Jack and Glen share a 30-ounce box of cereal. By the end of the week, Jack has eaten
1
10
of the box, and Glen has eaten
2
5
of the box of cereal. How many ounces are left in the box?

Answer:

Sophie's pyramid is approximately 4.8 inches.

Step-by-step explanation:

The formula for the volume of a square pyramid is given by:

V = (1/3) * B * h

where V is the volume, B is the area of the base, and h is the height of the pyramid.

We are given that the volume of Sophie's pyramid is 90 cubic inches, and the base has a side length of 7.5 inches. The area of the base is:

B = (7.5)^2 = 56.25 square inches

Substituting these values into the formula for the volume, we get:

90 = (1/3) * 56.25 * h

Multiplying both sides by 3, we get:

270 = 56.25 * h

Dividing both sides by 56.25, we get:

h = 4.8 inches (rounded to one decimal place)

Therefore, the height of Sophie's pyramid is approximately 4.8 inches.

Answer:

Step-by-step explanation:

We can use the law of sines to find the length of side a. The law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. In other words:

a/sin A = b/sin B = c/sin C

where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the angles opposite those sides.

We are given that A = 80°, B = 60°, and b = 15 cm. We can substitute these values into the law of sines and solve for a as follows:

a/sin 80° = 15/sin 60°

Multiplying both sides by sin 80°, we get:

a = 15*sin 80°/sin 60°

Using a calculator, we can evaluate sin 80° and sin 60° as follows:

sin 80° ≈ 0.9848

sin 60° = √3/2 ≈ 0.8660

Substituting these values, we get:

a ≈ 15*0.9848/0.8660

a ≈ 17.06

Rounding this to the nearest whole number, we get:

a ≈ 17

Therefore, the length of side a is approximately 17 cm.

The equation that shows the number of cookies Beverly has left is n = 6 - 5.

An integer is any positive or negative number, including zero, that has no decimal or fractional parts.

Natural numbers which start at 1, are categorised as whole numbers, along with 0 as well.

We can see that integers are a collection of numbers that include both positive and negative values as well as 0, whereas whole numbers are a set of numbers that include only positive numbers.

Given that, Beverly evenly shared a box of 24 cookies with three friends.

The number of cookies with Beverly = 24 / 4 = 6 cookies.

She ate 5 of her cookies.

Thus, the number of cookies Beverly has left is:

n = 6 - 5

n = 1

Hence, the equation that shows the number of cookies Beverly has left is n = 6 - 5.

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Answer: 0

Step-by-step explanation:

Y2 - Y1

________.

X2 - X1

A linear slope means that the Ys are the same and you can't divide by zero.

You have your points (8,7) and (3,7)

Use the template like I have above.

7 - 7

______

3 - 8

which equals....

0

__

-5

I hope that makes sense for you :)

15% of a price of 116 dollars would be a price decrease of $17.40. This means that the price when on sale would be $98.60 as you have to subtract 17.40 from 116.

The equation is given by 5n + 100n = 210

Peggy has 8 quarters and 2 nickels

Let's call q the number of quarters and n the number of nickels.

If Peggy has four times as many quarters as nickels, we can write the following equation:

q = 4n

Then, each quarter has a value of 0.25 dollars and each nickel has a value of 0.05 dollars, so

0.25q + 0.05n = 2.10

Because she had $2.10. Now, we can replace the first equation on the second one

0.25(4n) + 0.05n = 2.10

1n + 0.05n = 2.10

Finally, we can multiply both sides by 100, so

100n + 0.05(100)n + 2.10(100)

100n + 5n = 210

Therefore, the equation that can be used to solve the problem is

5n + 100n = 210

Now, we can solve the equation for n

105n = 210

105n/105 = 210/105

n = 2

Then, q is equal to

q = 4n

q = 4(2)

q = 8

It means that Peggy has 8 quarters and 2 nickels.

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complete question is listed below:

Peggy had four times as many quarters as nickels. She had $2.10 in all. How many nickels and how many quarters did she have?

Which of the following equations could be used to solve the problem?

On+4 n=210

5 n+100 n=210

n+4 n=2.10

5n+100 n=2.10.

