Max spent 3/5 of his money in a shop and 1/4 of the remainder in another shop. (a) What fraction of his money was left ?

The approximate volume of the cooking pot will be;  2009.6 cubic inches.

Since volume of the cylinder is the product of the height, pie, and square of the radius.

The volume of the cylinder = [tex]\pi r^{2} h[/tex]

We know that the volume of the cylinder is  [tex]\pi r^{2} h[/tex]

Here we are given that Trevor is making soup in a cylindrical cooking pot that has a diameter of 10 inches and a height of 8 inches.

h=10 in, and r= 8 in, so

[tex]\begin{gathered} V=(3.14)(10 in)(8 in)^2 \\ V= 2009.6 in^3 \end{gathered}[/tex]

Then, the pot can hold 2009.6 cubic inches

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The best prediction about the number of cookies the college will need is that they will have about 480 students who prefer cookies. Option A is the correct answer.

According to the table, out of 225 students, 27 students prefer cookies. To find an estimate of the number of cookies the college will need for its 4,000 students, we can set up a proportion:

27/225 = x/4000

Solving for x, we get:

x = (27/225) * 4000

x = 480

Therefore, the best prediction about the number of cookies the college will need is that they will have about 480 students who prefer cookies. Option A is the correct answer.

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On solving the provided question we can say that equation  As a result, the expedition can go 476 kilometres before running out of fuel.

A mathematical equation is a formula that connects two statements and denotes equivalence with the equals symbol (=). An equation is a mathematical statement that shows the equality of two mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the variables 3x + 5 and 14. A mathematical formula describes the connection between the two sentences that occur on opposite sides of a letter. The symbol and the single variable are frequently the same. As in 2x - 4 equals 2, for instance.

To calculate how far the expedition can travel before running out of gas, apply the following formula:

Miles = (Gallons of gas) x (Miles per gallon)

Plugging in the given values, we get:

Miles = 28 gallons x 17 mpg

Miles = 476 miles

As a result, the expedition can go 476 kilometres before running out of fuel.

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Answer: The null hypothesis for this scenario is that the proportion of readers who own a personal computer is 0.51 or less:

H0: p <= 0.51

The alternative hypothesis is that the proportion of readers who own a personal computer is greater than 0.51:

Ha: p > 0.51

To test this hypothesis, we would need to collect a random sample of readers and determine the proportion of readers who own a personal computer in the sample. We could then use a one-sample proportion test to determine whether the proportion in the sample is significantly different from the null hypothesis value of 0.51. If the p-value is less than 0.05, we would reject the null hypothesis and conclude that there is sufficient evidence to substantiate the publisher's claim that more than 51% of their readers own a personal computer. If the p-value is greater than or equal to 0.05, we would fail to reject the null hypothesis and conclude that there is not sufficient evidence to substantiate the publisher's claim.

Step-by-step explanation:

Answer:

Step-by-step explanation:

It should be 177.88

A statement 'The function f(x)=log0. 75x is decreasing' is True.

We know that a function, y = f(x) is a decreasing function when (dy/dx) ≤ 0 for all such values of interval (a, b).

Consider a function  f(x)=log(0.75^x)

We write a function f(x) as,

f(x) = log(0.75^x)

f(x) = log[(3/x)^x]

f(x) = log([tex]\frac{3^x}{4^x}[/tex])

Now we find the derivative of above function with respect to x.

f'(x) = d/dx [ log([tex]\frac{3^x}{4^x}[/tex])]

f'(x) = [tex]1/(\frac{3^x}{4^x} )[/tex] [d/dx ([tex]\frac{3^x}{4^x}[/tex])]

f'(x) = [tex](\frac{4^x}{3^x})[\frac{4^x[3^xlog(3)]-3^x[4^xlog(4)]}{4^{2x}} ][/tex]

f'(x) = log(3) - log(4)

f'(x) = -0.1249

f'(x) < 0

So, the function f(x) is a decreasing function.

Thus the statement is True.

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P(A and B) is not equal to P(A) * P(B), we can conclude that events A and B are dependent.

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

We can determine if events A and B are independent or dependent by comparing the probability of both events occurring together with the product of their individual probabilities.

P(A and B) = 1/7

P(A) = 2/3

P(B) = 3/7

If A and B are independent events, then P(A and B) = P(A) * P(B). However, in this case, P(A and B) is not equal to P(A) * P(B):

P(A) * P(B) = (2/3) * (3/7) = 2/7

Since P(A and B) is not equal to P(A) * P(B), we can conclude that events A and B are dependent.

Events A and B are dependent since the probability of their intersection is not equal to the product of their individual probabilities. Specifically, P(A and B) = 1/7 while P(A)*P(B) = 2/7.

Therefore, P(A and B) is not equal to P(A) * P(B), we can conclude that events A and B are dependent.

