A container in the shape of a triangular prism is used to hold a slice of pizza. The dimensions of the container are shown in the diagram.



Pizza, 10.8 inches, 7.2 inches, 1.5 inches, 9 inches



What is the volume of the container in cubic inches?

The total cost of the house we can afford is $⁢242,139.78.

What is compound interest?

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

First, we need to determine the maximum monthly payment we can afford based on the recommended guidelines. If we can only spend 1414 of our take-home pay on a house payment, then:

Monthly payment = 0.45 × take-home pay

1414 = 0.45 × 3160

1414 = 1422

Therefore, we can afford a maximum monthly payment of $⁢1422.

Next, we can use the present value formula to find the maximum loan amount we can afford:

Loan amount = (monthly payment / monthly interest rate) × (1 - (1 + monthly interest rate)^(-n))

where monthly interest rate = 4.35% / 12 = 0.003625, and n = 15 years × 12 months/year = 180 months.

Substituting the values, we get:

Loan amount = (1422 / 0.003625) × (1 - (1 + 0.003625)^(-180))

Loan amount = $⁢225,739.78

Therefore, the maximum cost of the house we can afford with a 15-year mortgage is $⁢225,739.78 + $⁢16,400 (down payment) = $⁢242,139.78. Rounded to the nearest cent, the total cost of the house we can afford is $⁢242,139.78.

Hence, the total cost of the house we can afford is $⁢242,139.78.

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let the number be x, next perform calculations on it

double : 2x

subtract 2 : 2x - 2

2x - 2 = 9

2x = 9 + 2

x = 11 ÷ 2 = 5.5

so the number is 5.5

The rate of increasing the area of the rectangle is 72cm²/s

We have, The length of a rectangle is increasing at a rate of 5 cm/s and its width is increasing at a rate of 4 cm/s. When the length is 13 cm and the width is 4 cm, we have to find how fast is the area of the rectangle increasing.

The area of a rectangle is given by, A = l × w

Where l is the length and w is the width.

Now we will differentiate the equation with respect to time t.

dA/dt = d/dt (l × w)

dA/dt = l(dw/dt) + w(dl/dt)

We can use this formula to calculate how fast the area of the rectangle increases when the length is 13 cm and the width is 4 cm.

Substituting the given values, l = 13 cm and dl/dt = 5 cm/s w = 4 cm and dw/dt = 4 cm/s

dA/dt = 13(4) + 4(5)

dA/dt = 72 cm²/s

Therefore, the area of the rectangle increasing at a rate of 72 cm²/s.

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Answer:

the answer is 13700m²

Step-by-step explanation:

cut this shape in two parts namely

A and B

from my view it could be cut into 1. two triangles or 2. a triangle and a rectangle

I will pick 2 because it seems much more simpler

let the triangle be A

let the rectangle be B

firstly you have to cut it then separate the shape with name given when dis is done you'll have

for ∆A=length=170-70=100m

but in B the small place is 110m,but the bigger one is 160

so to find height of triangle we say

160m-110m=50m for h of A

so for B we have

length=160m, width of breath=70m

Area of the total shape=area of A + area of B

=1/2(b×h) + (L×B)

=1/2×100×50 + (160×70)

=50m×50m+11200m²

=2500+11200

=13700m²

The difference quotient of the given function is\[\frac{f(x+h) - f(x)}{h} = \frac{-2x - h}{x^2(x+h)^2}\]The given function is\[f(x) = \frac{9}{x^2}\]

Now we have to find the difference quotient of this function, which is given as\[\frac{f(x+h) - f(x)}{h}\]

We are given that \(h ≠ 0\).