Answer:

No solution

Step-by-step explanation:

We are given the following equation and asked to solve for x

[tex]\dfrac{\left(x+2\right)}{2x-2}=\dfrac{1}{2}[/tex]

[tex]\mathrm{Apply\:fraction\:cross\:multiply:\:if\:}\dfrac{a}{b}=\dfrac{c}{d}\mathrm{\:then\:}a\cdot \:d=b\cdot[/tex]

[tex]\left(x+2\right)\cdot \:2=\left(2x-2\right)\cdot \:1[/tex]

[tex]\mathrm{Simplify}2x + 2 = 2x - 2\\\\\textrm{Subtract\;$2x$\;both\;sides}:\\-2 = 2[/tex]

Since the sides are not equal this indicates there is no solution to this system.

In the equation 11z=66-11, what is the next step in the equation solving sequence?

Two possibilities: You can subtract 66–11 then divide both sides by 11 OR you can divide both sides by 11 and do the subtraction as 6–1. I would usually do it the first way, but some might prefer the second.

The Definition of the Derivative correctly stated by

In mathematics, a derivative is the rate at which a function changes in relation to a variable. Calculus and differential equations issues must be solved using derivatives.

As, we know by definition of derivative

= [tex]\lim_{h \to 0}[/tex] f(x+h)- f(x) / h

Also, the Derivative also shows the Slope of the secant line.

and, derivative is widely used to the rate of change then it also shows

Instantaneous rate of change.

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The value of the function [tex]\lim_{x \to \ -1} \frac{2}{(x + 1)^{2}}[/tex] is ∞.

A value of the function, whenever the input values are substituted in the function then the function approaches some number.

And that number is a limit of the function.

Given:

A function,

f(x) = 2/{(x + 1)²}

And function increases without bounds as the values of x approach -1.

So,

[tex]\lim_{x \to \ -1} \frac{2}{(x + 1)^{2}}[/tex]

= 2/(x² + 2x + 1)

= 2/{1 + (-2) + 1}

= 2/0

= ∞

Therefore, the function approaches infinity.

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Answer:

Step-by-step explanation:

The volume of the triangular pyramid shown  is (c) 104 cubic units

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

X = 6 units, Y = 4 units, and Z = 13 units

The volume is calculated as

Volume = xyz/3

Substitute the known values in the above equation, so, we have the following representation

Volume = 6 * 4 * 13/3

Evaluate

Volume = 104

Hence, the volume is (c) 104 cubic units

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The elevator is now on the 6th floor.

Arithmetic operations are the basic part of mathematics which combines the basic operations like addition, subtraction, multiplication and division.

Given that the elevator is now on 9th floor.

First, it goes up 2 floors.

Position of elevator = 9 + 2 = 11th floor

Then, it goes down 5 floors.

Position of elevator = 11 - 5 = 6th floor

Hence the elevator is now on the 6th floor.

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The other endpoint has its coordinate to be (4, -1).

Represent the coordinates of the other endpoint of the line segment be (x, y).

Since the midpoint of the line segment is (5, 1/2), we can use the midpoint formula to write an equation relating the coordinates of the two endpoints:

((6 + x)/2, (2 + y)/2) = (5, 1/2)

Simplifying this equation, we get:

(6 + x)/2 = 5

(2 + y)/2 = 1/2

Solving for x and y, we get:

x = 4

y = -1

Hence, the coordinates of the other endpoint of the line segment are (4, -1).

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The length of the 180° arc as required in the task content is; 22/21 inches.

Recall that the length of an arc is given by the formula;

Length of arc = theta / 360 × 2 π r

Therefore, for a radius of 3 inches;

Length of arc = 180/360 × 2 × 22/7 × 3

Length of arc = 22/21 inches.

Ultimately, the length of the arc in discuss is; 22/21 inches.

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The total length of the stickers that are more than 2 inches long is 5 1/2 inches. The Option C is correct

A length is the measurement or extent of something from end to end; the greater of two or the greatest of three dimensions of an object.

