Evaluate functions from their graph

Interest is a fee charged by a lender to a borrower for the use of money or credit, usually expressed as a percentage of the amount borrowed or invested over a period of time. Brandon invested $\(4700\) at 3% interest and $\(1100\) at \(8\)% interest.  The total interest earned after one year is $229

How much was in each account?

Let x be the amount invested in the first account that pays 3% interest, and let y be the amount invested in the second account that pays 8% interest. Since the total amount invested is $5800, we have:

\(x + y = 5800\)

The amount of interest earned on the first account is 0.03x, and the amount of interest earned on the second account is 0.08y. Since the total interest earned after one year is $229, we have:

\(0.03x + 0.08y = 229\)

We now have two equations with two unknowns:

\(x + y = 5800\)

\(0.03x + 0.08y = 229\)

We can solve for x and y by using elimination or substitution method. Here, we will use the substitution method.

Solve the first equation for x:

\(x = 5800 - y\)

Substitute this expression for x into the second equation and solve for y:

\(0.03(5800 - y) + 0.08y = 229\)

\(174 - 0.03y + 0.08y = 229\)

\(0.05y = 55\)

\(y = 1100\)

Now substitute this value of y into either equation to solve for x:

\(x + 1100 = 5800\)

\(x = 4700\)

Therefore, Brandon invested $\(4700\) at 3% interest and $\(1100\) at \(8\)% interest.

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Answer:

OOk

Step-by-step explanation:

Each piece of pizza has an area of  4.08π square inches.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

The area of a circle with radius r is given by the formula A = πr².

The pizza has a radius of 7 inches

Area of pizza is A = π(7²) = 49π square inches.

The pizza is cut into 12 equal-sized pieces

which means each piece represents 1/12th of the total area of the pizza.

Therefore, the area of each piece is:

(1/12) × 49π = 4.08π square inches

Hence, each piece of pizza has an area of 4.08π square inches.

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The product between functions f(x) and g(x) gives:

(f·g)(x) = x⁵ - 2x³ + 2x² - 8x + 4

Here we have the functions:

f(x) = x³ - 4x + 2

g(x) = x² + 2

The product:

(f·g)(x) is just the product between the two functions, this gives:

f(x)·g(x)

Replacing these functions we will get.

(x³ - 4x + 2)*( x² + 2)

Expanding that product, we will get:

x³*x² + 2x³ - 4x*x² - 8x + 2x² + 4

x⁵ - 2x³ + 2x² - 8x + 4

That is the product.

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A repeating decimal is acceptable to use during calculations when you require a certain level of precision

A repeating decimal is acceptable to use during calculations when you require a certain level of precision, but it's important to keep in mind that the result will be an approximation rather than an exact value.

It is commonly used in situations where a rounded value is sufficient and the level of precision doesn't significantly impact the final result.

On the other hand, you should convert a repeating decimal to a fraction for calculations when you need an exact value or when further mathematical operations or comparisons are required.

Converting a repeating decimal to a fraction allows for precise calculations and eliminates any potential rounding errors associated with working with decimal approximations.

Converting a repeating decimal to a fraction involves identifying the repeating pattern and expressing it as a fraction. This allows for exact calculations and maintains the mathematical properties of fractions.

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\(\sf\large\underline{\star Given:-}\)

\(\rightarrow\) Length of rectangular prism = \(\sf\red{4m}\)

\(\rightarrow\) Width of rectangular prism = \(\sf\red{7m}\)

\(\rightarrow\) Height of rectangular prism = \(\sf\red{8.5m}\)

\(\sf\large\underline{\star To \: Find:-}\)

\(\sf\large\underline{\star Solution:-}\)

\(\rightarrow\) We can find the volume of given rectangular prism by using the formula:

\(\sf\blue{Length × Width ×Height}\)

So, let's begin:

\(\rightarrow\) Volume of rectangular prism = \(\sf{Length × Width ×Height}\)(putting the value of length, width and height from the above given)

\(\rightarrow\)\(\sf{=\:4× 7 ×8.5}\)

\(\rightarrow\)\(\sf{=\:28×8.5}\)

\(\rightarrow\)\(\sf{=\:238m^3}\)

Therefore, volume of the given rectangular prism = \(\sf\purple{238m^3.}\)

______________________________

Hope it helps you:)

The system has an infinite number of solutions, but the only solution is (a, b) = (0, 0).