So, first let's find \(f(x+h)\).\[f(x+h) = \frac{9}{(x+h)^2}\]

Now we can put both the values of \(f(x+h)\) and \(f(x)\) in the difference quotient.

\[\frac{f(x+h) - f(x)}{h} = \frac{\frac{9}{(x+h)^2} - \frac{9}{x^2}}{h}\]

Let's put the LCM of \((x+h)^2\) and \(x^2\) which is \(x^2(x+h)^2\) in the numerator.

\[\frac{\frac{9x^2 - 9(x+h)^2}{x^2(x+h)^2}}{h}\]

Now, simplify the numerator.

\[\frac{9x^2 - 9(x^2 + 2xh + h^2)}{x^2(x+h)^2h}\]\[\frac{9x^2 - 9x^2 - 18xh - 9h^2}{x^2(x+h)^2h}\]

Now we can cancel out the common factor of 9 from both numerator and denominator.

\[\frac{-2xh - h^2}{x^2(x+h)^2h}\]

Now cancel out h from both numerator and denominator.

\[\frac{-2x - h}{x^2(x+h)^2}\]

So, the difference quotient of the given function is\[\frac{f(x+h) - f(x)}{h} = \frac{-2x - h}{x^2(x+h)^2}\]

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Answer:

[tex]\huge\boxed{\sf 21 \ pencils}[/tex]

Step-by-step explanation:

Ali has 3 pencils.

Melvin has twice.

So,

Melvin pencils = 2 × 3

Zachary has four times as many pencils as Ali.

So,

Zachary' pencils:

= 4 × 3

So:

= 3 + 6 + 12

[tex]\rule[225]{225}{2}[/tex]

The area of the circle is 7 ft^2

Circle is an  closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre” which is measured in terms of its radius. It is also a closed shape formed by tracing a point that moves in a plane such that its distance from a given point is constant.

Area of a circle = πr^2 or π(d/2)^2

Where π = 22/7

Diameter = 3ft = 3ft/2 = 1.5 ft

Radius = 1.5ft

Area = 22/7 * (1.5)^2

Area = 22/7 * 2.25

Area = 7.07

Area = 7 ft^2 to nearest whole number

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x = -1/7.

To solve the absolute value equation or indicate that th |7x-4|+5=5, you should follow the steps given below:Step 1: Write the absolute value equation as two separate equations, one with a positive argument and one with a negative argument. |7x - 4| + 5 = 5, can be written as:7x - 4 + 5 = 5 or 7x - 4 - 5 = -5Step 2: Simplify both equations.7x = 4 or 7x = -1Step 3: Solve for x by dividing both sides by the coefficient of x.7x = 4 → x = 4/7 or7x = -1 → x = -1/7Therefore, the solution of the absolute value equation |7x-4|+5=5 is x = 4/7 and x = -1/7.

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The mean height of camp 1 is 2.5.

A dοt plοt is a type οf graphical display that shοws the distributiοn οf a set οf data values. In a dοt plοt, each data pοint is represented by a dοt that is placed abοve its cοrrespοnding value οn a number line οr axis. The dοts are stacked οn tοp οf each οther tο shοw the frequency οr density οf the data at each value οr range οf values.

Dοt plοts are useful fοr visualizing small tο mοderate-sized data sets and fοr identifying patterns, οutliers, and gaps in the data. They are alsο easy tο cοnstruct and interpret, making them a pοpular tοοl fοr explοratοry data analysis.

Mean height of club fit = (2 + 2 + 3 + 5 + 3 + 3 + 1 + 1)/8

                                      = 2.5

Thus, The mean height of camp 1 is 2.5.

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Complete question:

There are 132 entertainers who do not have red hair.

What is Percentage?

Percentage is a way of expressing a number or quantity as a fraction of 100. It is represented by the symbol "%". Percentages are commonly used to express the proportion or ratio of one quantity to another.

Percentages are widely used in many fields, including mathematics, science, finance, and economics, among others. They are a convenient way to express a relative quantity or change in quantity, and are easy to compare and interpret.

If 12% of the entertainers have red hair, then 100% - 12% = 88% do not have red hair.

To find out how many entertainers do not have red hair, we can calculate 88% of the total number of entertainers:

88% = 88/100 = 0.88

Number of entertainers without red hair = 0.88 x 150 = 132

Therefore, 132 entertainers do not have red hair.

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The correct option is d. If the correlation coefficient r is equal to 0.521, the coefficient of non-determination is 0.271.

Correlation is a term used to describe the relationship between two variables in a statistical context. The correlation coefficient is a measure of the strength and direction of the relationship between two variables.

The coefficient of non-determination is used in statistics to refer to the proportion of variability in one variable that is not accounted for by another variable. It is equal to 1 - r², where r is the correlation coefficient between the two variables.

