A cake has 65 slices.

Harry ate 1 slices; Jack ate 19 slices; Dave ate 40 & Mary ate 4 slices.

What fraction of the cake is remaining?

Answer:

110

Step-by-step explanation:

First, find the perimeter of 1 fence.

55/2 or \(27\frac{1}{2}\)

Multiply by the number of fences (4)

110

I hope this helps!

Answer:

Well 3/4 & 5/12 are already simplified and in fraction form, if youre

looking for decimal form its gonna be .75 &.41

Step-by-step explanation:

(a) 8 apartment buildings in the sample.

(b) The estimated regression equation is \(ŷ = 20.0 + 7.21x\)

(c) The value of sb1 is 1.3626

(d) we do not reject the null hypothesis and cannot conclude that the relationship between selling price and annual gross rents is significant.

(e) selling price of an apartment building with annual gross rents of $65,000 would be \(ŷ = 20.0 + 7.21x = 20.0 + 7.21(65) = $517.35\)

What is regression analysis?

A mathematical method for determining the average association between two or more variables in terms of the original units of the data is regression analysis.

(a) There were 8 apartment buildings in the sample, as indicated by the value of DF in the ANOVA table.

(b) The estimated regression equation is \(ŷ = 20.0 + 7.21x\), where x is the annual gross rents (in thousands of dollars) and ŷ is the predicted selling price (in thousands of dollars).

(c) The value of sb1 is 1.3626, which is the standard error of the slope estimate.

(d) The null hypothesis for the test is that the relationship between selling price and annual gross rents is not significant, or H0: β1 = 0. The alternative hypothesis is that the relationship is significant, or Ha: β1 ≠ 0.

The F statistic for the test is calculated as follows:

F = (sb1² / s²)

= (1.3626² / 7983.6) = 0.17

The p-value for the test can be calculated using the F distribution with 1 and 7 degrees of freedom. The p-value is 0.68, which is greater than the significance level of 0.05.

Therefore, we do not reject the null hypothesis and cannot conclude that the relationship between selling price and annual gross rents is significant.

(e) To predict the selling price of an apartment building with annual gross rents of $65,000, we can use the estimated regression equation: \(ŷ = 20.0 + 7.21x = 20.0 + 7.21(65) = $517.35\) (in thousands of dollars).

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Answer:

The only true statement is:

"∠3 + ∠4 = ∠1 + ∠2"

Step-by-step explanation:

When we have two lines intersect each other, there are 4 angles generated in the intersection.

Two vertical angles are angles whose only "contact point" is the intersection itself. The vertical angles are supplementary only if the two lines are perpendicular.

While a linear pair are two angles that are separated by one of the lines, and linear pairs are always supplementary.

Now let's look at the image and see which statements are true and which ones aren't.

"∠2 and ∠3 form a linear pair"

If we look at the image, we can see that ∠2 and ∠3 are not separated by one of the lines, ∠2 and ∠3 are vertical angles, then this statement is false.

"∠1 and ∠4 are supplementary angles"

Two angles are supplementary if the sum of the measures is equal to 180°, such that, as stated before, a linear pair of angles are supplementary angles.

In the case of ∠1 and ∠4, we can see that these angles are vertical angles, and we also can see that the lines are not perpendicular, then angles ∠1 and ∠4 are not supplementary.

"∠2 and ∠3 = 180°"

This is the same as saying that "∠2 and ∠3 are supplementary"

By the exact same reasoning than in the previous statement, we can find that this one is false.

"∠3 + ∠4 = ∠1 + ∠2"

We know that ∠1 and ∠2 are a linear pair, then ∠1 and ∠2 are supplementary angles, then:

∠1 + ∠2 = 180°

And we know that ∠3 and ∠4 also are a linear pair, and then also are supplementary angles, then we also have:

∠3 + ∠4 = 180°

Then is true that:

∠3 + ∠4 = ∠1 + ∠2

This statement is true.

"∠2 and ∠4 are vertical angles"

We can see that ∠2 and ∠4 are separated by one of the lines, then these angles form a linear pair.

The statement is false.

Answer:

Alternate interior

Step-by-step explanation:

They are inside making them interior angles and they are on opposite sides making them alternate angles as well.

Hope this helps!

Answer:

Step-by-step explanation:

alternate interior angles are congruent if and only lines are parallel.

∠4 ≅ ∠5

Answer:

C

Step-by-step explanation:

just did it rn

The value of difference quotient is \(3x^{2} +3xh +h^{2}\).

Here,

Given that;

Stephon wrote out steps to compute the difference quotient,

\(v(x) =x^{3} + 8\\\)

\(v(x+h) = (x+h)^{3} + 8\\\)

\(v(x+h) = x^{3}+3x^{2} h+3xh^{2} +x^{3} + 8\\\)

We have to find difference quotient.

What is difference quotient formula?

Difference Quotient formula is used in the definition of the derivative. Difference Quotient Formula,

\(\frac{f(x+h)-f(x)}{h}\)

Now,

\(v(x) =x^{3} + 8\\\)

And, \(v(x+h) = x^{3}+3x^{2} h+3xh^{2} +x^{3} + 8\\\)

Then,

Difference Quotient formula = \(\frac{v(x+h)-v(x)}{h}\)

                                           = \(\frac{ x^{3}+3x^{2} h+3xh^{2} +h^{3} + 8\\-(x^{3} + 8)\\}{h}\)

                                           = \(\frac{ x^{3}+3x^{2} h+3xh^{2} +h^{3} + 8\\-x^{3} - 8\\}{h}\)

                                           = \(\frac{ 3x^{2} h+3xh^{2} +h^{3} \\\\}{h}\)

                                           = \(3x^{2} +3xh +h^{2}\)

Hence, The value of difference quotient is \(3x^{2} +3xh +h^{2}\).

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Answer:

A

Step-by-step explanation:

P( music ) = number of students in music/ total number of students

P (music) = 4 / 14

= 2/7

Using the Pythagorean Theorem, the distance between Pole X and Pole Z is of 15.3 m.

The Pythagorean Theorem relates the length of the legs \(l_1\) and \(l_2\) of a right triangle with the length of the hypotenuse h, according to the following equation:

\(h^2 = l_1^2 + l_2^2\)

The first part of the distance is the hypotenuse of a right triangle of sides 0.5 and 2.5, tracing a right triangle at the top of pole X and tracing it to segment Y, hence:

df² = 0.5² + 2.5²

df = sqrt(0.5² + 2.5²)

df = 2.55m.

For the second part, we apply equivalent triangles, as we can also trace a right triangle at the top of segment Y to segment Z, hence:

0.5/2.5 = df/ds

1/5 = 2.55/ds

ds = 2.55 x 5 = 12.75m

Then the total distance is:

2.55 + 12.75 = 15.3 m.

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Answer:

84°

Step-by-step explanation:

Since they are vertical angles they share the same angle measurement.

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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Answer :

Step-by-step explanation :

We have been provided with the volume of water tank , it's length and breadth. We are asked to calculate the depth of tank (height), so we all know that water tank is always is in the shape of cuboid.

We would be using the formula of calculating the volume of cuboid and substitute the values in it.

Here,

We have :

Substituting the values :

>> 396 = 7.2 × 5.5 × h

>> 396 = (72 / 10) × (55 / 10) × h

>> 396 = 72 × 55 × h / 100

>> 396 = 3960 × h / 100

>> 396 × 100 = 3960 × h

>> 39600 = 3960h

>> h = 39600 / 3960

>> h = 3960 / 396

>> h = 10

__________________________

Answer:

108 inches²

Step-by-step explanation:

Rectangular prism = cuboid

To find how much paper is required to cover the box, we need to find the TSA of the cuboid.

TSA of cuboid = 2 [LB + LH + HB] = 2 [ (3×4) + (3×6) + (4×6) ] = 2 [ 12+18+24 ] = 2 × 54 = 108 inches²

Therefore, **x < 7** is the inequality that may be utilized to find x

A mathematical statement known as an inequality compares two expressions using an inequality sign, such as (less than), > (greater than), or (less than or equal to).

For instance, the inequality x + 2 5 signifies that "x + 2 is less than 5".

Let x represent how many days the client paid for pet sitting.

$15 per day plus a $20 fixed service fee equals the total cost of pet sitting.

We are aware that the customer's purchase was under $125. Consequently, we can write:

20 + 15x < 125

Putting this disparity simply:

15x < 105

x < 7

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Answer:

volume of a cylindrical water tank = 70,650cm³

Step-by-step explanation:

volume of cylinder, V = πr²h

where π = 3.14

h = 100cm

r = ?

given is diameter = 30cm

r = d/2 = 30/2 = 15cm

substituting the values in the formula,

V = 3.14 * 15² * 100

= 3.14 * 225 * 100

= 70,650cm³                        

Answer:

How much space it would take up: 706.86 square centimeters of floor space and extend vertically to a height of 100 cm

Volume: 706,500 cm³

Step-by-step explanation:

How much space it would take up:

To determine the space occupied by a cylindrical water tank in a room, we need to consider its dimensions and the area it covers on the floor.

The diameter of the tank is given as 30 cm, which means the radius is half of that, 15 cm.

To calculate the space it occupies on the floor, we need to find the area of the circular base. The formula for the area of a circle is A = πr², where A is the area and r is the radius.

A = π(15 cm)²

A = π(225 cm²)

A ≈ 706.86 cm²

So, the circular base of the tank occupies approximately 706.86 square centimeters of floor space.

The height of the tank is given as 100 cm, which represents the vertical space it occupies in the room.

Therefore, the cylindrical water tank would take up 706.86 square centimeters of floor space and extend vertically to a height of 100 cm in the room.

Volume:

To calculate the volume of a cylindrical water tank, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

First, we need to find the radius by dividing the diameter by 2:

Radius = 30 cm / 2 = 15 cm

Now we can calculate the volume:

V = π(15 cm)²(100 cm)

V = 3.14 * 225 cm² * 100 cm

V = 706,500 cm³

Therefore, the cylindrical water tank will occupy a volume of 706,500 cm³ or 706.5 liters.

On solving the provided question ,we can say that The statement "The number of new clients (x) is 149% of the number of old clients (y)" can be written mathematically as: x = 1.49y

A sequence is a grouping of "terms," or integers. Term examples are 2, 5, and 8. Some sequences can be extended indefinitely by taking advantage of a specific pattern that they exhibit. Use the sequence 2, 5, 8, and then add 3 to make it longer. Formulas exist that show where to seek for words in a sequence. A sequence (or event) in mathematics is a group of things that are arranged in some way. In that it has components (also known as elements or words), it is similar to a set. The length of the sequence is the set of all, possibly infinite, ordered items. the action of arranging two or more things in a sensible sequence.

The statement "The number of new clients (x) is 149% of the number of old clients (y)" can be written mathematically as:

x = 1.49y

-1.49y + x = 0

-149y + 100x = 0

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The linear equation in the required form is: x - 1.49y = 0

What is linear equation?

A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. It is an equation of the form:

y = mx + b

Let's start by assigning variables to the given information. We are told that "the number of new clients (x) is 149% of the number of old clients (y)."

Using this information, we can write:

x = 1.49y

To write this equation in the form ax + by = c, we need to move all the variables to one side of the equation and simplify.

Subtracting 1.49y from both sides, we get:

x - 1.49y = 0

So the linear equation in the required form is:

x - 1.49y = 0

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Answer:

Mean mass of 20 rugby player = 55

Step-by-step explanation:

Given:

Mass of 6 rugby players = 540 kg

Mean mass of 14 ballet dancer = 40 kg

Find:

Mean mass of 20 rugby player

Computation:

Total mass of ballet dancer = 14 x 40

Total mass of ballet dancer = 560 kg

Total mean mass of 20 rugby player = [540 + 560] / [6 + 14]

Mean mass of 20 rugby player = 1100 / 20

Mean mass of 20 rugby player = 55

Darlene is extruding a polygon of five sides. The end result will be a pentagonal prism.

Extrusion represents a 3D modeling technique that involves extending a two-dimensional shape into a three-dimensional object by pulling it along a given path. In this particular case, Darlene is applying extrusion to a polygon comprising of five sides, thereby stretching out the two-dimensional figure along a trajectory to yield a novel 3D construct.

It is worthy of mention that the structure obtained following the process solely depends on the pathway employed by Darlene in carrying out the extrusion procedure. Should she choose a direct line, the resulting creation will be a prism having five sides i.e. pentagonal prism.

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Answer:60 cups are left

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

\( - 2x - 4 + 5x = 8\)

Step 1: Collect like terms and simplify

\( - 2x + 5x = 8 + 4 \\ 3x = 12\)

Step 2: Divide both sides of the equation by 3

\( \frac{3x}{3} = \frac{12}{3} \)

Simplify

\(x = 4\)

Answer:

x=4

Step-by-step explanation:

Answer:  B) Scott sold 1 van

Step-by-step explanation:

A₂,₃ represents:  matrix A - 2nd row - 3rd column

The second row is Scott and and the 3rd row is Vans

If you look at Scott - Vans, you will see that Scott sold 1 van.

Answer:

180cm

Step-by-step explanation:

To find the volume you do Length times Width times Height

use this it'll help when you run into this again, it's formula is just

LxWxH, in this order good luck!

well, we know all three points are colinear, so the slope from the first two points is the same slope from either to the (c , -9) point, let's check the slope of the first two points given

\((\stackrel{x_1}{-5}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{1})~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{10}-\underset{x_1}{(-5)}}} \implies \cfrac{1 +3}{10 +5}\implies \cfrac{4}{15}\)

so then, the slope from say hmmmm let's use (-5 , -3), the slope from (-5 , -3) and (c , -9) must also be the same 4/15

\((\stackrel{x_1}{-5}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{c}~,~\stackrel{y_2}{-9}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-9}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{c}-\underset{x_1}{(-5)}}} \implies \hspace{5em}\cfrac{-9 +3}{c +5}~~ = ~~\stackrel{slope}{\cfrac{4}{15}}\implies \cfrac{-6}{c+5}=\cfrac{4}{15} \\\\\\ -90=4c+20\implies -110=4c\implies \cfrac{-110}{4}=c\implies -\cfrac{55}{2}=c\)

The x- intercept of the equation is (13,0) and y-intercept of the equation is (0,-39/8) when the equation is 3x-8y=39.

Given that,

The equation is 3x-8y=39.

We have to find the x- intercept and y- intercept of the equation.

We know that,

x/a + y/b = 1 is the intercept form of the line's equation. One of the key types of line equations is this one. In this equation, the sign of the intercepts also enables us to determine where the line is in relation to the coordinate axes.

To find the x- intercept of the equation.

We have to take y as 0.

3x-8(0)=39

3x=39

x=39/3

x=13

To find the y- intercept of the equation.

We have to take x as 0.

3(0)-8y=39

-8y=39

x=-39/8

Therefore, The x- intercept of the equation is (13,0) and y-intercept of the equation is (0,-39/8) when the equation is 3x-8y=39.

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Answer:

55.08

Step-by-step explanation:

6.12 times 9

55.08

Answer:

- 72 - 48i

Step-by-step explanation:

note that i² = - 1

(6i)(- 2i)(- 6 - 4i)

= - 12i²(- 6 - 4i)

= - 12(- 1)(- 6 - 4i)

= 12(- 6 - 4i) ← distribute parenthesis by 12

= - 72 - 48i

Answer:

2/9 or 22.22% and 4/9 or 44.44%

Step-by-step explanation:

6+4+8=18   4/18=2/9   8/18=4/9