The calculation of the total length of the stickers that are more than long is as follows:

= 2 1/4 + 2 1/2 + 2 3/4 + 3

= 9/4 + 5/2 + 11/4 + 3

= 9 + 10+ 11 + 12 / 4

= 42/4

= 10 2/4 inches

= 5 1/2 inches

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Full question "Jalesia has a set of train stickers. She measures the length of the stickers. Then she makes a line plot of the data. h of Stickers In jalesia takes all the stickers that are more than  long. She lays them end to end across her folder. What is the total length of the stickers that are more than  long?"

Therefore, the expansion of log(7x²) using the properties of logarithm is

log 7 + 2log x, expressed in terms of log x.

The mathematical idea of a logarithm illustrates the opposite of a power. It follows that the exponential that must be multiplied by bc to get the value of a number, x, is equal to its ground logarithm. As an illustration, 1000 = 103, so log10 = 3 is 1000's base-10 logarithm, which is 3. As an example, the square of ten is now only one twentieth of the base-10 exponential of ten, which is two. Log 100 = 2. Mathematicians use the logistic (or log) notion to respond to problems like these.

Here,

Using the product rule of logarithms, we can write:

log(7x²) = log 7 + log(x²)

Using the power rule of logarithms, we can write:

log(7x²) = log 7 + log(x²) = log 7 + 2log x

Therefore, the expansion of log(7x²) using the properties of logs is:

log 7 + 2log x, expressed in terms of log x.

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The completed blanks in Nyala's solution that is used to prove that the measure of angle x is 40° is as follows;

If we perform a 180° rotation about the point O the following happens

Ray [tex]\overleftrightarrow{EF}[/tex] maps unto ray [tex]\overleftrightarrow{GH}[/tex]

Ray [tex]\overleftrightarrow{GH}[/tex] maps unto ray [tex]\overleftrightarrow{FE}[/tex]x

[tex]\overleftrightarrow{FG}[/tex] maps unto itself

Therefore, the image of angle x will be exactly where the pre-image of 40° was. Since rotation preserve angle measure, the measure of angle x must be 40°.

The measure of an angle is the degree of rotation between the initial side and the terminal side of the angle.

The details of the method Nyala used to prove that the measure of the angle x is 40° can be found as follows;

The rotation of a line 180° about the center of the line maps onto itself, and the rotation of a line about a non colinear point, is parallel to the original line.

Whereby the center of rotation of the line [tex]\overleftrightarrow{EF}[/tex] is equidistant from both the line [tex]\overleftrightarrow{GH}[/tex] which is parallel to the line [tex]\overleftrightarrow{EF}[/tex], the image of the line [tex]\overleftrightarrow{EF}[/tex] maps to the line [tex]\overleftrightarrow{GH}[/tex] following a 180° rotation about the point O, and the rotation of the line [tex]\overleftrightarrow{FG}[/tex] about the point O maps unto itself, such that the angle x maps to the angle 40°, therefore;

∠x ≅ 40° (A rotation transformation is a rigid transformation)

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The angles which are co-terminal with the given angle and less than 1080 but greater than -720 are 450°, 810°, -270° and -630°. The solution has been obtained using concept of co-terminal angles.

What is co-terminal angle?

Co-terminal angles are those with a common terminal side that are in standard position (angles with the starting side on the positive x-axis). The angles where the difference could be 360 degrees or multiples of 360 degrees are known as co-terminal angles.

The calculation of the two positive angles and the two negative angles, which are co-terminal, is as follows:

(a) For 90°, the two positive angles are

90° + 360° = 450°

450° + 360° = 810°

(b) The two negative angles are

90° - 360° = -270°

-270° - 360° = -630°

Hence, the angles which are co-terminal with the given angle and less than 1080 but greater than -720 are 450°, 810°, -270° and -630°.

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The values to put in the box will be:

x

y

x.y

x^2

y^2

4

19

76

16

361

9

46

414

81

2116

7

30

210

49

900

6

31

186

36

961

5

23

115

25

529

5

28

140

25

784

4

21

84

16

441

8

42

336

64

1764

total

48

240

1561

312

7856

The sample size is the number of observations used for determining the estimations of a given population.

The size of the sample has been drawn from the population. Sampling is the process of selection of a subset of individuals from the population to estimate the characteristics of the whole population.