So, the coefficient of non-determination can be found using the formula:

Coefficient of non-determination = 1 - r²Given that the correlation coefficient, r = 0.521, substitute the value in the formula to find the coefficient of non-determination:

Coefficient of non-determination = 1 - (0.521)²= 1 - 0.271 = 0.729

Hence, the answer is (a) 0.729.

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Applying the definition of a diameter, we can conclude that m<AOE = 80 degrees. Therefore, m<AOE = 50 is FALSE.

The diameter is the longest chord passing through the center of a circle, while the radius is the distance from the center to any point on the circumference. The diameter forms two semicircles or divides the circle into two halves.

We are given that AD and EC are diameters of the circle O. This means that EOC is a straight angle or semicircle, which is equal to 180 degrees. Therefore:

m<EOC - m<AOB - m<BOC = m<AOE

Substitute:

180 - 50 - 50 = m<AOE

80 = m<AOE

m<AOE = 80°

Therefore, the statement, m<AOE = 50 is FALSE.

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The solution to the equation x² + 2x = 18 is x = 4 ± √19.

Karappan Poochi: Algebra vs The Cockroaches is a math-based game designed to help students learn and practice algebra. The objective of the game is to help Karappan, a character in the game, solve algebraic equations. Players must solve equations by manipulating the variables and constants to reach the correct answer. To reach level six, the player must solve six equations correctly.

The equation for level six is x² + 2x = 18. To solve this equation, the player must first recognize that it is a quadratic equation and can be solved using the quadratic formula. The formula is: x = [-b ± √(b²-4ac)]/2a. For this equation, a = 1, b = 2, and c = -18. Plugging these values in, the player gets: x = [-2 ± √(2²-4(1)(-18))]/2(1). This simplifies to x = [-2 ± √76]/2, which simplifies to x = [8 ± √76]/2. Therefore, the solution to this equation is x = 4 ± √19.

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Answer:

17%

Step-by-step explanation:

Calculate the difference in the population

181,000 - 150,230 = 30,770

Decrease is 30,770

Perecentage decrease = Decrease/ original population x 100%

30770/ 181,000 x 100 = 0.17 x 100

= 17%

Check 17% of 181,000

Deduct from 181,000 and you will get 150,230

1. The parts of the circle identified are as explained below. 2. Area = 153.94 m²; Circumference ≈ 43.98 m; 3. Area ≈ 706.86 ft²; Circumference ≈ 94.25 ft; 4. Area ≈ 326.85 in.; Circumference = 64.09 in.

A circle is a closed two-dimensional shape that consists of points that are equidistant from a central point called the center.

1. An example of each part using the diagram of the circle given would be:

a. a center is K

b. One radius is JK

c. A chord is JL

d. Diameter is JI

e. Secant is GI

f. Tangent is GJ

g. Point of tangency is J

h. A minor arc is IL

i. A major arc is HIL

j. Semicircle is JLI

k. A central angle is <JKL

l. An inscribed angle is <HIJ

Use the area and circumference formula to calculate each required measure for each circle.

2. Area = πr² = π*7² = 153.94 m²

Circumference = 2πr = 2·π·7 ≈ 43.98 m

3. Area = πr² = π·15² ≈ 706.86 ft²

Circumference = 2·π·15 ≈ 94.25 ft

4. Area = πr² = π·10.2² ≈ 326.85 in.²

Circumference = 2·π·10.2 ≈ 64.09 in.

5. Area = πr² = π·9² ≈ 254.47 mm²

Circumference = 2·π·9 ≈ 56.55 mm

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Therefore , the solution of the given problem of parallelograms comes out to be s intended, overline DE and overline FB are congruent.

In Euclidean mathematics, a simple quadrilateral of two sets of equal distances is referred to as a parallelogram. In a specific kind of quadrilateral known as a parallelogram, both set of opposite sides are straight and equal. There are four types of parallelograms, 3 of which are each mutually exclusive. Rhombuses, parallelograms, squares, but also rectangles are the four distinct shapes.

Here,

We can use the midpoint theorem and the fact that the opposing sides of a parallelogram are parallel and congruent to demonstrate that overline DE is congruent with overline FB.