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Step-by-step explanation:

f(x) = - 2 (x+1)^2 + 8     is already in vertex form

quadratic form can be found by expanding it :

f(x) = -2 ( x^2 + 2x +1)  + 8

f(x0 = -2x^2 -4x -2 + 8  

f(x) =  - 2x^2 - 4x + 6     <=====quadrtaic form

The difference between the two items are depends on sample size, the method of counting, or the criteria for classification can all impact the percentage calculation.

Percentage is a measure of the proportion of one value to another expressed as a fraction of 100. For example, if there are 100 apples, and 25 of them are red, then the percentage of red apples is 25%. Similarly, if there are 200 bananas, and 50 of them are ripe, then the percentage of ripe bananas is also 25%.

However, the context in which these percentages are calculated can be different. For instance, the way in which the 25% of red apples was calculated could be different from how the 25% of ripe bananas was calculated.

To illustrate this, let's consider an example. Suppose there are two cities, A and B, with populations of 10,000 and 5,000, respectively. In city A, 2,500 people have blue eyes, while in city B, 1,250 people have blue eyes. At first glance, it may seem that the percentage of people with blue eyes is the same in both cities, at 25%.

However, if we look closer, we can see that the actual number of people with blue eyes is different between the two cities. City A has twice as many people with blue eyes as city B, even though the percentage is the same.

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Answer:

  √37 ≈ 6.083

Step-by-step explanation:

You want the modulus of the complex number 6 -i.

The modulus of a number is written using absolute value bars:

  |6 -i|

The modulus of a complex number is the root of the sum of the squares of the real and imaginary parts:

  |6 -i| = √(6² +(-1)²)

  |6 -i| = √37 ≈ 6.083

Answer:

7) 760

8) 34

Step-by-step explanation:

7)  95x8=760

8)  (103-35)/2=34

In the above scenario, it can be estimated with 95% confidence that the true proportion of young adult novels that include a love triangle are between 0.6854 and 0.8890

First we compute the Point Estimate

PE = 59/75 = 0.7867

Next we compute the standard error

SE = √((- - hat x (1 - p- hat) )/n)

= √( (o.7867 x (1 - 0.7867 ))/ 75
= 0. 509

Since the expected confidence level is 95%,

Margin of error = t - critical x S E

= 1.99 x 0.0509
= 0.101291

Thus,

point estimate ± margin of error

0.7867  ±  0.1013

(0.6854, 0.8880)

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Here he formula for v is:

v = √(2gh)

What is meant by the term formula?

A formula is a mathematical relationship or rule that is expressed using symbols and mathematical operations. It is used to represent a relationship between quantities or to calculate a value based on given variables or inputs. Formulas are often used in various branches of mathematics, science, and engineering.

According to the given information

To change the subject of the formula mgh = (1/2)mv² to v, we need to isolate v on one side of the equation.

First, we can multiply both sides of the equation by 2 to eliminate the fraction:

2mgh = mv²

Next, we can divide both sides of the equation by m:

(2mgh) / m = v²

Simplifying the left side, we get:

2gh = v²

Finally, we can take the square root of both sides of the equation to solve for v:

v = √(2gh)

Therefore, the formula for v is:

v = √(2gh)

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To find the missing value in the equivalent ratio 12:18 = 16:___, you can use cross-multiplication.

First, you multiply the first term of the first ratio by the second term of the second ratio, and then you set it equal to the product of the second term of the first ratio and the missing value in the second ratio.

So, you get:

12 x ___ = 18 x 16

To solve for the missing value, you can divide both sides of the equation by 12:

___ = (18 x 16)/12

Simplifying the right-hand side, you get:

___ = 24

Therefore, the missing value in the equivalent ratio 12:18 = 16:___ is 24

Answer:24

Step-by-step explanation:

12:18

= 6:9

= 2:3

=16:24

First, you simplify it as much as you can and then scale it up to the number necessary.

Opposite rays can be defined as a figure formed by two collinear rays with a common endpoint, since the two rays lie on the same line.

The solution is: number of cubes are 1120.

Here, we have,

Volume of wood block :

V = (n+5)(n+8)(n+14)

Number of cubes = Volume of wood block/ Volume of small cubes

Number of cubes, N = (n+5)(n+8)(n+14)    ....1)

Number of cubes with on sides painted is :

n = (n+5-2)(n+8-2)(n+14-2)

n = (n+3)(n+6)(n+12)

It is given that :

n = N/2

(n+3)(n+6)(n+12) = (n+5)(n+8)(n+14)/2

Solving above equation, we get :

n = 2

Putting value of n in equation 1, we get :

N = (2+5)(2+8)(2+14)

N = 7×10×16

N = 1120  cubes

Therefore, number of cubes are 1120.

Hence, this is the required solution.

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complete question:

A block of wood is in the shape of a rectangular prism with dimensions n+5 cm, n+8 cm, and n+14 cm. All faces of the block are painted, and then the block is cut into 1cm cubes using parallel cuts to each face. If exactly half of the cubes have no paint on them, find the total number of cubes.

Answer:

True

hope it helps :) !!!

Answer:

the answer is true, it's the objects net is the same as the surface area.