The given system of equations can be solved using the substitution method. We can begin by solving the first equation,\(a^2 + b^2\), for either a or b. Let's solve for a:

\(a^2 + b^2 = 0\)

\(a^2 + b^2 = 0\)

\(a^2 = -b^2\)

\(a = \pm\sqrt(-b^2)\)

We can substitute this expression for a into the second equation, \(3a^2 - 2ab - b^2 = 0\), and simplify:

\(3(\pm\sqrt(-b^2))^2 - 2(\pm\sqrt(-b^2))b - b^2 = 0\)

\(3b^2 - 2b^2 - b^2 = 0\)

0 = 0

Since 0 = 0, this means that the system of equations has an infinite number of solutions. In other words, any values of a and b that satisfy the equation \(a^2 + b^2 = 0\) will also satisfy the equation \(3a^2 - 2ab - b^2 = 0\)

However, the equation \(a^2 + b^2 = 0\) only has a single solution, which is a = b = 0. Therefore, the solution to the system of equations is (a, b) = (0, 0).

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A solution lies where two functions intersect. Given the following functions:

The function intersects at the point where f(x) = g(x) that is:

Recall from trigonometry identity that:

Substitute the expression for cos2x into the quadratic function to have:

Simplify the result for the value(s) of "x"

Since cosine is positive in the first and fourth quadrant, the other angles will be:

For cos x = 0;

Since cos is also positive in the fourth quadrant, hence;

Therefore the values in the interval [0, 2π) that will make the functions

f (x) = cos 2x + 2 and g(x) = cos x + 1 intersect are:

When it comes to arrays in mathematics, it usually involves objects or numbers that are arranged in rows and columns.In order for a set of squares to be considered an array, it must meet certain requirements. These requirements are:All rows must have the same number of squares. All columns must have the same number of squares. Squares must be organized in an orderly manner. A set of squares that does not meet these requirements is not an array.

An array is a set of objects or values that are organized in a specific order. It is used in programming, mathematics, and other fields to make data manipulation and analysis easier.

When it comes to arrays in mathematics, it usually involves objects or numbers that are arranged in rows and columns.In order for a set of squares to be considered an array, it must meet certain requirements. These requirements are:All rows must have the same number of squares. All columns must have the same number of squares. Squares must be organized in an orderly manner. A set of squares that does not meet these requirements is not an array.

For example, if a set of squares is arranged in a random or disorganized manner, it cannot be considered an array because it does not meet the orderly requirement. Additionally, if the number of squares in each row or column is different, it cannot be considered an array because it does not meet the uniformity requirement.

Overall, it is important to remember that an array is a specific type of organization and cannot be applied to any random set of objects or values.

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At x=2, the function in the graph is approaches to infinity. This is satisfied by equation 1 that models the rational function, hence option 1 is the correct answer.

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.

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

From given graph we can see that

At x=2, the function in the graph is approaches to infinity.

It means function is not defined at x=2

We know that a rational function is undefined when denominator is equal to zero.

For equation 1:

f(x)= 2(x+2)/(x-2)

Equating the denominator:

x-2=0

x=2

It means function is not defined at x=2

The y-intercept is: y= -2

The function is passing through the point (1,-6).

When we substitute x=1

Hence, option 1 is true.

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Answer:-5.25x-21

Step-by-step explanation:7 * -3/4x = -5.25x

                                              7  * -3 = -21

                                                 7(-3/4x-3)= -5.25x - 21

Answer: Yo MAMA + Yo nasty daddy = them having a mistake which is you lol

Step-by-step explanation:

The labeling of bases and height in a trapezium is not fixed and can vary based on the context or problem. It doesn't matter where they are on the trapezium, as long as they are clearly defined and consistent within the given situation.