The midpoint theory tells us that DE EA because we first know that E is the midpoint of overline AB.

The midpoint theory tells us that BF FC because we also know that F is the midpoint of overline DC.

As a result, overline DE and overline BC are parallel, and overline BF and overline AD are parallel.

DE EA and BF FC resulted in:

=> FC = EA Plus DE (Preserving equality by adding identical lengths)

If we replace FC with EA and DE with BF, we get:

=> BF + FC = DE + DE

If we simplify, we get:

=> 2DE = 2BF

When you divide both parts by 2, you get:

=> DE = BF

We have thus demonstrated that, as intended, overline DE and overline FB are congruent.

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A bar graph or a histogram is best suited for displaying the number of hours spent watching television by people from different age ranges.

What is a bar graph?

A bar graph is a type of graph that uses bars or rectangles to represent data, with the height or length of each bar proportional to the value it represents.

Both types of graphs can easily show the distribution of data across different age groups and allow for easy comparison of the number of hours spent watching television.

The choice between a bar graph or a histogram depends on the nature of the data and the desired level of detail.

A bar graph is appropriate when the data is categorical (e.g., age ranges) while a histogram is used when the data is continuous (e.g., number of hours).

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[tex]TU = 2QS = 2(7)[/tex]

[tex]\implies \bf TU = 14[/tex]

The events H1 and H2 are independent.

Let P(B) be the probability that the selected coin is the biased one. Since we're picking the coin at random, P(B) = 0.5. Now, suppose we get two heads in a row. Let's call this event E. If E happens and the coin we picked is the biased coin, then the probability of getting two heads in a row is given by the probability that the biased coin gives heads twice, which is (2/3)² = 4/9. Therefore, the probability that we picked the biased coin given that we got two heads in a row is: P(B|E) = P(E|B)P(B) / [P(E|B)P(B) + P(E|F)P(F)], where F is the event that the fair coin is chosen. Note that the probability of getting two heads in a row with the fair coin is 1/4. Hence, the above formula becomes P(B|E) = (4/9 x 0.5) / [(4/9 x 0.5) + (1/4 x 0.5)] = 16/29. Therefore, the probability that we picked the biased coin given that we got two heads in a row is 16/29. b) The outcomes are independent given the picked coin, hence P(H1 ∩ H2) = P(H1)P(H2). Therefore, the events H1 and H2 are independent.

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The perimeter of the figure is 52 cm

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

The composite figure

The perimeter of the figure is the sum of the side lengths of the figure

So, we start by calculating the missing lengths as follows

Missing = 12 cm/4

Missing = 3 cm

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

Perimeter = 12 + 9 + 3 + 3 + 3 + 3 + 3 + 3 + 7 + 9 - 3

Evaluate

Perimeter = 52

Hence, the perimeter is 52 cm

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Answer: -3, -2, -1, 0, 1 and 2

Answer:

0, 1, and 2

Step-by-step explanation:

A whole number is any number that does not contain a fraction, decimal, or negative value. For example, 1, 25, and 365 are whole numbers. Whereas the values of -3, 100.01, 365 ¼, and 2006.3 are not.

The fifth term of the given sequence is: a₅ = 63

We are told the formula for the nth term of the sequence is given as:

aₙ = aₙ₋₁ + 6(n - 1) for n ≥ 2

We are given:

a₁ = 3

a₂ = 9

a₃ = 21

a₄ = 39

Thus:

a₅ = a₅₋₁ + 6(5 - 1)

a₅ = a₄ + (6 * 4)

a₅ = 39 + 24

a₅ = 63

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Answer:

Para saber cuántas galletas puso Mark en cada paquete, podemos dividir el número total de galletas por el número de paquetes:

195 galletas ÷ 13 paquetes = 15 galletas por paquete

Por lo tanto, Mark puso 15 galletas en cada paquete.

¡Espero que esto haya ayudado! Si no es así, lo siento. Si necesitas más ayuda, ¡pregúntame! :]

The social media stock would earn $ more than the conglomerate corporation's stock.

When answering questions on Brainly, it is important to always be factually accurate, professional, and friendly, be concise and not provide extraneous amounts of detail, repeat the question in your answer, provide a step-by-step explanation in your answer, and use the following terms in your answer: geometric, Compare, invested.The value of a conglomerate corporation's stock was $1,145 in 2014.