On solving the provided question we can say that As a result, the surface area of the rectangular prism with 3 cm, 9 cm, and 6 cm dimensions is [tex]198 cm^2.[/tex]

The surface area of an object indicates the overall space occupied by its surface. The surface area of a three-dimensional form is the entire amount of space that surrounds it. The surface area of a three-dimensional form refers to its full surface area. By summing the areas of each face, the surface area of a cuboid with six rectangular faces may be computed. As an alternative, you may use the following formula to name the box's dimensions: 2lh + 2lw + 2hw = surface (SA). Surface area is a measurement of the total amount of space occupied by the surface of a three-dimensional object (a three-dimensional shape contains height, breadth, and depth).

The surface area of a rectangular prism is given by the formula:

SA = 2(lw + lh + wh),

where l, w, and h are the rectangular prism's length, width, and height.

SA = 2(3×9 + 3×6 + 9×6)

= 2(27 + 18 + 54)

= 2(99)

= 198 cm²

As a result, the surface area of the rectangular prism with 3 cm, 9 cm, and 6 cm dimensions is [tex]198 cm^2.[/tex]

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Answer:

To find the hypotenuse (c) of a right triangle with a height of 4 units and a base of 12 units, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

The Pythagorean Theorem can be expressed as:

c^2 = a^2 + b^2

where c is the hypotenuse, and a and b are the lengths of the other two sides.

In this case, the height (a) is 4 units and the base (b) is 12 units.

Plugging these values into the Pythagorean Theorem equation, we get:

c^2 = 4^2 + 12^2

c^2 = 16 + 144

c^2 = 160

Taking the square root of both sides to solve for c, we get:

√(c^2) = √160

c = √160

So, the hypotenuse (c) of the triangle is √160

Sorry that you got that question wrong. Hope you do well on your tests/quizzes in the future.

Answer:

The slope of that line is 13/8 = 1.625

(1.63 to two decimal places).

Answer: The compound interest is $409.49, and the total amount after one year is $3,665.49.

Step-by-step explanation:

We can use the formula for compound interest to solve this problem:

A = P(1 + r/n)^(nt)

where:

P = the principal (in this case, $3,256)

r = the annual interest rate (100%, or 1 as a decimal)

n = the number of times the interest is compounded per year (4, since it's compounded quarterly)

t = the number of years (1)

Plugging in the values we know, we get:

A = $3,256(1 + 1/4)^(4*1)

A = $3,256(1.25)^4

A = $3,665.49 (rounded to the nearest cent)

To find the compound interest, we can subtract the principal from the total amount:

Compound interest = $3,665.49 - $3,256 = $409.49

Therefore, the compound interest is $409.49, and the total amount after one year is $3,665.49.

The domain of the relation include the following: B. {−5, −2, −1, 0, 5}.

In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown above, we can reasonably and logically deduce the following domain and range:

Domain = {−5, −2, −1, 0, 5}

Range = {1, 0, 3, -2, 2, 1}.

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Given statement "3-2 Roof area can be broken down into three basic shapes: rectangle, triangle, and trapezoid"

Given statement is True.
Because: When calculating the roof area, we can generally break it down into three basic shapes:

The term "roof area" typically refers to the total surface area of a roof. This can be calculated by measuring the length and width of each section of the roof, and multiplying those measurements together to get the area of each section.

Then, the areas of all the sections can be added together to get the total roof area.

It's important to accurately measure the roof area when planning for construction or repairs, as it will affect the amount of materials needed and the cost of the project.

Roof area can also be used to calculate the amount of insulation needed or to estimate the potential energy savings of installing solar panels.

Rectangle:

A four-sided polygon with opposite sides parallel and equal in length.
Triangle:

A three-sided polygon with three vertices and three angles.
Trapezoid:

A four-sided polygon with one pair of parallel sides.
By dividing a roof's surface into these shapes, you can calculate the total area more easily.

Hence statement is True.

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Answer: The point (4, 1) is a solution to this system of equations.

Step-by-step explanation:

To determine if (4, 1) is a solution to this system, you must plug it in to both of the equations. It is in the form of (x, y); so x = 4, and y = 1

Equation #1: y = -x + 5

                     1 = -(4) + 5

                     1 = 1      <————— This is part of the solution to this equation.

Equation #2: y = 2x - 7

                      1 = 2(4) - 7

                      1 = 8 - 7

                      1 = 1       <———- This is part of the solution to this equation.

The point (4, 1) is a solution to this system of equations.

Answer:

[tex] \sqrt{ \frac{4}{49 {d}^{4} } } = \frac{2}{7 {d}^{2} } [/tex]

This is the formula for calculating the present value of a future payment, where P1 is the present value, P2 is the future payment, and R is the interest rate.

To use the formula, you need to know the value of P2, the future payment, and the interest rate, R. Then, you can solve for P1, the present value of that payment. The formula works by discounting the future payment to account for the time value of money, which means that money today is worth more than the same amount of money in the future.

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