Inthi case, sample size n = 8 and the correlation coefficient is 0.9643.

The appropriate values are given above.

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Answer:

Confidence interval = -0.1013 ± 0.1991

Confidence interval = (-0.30, 0.10)

Step-by-step explanation:

We can use the following formula to find the confidence interval for the difference in two population proportions:

Confidence interval = (p1 - p2) ± z*sqrt[p1(1-p1)/n1 + p2(1-p2)/n2]

where p1 and p2 are the sample proportions, n1 and n2 are the sample sizes, and z is the z-score corresponding to the level of confidence.

First, we need to calculate the sample proportions:

p1 = 104/252 = 0.4127

p2 = 55/107 = 0.5140

Next, we need to find the value of z for a 99% confidence level. We can look up this value in a standard normal distribution table or use a calculator, which gives us a z-score of 2.576.

Then, we can plug in the values:

Confidence interval = (0.4127 - 0.5140) ± 2.576*sqrt[0.4127(1-0.4127)/252 + 0.5140(1-0.5140)/107]

Simplifying this expression, we get:

Confidence interval = -0.1013 ± 0.1991

Rounding to two decimal places and using interval notation, we get:

Confidence interval = (-0.30, 0.10)

With a weekly budget of $12, Mark will need to save money for 9 weeks, 5 days in order to purchase the guitar.

The value is said to be in its simplified form when divided through its smallest equivalent fraction. How to find the most basic form. Find common factors in the denominator and numerators. Verify a minority integer t verify if it qualifies like a prime number. A statement comprising two rotational symmetry and an equal sign in the middle is called an equation in mathematics. The general form of almost any equation contains the degrees of all variables in descending order. The conventional form of something like a linear equation is an x + b = 0. The general form of a mathematical expression with two variables is an x + b y + c = 0. (or something similar). Equations can be categorized as identities or conditional solutions. An identity holds true irrespective of the value given to the variables.

given

let the week be x

equation =  $55 + 12x = $169.00

55 + 12x = 169

12x = 169 - 55

12x = 114

x = 9.5

With a weekly budget of $12, Mark will need to save money for 9 weeks, 5 days in order to purchase the guitar.

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The optimal Bayesian classifier is the one that minimizes the probability of misclassification. This can be achieved by choosing the class that has the highest posterior probability given the observed data. In this case, we need to compare the conditional class probabilities P2(t) and P0(I) for each data point and choose the class with the higher probability.

To find the optimal Bayesian classifier, we need to find the values of a and b that define the decision boundary between the two classes. This can be done by setting P2(t) = P0(I) and solving for x:

P2(t) = P0(I)
Pr(Y; = 1|X, = x) = Pr(Y; = 0[Xi = 1)
1 - P2(I) = P2(I)
2P2(I) = 1
P2(I) = 0.5

Now we can solve for x to find the decision boundary:

0.5 = Pr(Y; = 1|X, = x)
0.5 = P2(I)
x = a + b

Therefore, the optimal Bayesian classifier is of the form:

if Xe [a, b] then yi = 1
if Xe [b, a] then yi = 0

where a and b are the values of x that satisfy P2(I) = 0.5.

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If rectangles S and T are similar then the area of rectangle T is 96 units².

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

Since the rectangles S and T are similar, their corresponding sides are proportional.

Let the length of rectangle T be "x" units. Then -

width of S / width of T = length of S / length of T

Using the given values -

16/9.6 = (√160) / (√x)

Simplifying this equation it is obtained-

x = (9.6/16) × (√160)²

x = 10

Therefore, the length of rectangle T is 10 units.

The area of rectangle T is then -

Area of T = width of T × length of T

Area of T = 9.6 × 10

Area of T = 96 units²

Therefore, the area of rectangle T is 96 units².

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Answer:

The volume of the rectangular prism is 96.

Step-by-step explanation:

Use the formula L × W × H to get your answer. Plug in the givem measurements. 8 × 4 × 3 = 96.

