Find the volume of this right triangular prism.
5 cm
m
60 cm³
8 cm
b. 90 cm³
C.
120 cm³
d. 150 cm³

Answer:

The distance between A and B is 2.6

Step-by-step explanation:

We know that there are 2 whole numbers from -1 to 0 and 0 to 1. Then we can add the 0.3 from both sides. 0.3 plus 0.3 is 0.6.

I hope this helped and if it did I would appreciate it if you marked me brainliest, thank you and have a nice

day

Answer:

27 cm or 2in and 6cm!

Step-by-step explanation:

count the lines.

we have is as follows to the query that was asked The cannonball strikes the ground after 14 seconds in the air because t = 0 represents the cannonball's initial position quadratic equation \(16t^2 + 224t = 0\)

A quadratic formula in a single variable is x ax2+bx+c=0, which is a quadratic equation. a 0. The fact that this polynomial is of the second rank guarantees that the it has at least a single option according to the Central Theorem of Algebra. Solutions could be straightforward or difficult. A quadratic equation is one that has four variables. This suggests that at least one term in it needs to be squared. One of the common formulas for solving quadratic problems is "ax2 + bx + c = 0." where the undefined variable "X" is represented by the numerical factors or variables a, b, and c.

\(16t^2 + 224t = 0\)

By subtracting 16t, we obtain:

16t(t + 14) = 0

T must therefore be either 0 or -14. Since t = 0 corresponds to the cannonball's starting location, we can disregard it. The cannonball consequently strikes the earth at t = -14 seconds. However, since this negative number of t is illogical from a physical standpoint, we can ignore it.

The only viable option is:

initial location t = 0 or position t = -14 (ground)

The cannonball strikes the ground after 14 seconds in the air because t = 0 represents the cannonball's initial position.

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It would take Abigail 10 hours to drive 215 miles at this speed.

A proportion to solve this problem:

Let x be the number of hours it would take Abigail to drive 215 miles.

Then, we can set up the following proportion:

4/86 = x/215

To solve for x, we can cross-multiply:

4 × 215 = 86 × x

860 = 86x

Finally, we can isolate x by dividing both sides by 86:

x = 10

To fill out the table of equivalent ratios:

Hours Distance

4 86

x 215

We can set up the equivalent ratio as:

4/86 = x/215

Cross-multiply and solve for x as shown above.

A ratio to address this issue is:

Let x be the total time Abigail would need to go 215 miles.

Then, we may establish the ratio shown below:

4/86 = x/215

We can cross-multiply to find x:

4 × 215 = 86 × x 860 = 86x

By dividing both sides by 86, we can finally isolate x: x = 10.

To complete the corresponding ratios table:

Hours Distance

4 86 x 215

The corresponding ratio may be written as follows:

4/86 = x/215

Cross-multiply and find x as previously demonstrated.

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The Laplace transformation of given equation is \(y=-\frac{9}{2}e^{3t}\sin \left(2t\right)\).

According to the statement

we have given that the equation and we have to find the Laplace transformation of that equation.

So, For this purpose, we know that the

Laplace transformation is an integral transform that converts a function of a real variable to a function of a complex variables.

And the given equation is

y'' − 6y' + 13y = 0, y(0) = 0, y'(0) = −9

To convert into the Laplace transformation

firstly find the single derivative of given equation in the Laplace transformation and put y = -9 in this.

And now find second derivative of given equation in the Laplace transformation.

And and put y = 0 in the given equation.

After the Laplace transformation give value as a Laplace transformation is \(y=-\frac{9}{2}e^{3t}\sin \left(2t\right)\).

So, The Laplace transformation of given equation is \(y=-\frac{9}{2}e^{3t}\sin \left(2t\right)\).

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Answer:

1. 34.4°

2. 18.8°

3. 37.7°

4. 36.6°

5. 40.6°

6. 7.5

7. 12.3

8. 14.7

9. 22.0

10. 6.3

Step-by-step explanation:

1. The missing angle is found by the use of the sine.

Sine ∅= opposite/ hypotenuse

=13/23

sin⁻¹(13/23)=34.4°

2. The missing angle is calculated by the use of the tan.

Tan∅=opposite/adjacent

=17/50

Tan⁻¹(17/50)=18.8°

3. The missing angle is calculated by the use of the tan.

Tan∅=opposite/adjacent

=17/22

Tan⁻¹ (17/22) = 37.7°

4. The missing angle is calculated by the use of the tan.

Tan∅=opposite/adjacent

=21/28

Tan⁻¹ (21/28)=36.9°

5. The missing angle is calculated by the use of the tan.

Tan∅=opposite/adjacent

=24/28

Tan⁻¹ (24/28) = 40.6°

6. Missing side is calculated by considering the tan of 58°

Tan 58°=12/x

x=12/Tan 58°

=7.5

7.  Missing side is calculated by considering the sine of 43°

Sin 43°= opposite / hypotenuse

Sin 43 =x/18

x= 18 Sin 43

=12.3

8.  Missing side is calculated by considering the sine of 62°

Sin 62° = 13/x

x=13/Sin 62°

=14.7

9.  Missing side is calculated by considering the tan of 36°

Tan 36°= 16/x

x=16/Tan 36°

=22.0

10. Missing side is calculated by considering the sine of 23°

Sin 23° = x/16

x=16 Sin 23

=6.3

Answer:

160 + 3 g; $265

Step-by-step explanation:

Answer:

Hello! answer: 18

Step-by-step explanation:

The mode is just the number that is showed the most in a data set. Since 18 is showed the most 18 is the answer Hope that helps!

Answer:

18

Step-by-step explanation:

The mode is the number that appears the most in a group of numbers. 18 appears twice, while the rest of the numbers only appear once.

Answer:

?

Step-by-step explanation:

Answer:

28 minutes

Step-by-step explanation:

45-17=28

Greatest number that divides 300, 560 and 500 is 20 .

Given numbers : 300, 560 and 500

First let’s find prime factors of 300,560 and 500

300 = 2^2 *3^1 *5^2

560= 2^4 * 7^1 *5^1

500 = 2^2 * 5^3

So,

Here highest common power of 2 is 2

Here highest common power of 3 is 0

Here highest common power of 5 is 1

Here highest common power of 7 is 0

Thus HCF (300, 560 and 500) = 2^2 * 5^1 * 3 ^0 * 7 ^0

=4*5*1*1

= 20

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Using the definition of expected value, it is found that Ayo can be expected to make a profit of £55.8.

The expected value is given by the sum of each outcome multiplied by it's respective probability.

In this problem:

Hence, his expected profit for a single game is:

\(E(X) = -6\frac{1}{72} - 3\frac{17}{72} + 1.4\frac{54}{72} = \frac{-6 - 3(17) + 54(1.4)}{72} = 0.2583\)

For 216 games, the expected value is:

\(E = 216(0.2583) = 55.8\)

Ayo can be expected to make a profit of £55.8.

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Answer:

one angle = 162

another = 18

Step-by-step explanation:

one angle = x = 162

another angle = x - 144 = 162 - 144 = 18

x + x - 144 = 180

x + x = 180 + 144

2x = 324

x = 324/ 2 = 162

I hope im  Right!  !!

Answer:

13

Step-by-step explanation:

12^2 + 5^2 = c^2

144 + 25 = c^2

169 = c^2

13 = c

Answer:

If a function has an axis of symmetry x = a,

Step-by-step explanation:

then f (x) = f (- x + 2a). The following graph is symmetric with respect to the origin. In other words, it can be rotated 180o around the origin without altering the graph. Note that if (x, y) is a point on the graph, then (- x, - y) is also a point on the graph.The graph of a quadratic function is a parabola. The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. The axis of symmetry always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.

Answer: Y= -1/4x + 1 1/4

Step-by-step explanation: Perpendicular means the slope will be negative reciprocals

Form the given five quadratics , the one representing the repeated roots is equal to option d. 25x² - 30x + 9 and repeated roots are 3/5 or 3/5.

Quadratics representing repeated roots has discriminant equals to zero.

Standard quadratic equation is:

ax² + bx + c = 0

Discriminant 'D' = b² - 4ac

option a. -x²+ 18x + 81

Discriminant

'D' = 18² - 4(-1)(81)

      = 324 + 324

      = 648

D>0 has distinct roots.

option b. 3x²- 3x - 168

Discriminant

'D' = (-3)² - 4(-3)(-168)

      = 9 - 2016

      = -2007

D< 0 has distinct roots.

option c. x²- 4x -  4

Discriminant

'D' = (-4)² - 4(1)(-4)

      = 16 + 16

      = 32

D>0 has distinct roots.

option d. 25x²- 30x + 9

Discriminant

'D' = (-30)² - 4(25)(9)

      = 900 - 900

      = 0

D = 0 has repeated roots.

Repeated roots are:

x = ( -b ±√D ) / 2a

  = [-(-30)±√0 ]/ 2(25)

  = 30/ 50

  = 3/5.

option e.  x² - 14x + 24

Discriminant

'D' = (-14)² - 4(1)(24)

      = 196 - 96

      = 100

D>0 has distinct roots.

Therefore, the quadratics which represents the repeated roots are given by option d. 25x² - 30x + 9 and its repeated roots are 3/5 or 3/5.

The above question is incomplete, the complete question is:

One of the five quadratics below has a repeated root. (There other four have distinct roots.) What is the repeated root?

a. -x²+ 18x + 81

b. 3x² - 3x - 168

c. x² - 4x - 4

d. 25x² - 30x + 9

e. x² - 14x + 24

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By identifying the maximum value (75) and the minimum value (59) in the data set, we can determine the range, which is 16 inches .

The range of a data set measures the spread or variability of the data. It is calculated by subtracting the minimum value from the maximum value. In this case, the minimum value is 59 (the shortest height) and the maximum value is 75 (the tallest height) in the given data set.

Range = Maximum value - Minimum value

Substituting the values, we have:

Range = 75 - 59 = 16

Therefore, the range of the given data set is 16. This means that the heights of the students in the high school class range from a minimum of 59 inches to a maximum of 75 inches, with a difference of 16 inches between them.

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Answer:

see explanation

Step-by-step explanation:

Using the rule of exponents

\(a^{-m}\) = \(\frac{1}{a^{m} }\), then

(a)

\(4^{-1}\) = \(\frac{1}{4}\)

(b)

\(2^{-3}\) = \(\frac{1}{2^{3} }\) = \(\frac{1}{8}\)

(c)

\(3^{-4}\) = \(\frac{1}{3^{4} }\) = \(\frac{1}{81}\)

Answer:

AC=42

EB=21

BC=26

thats all i know, sorry hope u figure it out

Step-by-step explanation:

The sides are AC = 42, EB = 21, BC = 26, AB = 38 and the measures of angles are ∠ADC = 90°, ∠ABD = 38°, ∠BCA = 52°, ∠DEC = 104°.

Rectangle is a two dimensional figure which has four sides and four angles and all the angles are right angles

Given is a rectangle ABCD.

AC and BD are diagonals intersecting at E.

Given  DB=42, AD=26 and m ∠DAE=52°

(a) Diagonals of a rectangle are of equal length.

AC = DB = 42

(b) Diagonals of a rectangle bisect each other.

DE = EB = DB / 2 = 42/2 = 21

(c) Opposite side are equal.

BC = AD = 26

(d) Using Pythagoras theorem,

AB = \(\sqrt{(AC)^2-(BC)^2}\) = \(\sqrt{42^2-26^2}\) = 37.947 ≈ 38

(e) Measure of all the interior angles in a rectangle is 90°.

So, ∠ADC = 90°

(f) Given ∠DAE = 52°

∠BAE = 90° - 52° = 38°

ΔBAE is an isosceles triangle, since the two sides which are the bisectors of the diagonals are equal.

So, ∠ABD = ∠BAE = 38°

(g) ∠BCA = ∠DAE [Alternate interior angles]

∠BCA = 52°

(h) Sum of interior angles of a triangle is 180°.

∠DEC + ∠BDC + ∠ACD = 180°

∠BDC = ∠ABD = 38° and ∠ACD = ∠BAE = 38°

∠DEC = 180° - (38° + 38°)

          = 104°

Hence the measures are found.

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Answer:

-11/6

Step-by-step explanation:

you can use rise over run to find your answer

First find the areas of the two separate rectangles where:

Area of rectangle = length x width

Area of the small rectangle = x(x–4)

Area of small rectangle = \(x^{2} -4x\)

Area of big rectangle = (x–2)(2x+x)

Area of big rectangle = (x–2)(3x)

Area of big rectangle = \(3x^{2} -6x\)

The total area of the compound shape is 36, therefore:

\(3x^{2} -6x +x^{2} -4x=36\)

\(4x^{2} -10x-36=0\) (collecting like-terms and by bringing the +36 to the other side)

By dividing this by 2, you get:

\(2(2x^{2} -5x-18)=0\)

\(2x^{2} -5x-18=0\)

To find the length of AB (x), solve the quadratic by either factorising, completing the square or by using the quadratic formula, etc to solve for x.

\(2x^{2} -5x-18=0\)

\((2x-9)(x+2)=0\)

\(x=\frac{9}{2}\)

\(x=-2\)

However, a length cannot be negative, so x must be \(\frac{9}{2}\) or 4.5cm, so length AB = 4.5cm.

Hope this helps :)

The total cashback you will get back is\($ 49.75}\)

The Given, original price \($=\$ 50$\) Sales fax\($=9.5 \%$\\\)

For first sale

                 \(\begin{aligned}\text { Price of item } & =\$ 50 \\\text { sales tax } & =+\$ 4.75 \\10 \% \text { discount } & =\frac{-\$ 5}{\$ 49.75}\end{aligned}\)

A sale is a transaction between two or more parties that involves the exchange of tangible or intangible goods, services, or assets for money. In some cases, assets other than cash are paid to a seller.

In the financial markets, a sale can also refer to an agreement that a buyer and seller make regarding a financial security, its price, and specific arrangements for its delivery.

Regardless of the context, a sale is essentially a contract between a seller of a particular good or service and a buyer who is willing to pay for that good or service.

for second Sale:-

There is no tax

So price\($=\$ 50$\)

For third sale: - Buy 3 and get 1 half of

\(\begin{aligned}\text { Price }=50 \times 3 & =\$ 150 \\\text { Sales tax }= & +\$ 14.25 \\\text { Discount } & =\frac{-\$ 25}{\$ 139.25}\end{aligned}\)

So, price of 1 piece \($=\$ 46.42$\)

for fourth Sale; - Buy anything over \(\$40\) and get \($\$ 5$\) gift card.

\(& \text { Price }=\$ 50 \\& \text { sales tax }=+\$ 4.75 \\& \text { Gift card }=\frac{-\$ 5}{\$ 49.75}\end{aligned}\)

Therefore, the cashback you will get back is \($ 49.75}\)

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Answer:

Step-by-step explanation:

x^2 cannot be negative so the minimum value of x^2 is at (0.0)

When x = -1 y = 1 and when x = 1 y = 1

- and so on for all values of x

SO, y = x^2 is symmetrical about the y axis.

and the axis of symmetry is the y axis or we can write it as the line x = 0.

ANOVA is a method for determining whether group means differ more than group means do. It lets us see if the means of two or more groups differ significantly. If the null hypothesis is rejected, it suggests that at least one group is distinct from the others.

An analysis of variance (ANOVA) method is used to determine whether two or more population means are equal. The variability within and between the various samples is compared using the ANOVA method. It is more likely that the population means are equal when the variability within the samples is comparable to the variability between them.

When the examples' changeability is greater than their variation, the populace means almost certainly are not equivalent. ANOVA is used to test the hypothesis that the method for at least two populaces is equivalent. It indicates that the means of more than two populations are not equal if the null hypothesis is rejected.

However, the null hypothesis suggests that the means of multiple populations are identical if it is not ruled out. To put it another way, the purpose of ANOVA is to ascertain whether group means differ more than group means do. It lets us see if there is a significant difference in the means of two or more groups. It suggests that at least one group is distinct from the others if the null hypothesis is rejected.

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Answer:

Step-by-step explanation:A vertical line has undefined slope because all points on the line have the same x-coordinate

Answer:

VERTEX: (1,1)     Directrix: Y=0.88    

Step-by-step explanation:

Answer:

vertex = (1, 1 )

Step-by-step explanation:

Given the equation of a parabola in standard form

f(x) = ax² + bx + c ( a ≠ 0 )

Then the x- coordinate of the vertex is

x = - \(\frac{b}{2a}\)

f(x) = 2x² - 4x + 3 ← is in standard form

with a = 2 and b = - 4 , then

\(x_{vertex}\) = - \(\frac{-4}{4}\) = 1

Substitute x = 1 into f(x) for corresponding y- coordinate of vertex

f(1) = 2(1)² - 4(1) + 3 = 2 - 4 + 3 = 1

vertex = (1, 1 )

Answer:  

A boxplot is a way to show a five number summary in a chart. The main part of the chart (the “box”) shows where the middle portion of the data is: the interquartile range. At the ends of the box, you” find the first quartile (the 25% mark) and the third quartile (the 75% mark). The far left of the chart (at the end of the left “whisker”) is the minimum (the smallest number in the set) and the far right is the maximum (the largest number in the set). Finally, the median is represented by a vertical bar in the center of the box.

Box plots aren’t used that much in real life. However, they can be a useful tool for getting a quick summary of data.

How to Read a Box Plot: Steps

Step 1: Find the minimum.

The minimum is the far left hand side of the graph, at the tip of the left whisker.  

Step 2: Find Q1, the first quartile.

Step 3:  Find the median.

Step 4: Find Q3, the third quartile.

Step 5: Find the maximum.

hope this helps!!

The value of the given expression [\(87^3+ 13^3/87^2 -87 * 13 + 13^2\)] by simplifying the numerator and denominator using suitable identities is 100.

We will first calculate the numerator:

As  (\(a^3\) + \(b^3\)) = (a + b)(\(a^2\) - ab + \(b^2\)) :

\(87^3\) + \(13^3\) = (87 + 13)(\(87^2\) - \(87 * 13\) + \(13^2\))

= 100(\(87^2\) - 87 * 13 + \(13^2\))

Now, calculate the denominator:

\(87^2 - 87 * 13 + 13^2\)

As,(\(a^2 -2ab +b^2\)) =\((a - b)^2\):

\(87^2 - 87 * 13 + 13^2 = (87 - 13)^2\)

\(= 74^2\)

So by solving the equation further:

\((87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)\)

As we can see the numerator and denominator are the same expressions (\(87^2 - 87 * 13 + 13^2\)). so, they cancel each other:

\((87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100\)

So, the value of the given expression is 100.

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The objective of this research is to collect data on a specific component of the off-campus student population.The amount of time they spend travelling to courses each week.

a) The population for this study is all off-campus students at this college, and the sample is a random sample of 45 off-campus students who are polled. The sample is chosen at random to be representative of the entire population.

b) The data being gathered is the amount of time the surveyed students spend each week travelling to school. Because it reflects a numerical measurement, this is quantitative data. This information will be used to calculate the average commuting time for off-campus students and to identify any possible concerns or areas for improvement in commuting.

c) This is a descriptive research, since it seeks to characterise and summarise the features of the off-campus student population in terms of commuting time. The study's purpose is to better understand off-campus students' commuting patterns and gather ideas into how to enhance their commuting experience.

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Answer:

Step-by-step explanation:

Since 3 8/6 is an improper fraction, 8/6 creates a whole number because 6/6 = 1. The remainder of the fraction would be 2/6.

Which, the equivalent is 4 2/6.