In a trapezium (or trapezoid), the labeling of the bases and height is not fixed or standardized. It can vary depending on the context or the specific problem being considered. However, there are a few general guidelines to keep in mind when labeling a trapezium.

Bases: The trapezium has two parallel sides, often referred to as the "top base" and the "bottom base." The bases are usually labeled based on their relative lengths or position in the trapezium. The longer parallel side is commonly referred to as the "top base," while the shorter parallel side is referred to as the "bottom base." However, this is not a strict rule and can vary depending on the problem or preference.

Height: The height of a trapezium is the perpendicular distance between the bases. It is generally labeled as a vertical line segment connecting the bases. The placement of the height is not fixed, and it can be drawn from any point on the top base to any point on the bottom base, as long as it forms a perpendicular line. The height is usually labeled with the symbol "h" or sometimes "x" or "y" depending on the context.

It's important to note that the labeling of the bases and height is primarily for communication and clarity. As long as the labeling is consistent and clearly defined within the given problem or context, it does not have to conform to any specific arrangement or be in a rectangular shape. The key is to ensure that the labels are clearly understood and can be used to calculate the desired quantities or solve the problem at hand.

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According to the Pythagorean theorem, The Answer is Yes the third side is greater than 1 foot.

A right triangle is one that has an interior angle of 90 degrees. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The height and base make up the two arms of the right angle.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

p=1 foot

b=1 foot

\(h^{2} = p ^{2} + b ^{2}\)

\(h=\sqrt {1^{2}+1^{2}}\\=\sqrt 2\\=1.41\\\)

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Answer:

2 1/24

Step-by-step explanation:

1. \(\frac{7}{8} * \frac{7}{3}\)

2. \(\frac{7*7}{8*3}\)

3. \(\frac{49}{24}\)

4. \(2 \frac{1}{24}\)

all work should be in the picture, lmk if theres anything confusing

Answer:

a)H0: β1= 1 and Ha: β1 ≠1

b) The test statistic is____.t= b- β/ sb

c) The p-value is____.0.999144

(d) Therefore, we can conclude that:_____. there is not enough evidence to reject the null hypothesis.    

The data provides no evidence at the 0.1 significance level that these thermometers are not consistent.

Step-by-step explanation:

This is called testing hypotheses about β, the population regression co efficient.

The null and alternate hypotheses are

H0: β1= 1 and Ha: β1 ≠1

The significance level is ∝=0.1 and ∝/2 is 0.05

The critical region at t ∝/2 (29)=  t ≤ - 1.699 , t ≥ 1.699

The test statistic is

t= b- β/ sb

which has t distribution with υ= 31-2= 29 degrees of freedom.

Calculations

Ŷ = a +bX

b = SPxy /SS x= Σ(xi-x`)(yi-y`)/Σ(xi-x`)²

b = 39671.6/39680= 0.9998

a = y` - bx`

x`= 60

y`= 59.989

a = 59.989 -0.9998*60 = 0.001734

Syx²= Σ( yi -y`)²/ n-2= 39663.3857/ 29=1367.68965

Syx= 36.9822

Sb= Syx/ √∑  (x-x`)²

Sb= 36.9823/ √39680

Sb= 36.9823/ 199.984

Sb= 0.18493

x-x`                 y-y`                    (x-x`)²     (x-x`)(y-y`)