If $1,000 were invested in this stock, what would its value be in 2017 if the stock had increased 3.5% annually?The solution to the given problem is as follows:Calculate the value of the stock when $1,000 was invested in 2014.Using the geometric mean formula,$\text{Geometric mean} = \sqrt[n]{a_1a_2a_3\cdots a_n}$Here, $n = 3$ since the value is given for the years 2014, 2015, and 2016. $a_1 =$ the value of the stock in 2014, $a_2 =$ the value of the stock in 2015, and $a_3 =$ the value of the stock in 2016.

We have to find $a_1$.Solve for $a_1:$\[a_1 = \frac{\text{Geometric mean}}{\sqrt[n-1]{a_2a_3\cdots a_n}} = \frac{\sqrt[3]{1145}}{\sqrt[2]{1.035^2}} \approx 1042.97\]Therefore, the value of the stock when $1,000$ was invested in 2014 was approximately $1,042.97$.

Calculate the value of the stock in 2017.Using the same formula as before, we have:\[\text{Geometric mean} = \sqrt[3]{1042.97 \cdot 1.035 \cdot 1.035} \approx 1,124.54\]Therefore, the value of the stock in 2017 would be approximately $1,124.54$ dollars.Compare the results obtained from the above two parts to the value of $1,000$ of the social media stock.

The value of $1,000$ of the social media stock after three years with a 7% annual increase is given by:\[\text{Social media stock} = 1000 \cdot (1 + 0.07)^3 \approx 1225.04\]Therefore, we can compare the results obtained from the two previous parts to see which one is greater. It is clear that the social media stock value of $1,000$ is greater than that of the conglomerate corporation's stock. Therefore, the correct answer is:The value of the $1,000 invested in the conglomerate corporation's stock in 2014 was less than that of the value of the $1,000 invested in the social media stock. The social media stock would earn $ more than the conglomerate corporation's stock.

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Answer:

B

Step-by-step explanation:

This is just the prosses of elmiation. How is A even possablie, C doesnt make sense, and D is also a non logical or solvable question. Thus its b.

Answer: 5 bags

Step-by-step explanation: convert the proper fraction (3 1/3) into improper fractions (10/3)
then do 10 / 2 because the denominators are the same
5 bags

Answer:

Step-by-step explanation:

Describe the situation with a division equation

The length of the string which is pulled taut as described in the task content is; 100.2 ft.

As evident in the task content; the kite is flying 85 ft off the ground, and the angle of elevation is; 58°.

It therefore, follows from trigonometric ratios that the ratio which holds true is;

sin (58°) = 85 / l

where l = Length of the string.

Therefore;

Multiply both sides by l;

l sin (58) = 85

Divide both sides by sin (58);

l = 85 / sin (58)

I = 100.2 ft (nearest tenth)

Ultimately, the length of the string as described in the task content is; 100.2 ft.

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The distance between point M and point N is 12 units.

Coordinates are a set of numbers or vaIues that describe the position or Iocation of a point in space. In two-dimensionaI space (aIso known as the Cartesian pIane), coordinates are typicaIIy represented by two vaIues, usuaIIy denoted as (x, y), that describe the horizontaI and verticaI position of a point reIative to a set of axes.

The distance formuIa is a mathematicaI formuIa used to find the distance between two points in a two- or three-dimensionaI space.

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

The distance formuIa is based on the Pythagorean theorem, which states that in a right triangIe, the square of the Iength of the hypotenuse (the side opposite the right angIe) is equaI to the sum of the squares of the Iengths of the other two sides.

In the given question,

We can use the distance formuIa to find the distance between point M and point N:

d = √[(x₂ - x₁)²+ (y₂ - y₁)²]

where (x₁, y₁) are the coordinates of point M and (x₂, y₂) are the coordinates of point N.

PIugging in the given vaIues, we have:

d = √[(-8 - 4)² + (-8 - (-8))²]

d = √[(-12)² + 0²]d = √[144]

d = 12

Therefore, the distance between point M and point N is 12 units.

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Answer:

the left one is cheaper, the difference is 4.2 pounds cheaper

Step-by-step explanation: