So, when we apply the value of (x,y) as (0,0) then we get,

=> | 152(0) - 165(0) - 15112 |/√(152²+165²)

=> 15112/√50329

=> 15112/224.34

≈ 67.362

Therefore at the constant speed of  800 km/hr, you will have flown that 67. 362 km.

Then for one km you would take,

=> 62.076/800 hr ≈ 0.0842 hr

When we convert this then we get,

=> 0.0842 = 5 minutes 3 seconds.

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The perimeter of a figure or shape is the distance around it.

The perimeter of the given path would be

9x + 10x^2 - x^3 + 4x^2 - 7x + 8 - x^2 + 9x + 12

We would collect like terms. It becomes

- x^3 + 10x^2 + 4x^2 - x^2 + 9x + 9x - 7x + 8 + 12

= - x^3 + 13x^2 + 11x + 20

The correct option is C

Distance Between Two Points

We are given two points on the graph attached to the question.

The red point has coordinates (7,3) and the origin is at (0,0)

I'll work out the graph to show the required distance.

The required distance (in the red drawing) is the hypotenuse of a right triangle of lengths 7 and 3, thus the distance is calculated as:

Calculating, we get d is approximately 7.62

the Given

We are asked to find the x-intercept of the linear equation. This can be seen below.

Explanation

To find the x-intercept, we must recall that x-intercept is the point at which the graph of the equation crosses the x-axis. We can find this point by plotting the given equation.

From the graph, we can determine the x-intercept as

Answer: (2,0)

Solution:

Given the graphed polygon below:

To determine the coordinates of the vertices after reflection over the x-axis,

step 1: Give the coordinates of DEFG.

Thus, we have

step 2: Give the reflection formula, over the x-axis.

For reflection over the x-axis, we have

step 3: Give the coordinates after reflection over the x-axis.

From the formula in step 2,

we thus have

The exponential equation that represents the growth of the flying squirrels is F = 350 X 3^t.

An exponential equation can be described as an equation with exponents. The exponent is usually a variable. An exponential equation exhibits a compound growth rate.

The general form of exponential function is f(x) = [tex]e^{x}[/tex]

Where:

The population of the bird = present population x (1 + growth rate)^number of years

350 x (1 + 2)^t

F = 350 X 3^t

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Considering the parameters of the normal distribution for American men's heights, it is found that:

a) The percentage greater than 74 inches is: 2.5%.

b) The proportion between 64 and 71.5 inches is: 0.815.

The z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the following equation:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In the context of this problem, the mean and the standard deviation of the heights of American men are given as follows:

[tex]\mu = 69, \sigma = 2.5[/tex]

The proportion of heights that is greater than 74 inches is one subtracted by the p-value of Z when X = 74, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (74 - 69)/2.5

Z = 2.5

Z = 2.5 has a p-value of 0.9772.

1 - 0.9772 = 0.0228, hence the percentage is of 2.28%. Using the Empirical Rule, this percentage is rounded to 2.5%.

The proportion of heights between 64 inches and 71.5 inches is the p-value of Z when X = 71.5, subtracted by the p-value of Z when X = 64, hence:

X = 71.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (71.5 - 69)/2.5

Z = 1

Z = 1 has a p-value of 0.84. (rounded with the Empirical Rule).

X = 71.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (64 - 69)/2.5

Z = -2

Z = -2 has a p-value of 0.025. (rounded with the Empirical Rule).

Hence the proportion is:

0.84 - 0.025 = 0.815.

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