-60                 -59.969            3600              3598.1419

-56                  -55.999           3136          3135.9458

-52                 -52.079             2704          2708.1097

-48                -47.959              2304           2302.0335

-44                 -43.899              1936          1931.5574

-40                -39.989               1600          1599.5613

-36              -36.009                1296            1296.3252

-32               -31.899              1024              1020.769

-28               -28.049             784                785.3729

-24                -23.959             576               575.0168

-20               -19.989             400                  399.7806

-16                 -15.939            256                  255.0245

-12               -12.039             144                    144.4684

-8                  -7.989             64                       63.9123  

-4                 -4.119                16                      16.4761

0                 -0.08903           0                         0

4                  3.921              16                      15.6839

8                7.961                64                       63.6877

12                12.121             144                     145.4516

16                16.031             256                   256.4955

20               20.021           400                  400.4194

24               24.111              576                   578.6632

28                28.071           784                     785.9871

32                 31.751            1024                    1016.031

36               36.031           1296                    1297.1148

40                39.961          1600                    1598.4387

44                43.881           1936                     1930.7626

48               48.021           2304                     2305.0065

52              52.001             2704                     2704.0503

56             56.051              3136                       3138.8542

60            60.041                3600                     3602.4581

∑0          0                 39680 (SSx)     39671.6 (SPxy)

Putting the values

The test statistic is

t= b- β/ sb

t= 0.9998-1/ 0.18493

t=-0.0010815

Since the calculated t=-0.0010815  does not lie in the critical region  t ∝/2 (29)=  t ≤ - 1.699 , t ≥ 1.699 we conclude that these thermometers seem to be measure temperatures.

The p-value is  ≈ 0.999144

there is not enough evidence to reject the null hypothesis.    

Answer:

Yes 6/3=2 simplified which is way bigger than 2/3

Step-by-step explanation:

Answer:

\( \frac{6}{3} > \frac{10}{15} \)

Step-by-step explanation:

6/3=2

10/15 = 2/3 = 0.66...

2 > 0.66

To find out how many visitors Jackson's Ice Cream Shop needs on Saturday to make a profit for the week, we need to first calculate the total number of visitors for the six days already given in the table. Then we can find out the number of visitors needed on Saturday to reach the required mean of 110 visitors per day for the week.

Total number of visitors for the six days = 63 + 77 + 121 + 96 + 137 + 154 = 648

To make a profit for the week, the total number of visitors for the entire week needs to be:

110 visitors/day × 7 days/week = 770 visitors/week

We already have 648 visitors for the six days, so the number of visitors needed on Saturday to make a profit can be found by subtracting the total number of visitors already counted from the total number of visitors needed for the week:

770 - 648 = 122

Therefore, the answer is (C) 122 visitors on Saturday are needed to make a profit for the week.

Answer:

-75 and 75

Step-by-step explanation:

The two numbers chosen or plotted by them are:

-75 and 75

Step-by-step explanation:

It is given that Bernita and Derek each plot a number on a number line with the properties:

1. The two numbers they have plotted are unique or different.

2. Also there absolute value is same.

3. The sum of the absolute values of the numbers is 150.

We know that Absolute value of a positive number is a number itself and absolute value of a negative number is it's inverse.

So the two numbers that satisfy the above three properties are:

-75 and 75.

Answer:

B. There is sufficient sample evidence to support the claim that the true mean weight, in ounces, of all Colgate toothpaste tubes is not 6 oz.

Step-by-step explanation:

A two-tailed hypothesis test is performed.

The null and alternative hypothesis are:

\(H_0: \mu=6\\\\H_a:\mu\neq 6\)

The P-value calculated in this test is 0.0104.

As this P-value (0.0104) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the mean fill volume differs significantly from 6 oz.

solution

Part a

For this case we have this:

2 1/2 = 2.5 ft * 4 walls =10ft

21 1/4 = 21.25 ft * 3walls = 63.75 ft

32 ft * 1 wall = 32 ft

Part b

3.5 ft * 3walls = 10.5 ft

22.75 ft * 2walls = 45.5 ft

58 ft* 1 wall = 58ft

Part c

P = Number of walls * lenght of wall

Part D

For Valerie we have:

10ft + 63.75 + 32 ft= 105.75 ft

And for Seth we have:

10.5 + 45.5 + 58ft= 114 ft

Part E

We have different answers since both measures different values

And we can see that we dont have the same answer since 105.75 ft is not equal to 114 ft

The corresponding values of g(x) \(g(x)=-3(\frac{1}{2} )^x\) are -12, -6, -3, and -1.5.