The two equations that have the same solution as the original equation are: 23p - 101 = 65p - 40 - p, 2.3p - 14.1 = 6.4p - 4

An equation is a mathematical statement that shows that two expressions are equal. It is usually written as an expression on the left-hand side (LHS) and an expression on the right-hand side (RHS) separated by an equal sign (=).

The expressions on both sides of the equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The variables in an equation represent unknown values that can vary, while the constants are fixed values that do not change.

Equations are used to represent mathematical relationships or describe real-world situations. They can be used to solve problems, make predictions, and test hypotheses.

To solve an equation, one must find the value of the variable that makes the LHS equal to the RHS. This is done by performing mathematical operations on both sides of the equation to isolate the variable. The goal is to get the variable by itself on one side of the equation, with a specific value on the other side.

Equations can be simple or complex, linear or nonlinear, and can involve one or more variables. Examples of equations include:

2x + 5 = 13

y = 3x^2 - 2x + 7

4a + 2b - 3c = 10

Equations are used in many areas of mathematics and science, including physics, chemistry, and engineering, among others.

The equations that have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p are:

23p – 101 = 65p – 40 – p

2.3p – 14.1 = 6.4p – 4

To rewrite the given equation in a different form, we can simplify it using the distributive property and combining like terms:

2.3p - 10.1 = 6.5p - 4 - 0.01p

2.3p - 6.5p + 0.01p = -4 + 10.1

-4.19p = 6.1

p = -1.456

Now we can plug this value of p into each of the answer choices and see which ones give the same result:

23p - 101 = 65p - 40 - p

24p - 101 = 64p - 40

p = 3.5

This solution is not the same as the solution we found for the original equation, so this choice is not correct.

2.3p - 14.1 = 6.4p - 4

8.7p = 10.1

p = 1.16

This solution is also not the same as the solution we found for the original equation, so this choice is not correct.

Therefore, the two equations that have the same solution as the original equation are:

23p - 101 = 65p - 40 - p

2.3p - 14.1 = 6.4p - 4

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When a cube's top is chopped off to create a rectangular box, the original cube's side length is 5.43 feet as a result.

A rectangular is a square with four right angles in Euclidean geometry and trigonometry. You may also speak to it as an equiangular tetra, meaning that all of its edges are equal. A straight angle could also be found in the parallelogram. Rectangles with four evenly sized sides are called squares. Four 90 ° vertices and equal equal sides make up a quadrant with the look of a rectangle. As a basis, it's also known as a raster images rectangle. A rectangle is also referred to as a trapezoidal since its opposite angles are equal but parallel.

given

Let x represent the cube's edge in feet.

Cube volume equals side 3

Hence, the given cube's volume,

The top of a cube is now chopped off in a 4 foot thick chunk.

The slice's volume is equal to x x x 4 = 4x2 ft2.

The volume of the final figure is therefore equal to the sum of the volumes of the cut and cube figures.

= ( x³ - 4x² ) ft²

The answer to the query is

Finding the zeros of the function will lead to the discovery of the solution to the aforementioned equation ( by graphing ),

We discovered that

The equation's graph crosses x at (5.426,0)

Hence, 5.426 is the equation's zero.

⇒ x = 5.426 ≈ 5.43

When a cube's top is chopped off to create a rectangular box, the original cube's side length is 5.43 feet as a result.

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Are you more likely to see a twelve-pack from the local brewery or a twelve-pack from the large chain with an average fill of 327.9 ml?

Local brewery.

a. At the local brewery the middle 95% of six-packs will have an average fill between ml 326.828 and 329.572 ml

b. At the large chain brewery, the middle 95% of six-packs will have an average fill between 326.824 ml and 329.176 ml.

X ζ N (328.2, 0.7^2)

YζN (328, 0.6^2)

P (X> 327.9) = 0.6659

P (Y> 327.9) = 0.5662

Since, P (X> 327.9) > P (Y> 327.9)

We are more likely to see 12-pack from the local brewery.

a. To find a, b such that P(a<x<b) = 0.95

a= 326.828

b= 329.572

b. To find c, d such that P(c<Y<d) = 0.95

c= 326.824

d= 329.176

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The answer is the expected value is - 2. The equation for expected value is the sum of the values times their probabilities.