A graph of each of the point of g(x) is shown in the image below.

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

Next, we would determine the corresponding y-values of g(x) for each x-values given in the table as follows;

When the x-value = -2, the corresponding y-values of g(x) is given by:

\(g(-2)=-3(\frac{1}{2} )^{-2}\)

g(-2) = -3 × 4

g(-2) = -12.

When the x-value = -1, the corresponding y-values of g(x) is given by:

\(g(-1)=-3(\frac{1}{2} )^{-1}\)

g(-1) = -3 × 2

g(-1) = -6.

When the x-value = 0, the corresponding y-values of g(x) is given by:

\(g(0)=-3(\frac{1}{2} )^{0}\)

g(0) = -3 × 1

g(0) = -3.

When the x-value = 1, the corresponding y-values of g(x) is given by:

\(g(1)=-3(\frac{1}{2} )^{1}\)

g(1) = -3 × 0.5

g(1) = -1.5.

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If you have any specific questions or need assistance, feel free to ask, and I'll do my best to provide a helpful response within the scope of my training

As an AI language model my understanding of subjects and skills is based on the information and data available to me up until my last training update in September 2021. I can provide accurate and comprehensive responses within the limits of my training, but please keep in mind that I may not have knowledge of events or developments that have occurred after that cutoff date.

With a wide range of general knowledge, I can understand and generate responses on various topics such as science, history, literature, mathematics, and more. I can also assist with specific skills like writing, editing, brainstorming ideas, offering explanations, and providing recommendations.

However, it's important to note that while I strive to be helpful, I am still an AI and may not always provide perfect answers. I do not possess personal experiences or opinions, and I am not able to perform physical actions. My responses are generated based on patterns and examples from my training data.

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.

Answer:

\( - \frac{3}{4} n + \frac{3}{8} \)

Step-by-step explanation:

\( \frac{1}{4} ( - 3n + \frac{3}{.2} \)

1/4multiply both -3n and 3/2

The probability that next year there will be no snowfall in that town on January 1 is,

P (no snowfall) = 0.770

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

We have to given that;

Based on a weather record, the probability of snowfall in a certain town in New York on January 1 is 0.230.

Now, WE get;

the probability that next year there will be no snowfall in that town on January 1 is,

P (no snowfall) = 1 - P (snowfall)

P (no snowfall) = 1 - 0.230

P (no snowfall) = 0.770

Thus, The probability that next year there will be no snowfall in that town on January 1 is,

P (no snowfall) = 0.770

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The probability of having a height that is between 158 cm and 163 cm is 0.69011 and the value of x is 169 centimeters

The given parameters are:

Calculate the z-scores at x = 158 and x = 163 using:

\(z = \frac{x - \mu}{\sigma}\)

So, we have:

\(z = \frac{158 - 161}{6} = -0.5\)

\(z = \frac{163 - 161}{6} = 0.33\)

The probability is then represented as:

P(158 ≤ x ≤ 161) = P(-0.5 ≤ z ≤ 0.33)

Using the z table, we have:

P(158 ≤ x ≤ 161) =  0.69011

Hence, the probability of having a height that is between 158 cm and 163 cm is 0.69011

The probability is represented as:

P(X ≥ x) = 1%

Express as decimal

P(X ≥ x) = 0.10

The z-score at p = 0.10 is:

z = 1.282

Substitute z = 1.282 in \(z = \frac{x - \mu}{\sigma}\)

\(1.282 = \frac{x - \mu}{\sigma}\)

Make x the subject

\(x = 1.282\sigma + \mu\)

Substitute values for standard deviation and mean

x = 1.282 * 6 + 161

Evaluate

x = 168.692

Approximate

x = 169

Hence, the value of x is 169 centimeters

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