what is the volume of the triangular prism

A) 12 cm
B) 18
C) 24
D) 48

The function f(x)=4sin(2πx) is a sinusoidal function

The graph of the function f(x)=4sin(2πx) is graph (c)

The parent function of a sine function is

f(x) = sin(x)

The function f(x)=4sin(2πx) implies that the parent function f(x) = sin(x) has been horizontally and vertically stretched

So, the graph of the function f(x)=4sin(2πx) would have a higher amplitude and shorter period than its parent function

Hence, the graph of the function f(x)=4sin(2πx) is graph (c)

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Answer:

A° = 44.42°

Step-by-step explanation:

Soh Coh Toa
Soh: sin(theta) = Opp/Hyp

Coh: cos(theta) = Adj/Hyp

Toa: tan(theta) = Opp/Adj

We are using Coh: cos(theta) = Adj/Hyp because we need to find Angle A and that 5 is Adjacent and 7 is the Hypotenuse.

cos(A°) = 5/7

A° = cos^-1 (5/7)

A° ≈ 44.4153086

A° = 44.42°

Answer:

Step-by-step explanation:

The amount of interest is found using the simple interest formula. That is added to the principal to find the total account balance.

__

  I = Prt . . . . . P = principal, r = annual rate, t = number of years

  I = $800·0.06·3 = $144

The simple interest earned in 3 years is $144.

__

Adding that to the principal gives ...

  $800 +144 = $944

The total principal plus interest is $944.

Answer:

58

Step-by-step explanation:

B=base

A=side

X=2(a+b)=2·(13+16)=58

Step-by-step explanation:

58 maybe coz I got 58 so??

Answer:

1,3

Step-by-step explanation:

Answer:

7

Step-by-step explanation

2x = 14

divide by 2

The options that are true about the system of linear equations are;

A) The solution is (4,0).

C) The solution is (0,−1).

D) There are infinitely many solutions.

From the given linear equation graph, we see that the linear equation that is graphed is given by;

y = ¹/₄x - 1

Now, the solution to the given equation will be the value of x that corresponds with the value of y when traced on the graph.

Let us access (4, 0)

At x = 4, we have;

y = ¹/₄(4) - 1

y = 0

Thus, (4, 0) is a solution of the graph.

Let us access (0, -1)

At x = 0, we have;

y = ¹/₄(0) - 1

y = -1

Thus, there are many solutions to the graph

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Answer:

416.84 m

Step-by-step explanation:

First Step:

Multiple 312.63 by 1/3

312.63*1/3=104.21

Second Step:

Add 312.63 to 104.21

312.63+104.21=416.84

[tex]✤ \: \underline{ \underline{ \frak{Understanding~the~question : - }}} \\ \\ [/tex]

In this question, we have been provided that Evan swims 1/3 times farther than Drake, thus, the total distance covered by Evan will be equal to the sum of 312.63 m and the 1/3rd of 312.63 m. Thus, at first we will calculate the one third of the distance and then add them up to get our final answer.

⠀

[tex]✤ \: \underline{ \underline{ \frak{Given:-}}} \\ \\ [/tex]

⠀

[tex]✤ \: \underline{ \underline{ \frak{To~Find :-}}} \\ \\ [/tex]

⠀

[tex]✤ \: \underline{ \underline{ \frak{Solution :-}}} \\ \\ [/tex]

Calculating the one - third,

[tex] \sf \longrightarrow \dfrac{1}{3} \: of \: 312.63 \: m \\ \\ \\ \sf \longrightarrow \dfrac{1}{3} \times 312.63 \: m \\ \\ \\ \sf \longrightarrow \dfrac{1}{ \cancel3} \times \cancel{312.63} \: m \: \\ \\ \\ \sf \longrightarrow 1 \times 104.21 \: m \: \: \\ \\ \\ \sf \longrightarrow 104.21 \: m \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]

Thus,

⠀

[tex] \sf \longrightarrow Distance~covered~by~Evan =312.63 \: m + 104.21 \: m \\ \\ \\ \sf \longrightarrow Distance~covered~by~Evan =416.84 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]

Thus, the distance covered by Evan is 416.84 m.

⠀

[tex]\underline{\rule{227pt}{2pt}} \\ \\ [/tex]

Answer:

10

Step-by-step explanation:

Add all the numbers : 3+2+26+9 = 40

Divide the total with the number of data you have which is 4 so 40÷4= 10

Answer:

[tex]\textsf{B)} \quad \dfrac{1}{3^9 \cdot 6^{18}}[/tex]

Step-by-step explanation:

[tex](3^3 \cdot 6^6)^{-3}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]

[tex]\implies \dfrac{1}{(3^3 \cdot 6^6)^3}[/tex]

[tex]\textsf{Apply exponent rule} \quad (ab)^c=a^c \cdot b^c:[/tex]

[tex]\implies \dfrac{1}{(3^3)^3 \cdot (6^6)^3}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies \dfrac{1}{3^9 \cdot 6^{18}}[/tex]

[tex]\\ \rm\Rrightarrow (3^3.6^6)^{-3}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{1}{(3^36^6)^3}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{1}{3^96^{18}}[/tex]

Option B

Answer:

-5 ≤ x ≤ 5

Step-by-step explanation:

If x^2 = 25

x = -5 or 5

BUT inequality

IF x is POSITIVE 5

You can square root both sides

x ≤ 5

IF x is NEGATIVE 5

You can divide both sides by -5

BUT switch inequality sign

This is because basically dividing both sides by negative

x ≥ -5

FINAL INEQUALITY

-5 ≤ x ≤ 5

Using the distributive property to factorize the equation 3x² + 24x = 0, you get 3x(x + 8) = 0 and the solution of the equation is x = -8

The expression is given as:

3x² + 24x = 0

Factor out 3x

3x(x + 8) = 0

Divide both sides by 3x

x + 8 = 0

Subtract 8 from both sides

x = -8

Hence, the solution of the equation is x = -8

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Answer:

3x(x + 8) = 0 and x = -8

Step-by-step explanation:

It was correct for me

The centers and radius for the equations are:

And the circles are in the graph below.

A general circle equation centered at the point (a, b), with a radius of R, is written as:

(x - a)^2 + (y - b)^2 = R^2

Then for the given equations we have:

1) (y-6)^2 + (x - 1)^2 = 9

So the center is at (1, 6) and the radius is 3.

2)  (x-2)^2 + (y + 3)^2 = 36 = 6^2

So the center is at (2, -3) and the radius is 6.

3) (x + 4)^2 +(y-5)^2 = 25 = 5^2

So the center is at (-4, 5) and the radius is 5.

The graphs of the 3 circles can be seen below. Green is the first circle, blue is the second circle, and red is the last circle.

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Answer:

Step-by-step explanation:

Answer:

A and  D

Step-by-step explanation:

A  true

B   false

C   false

D   true

E   false

F   false   ==>   10 years from now is 32 years since turn of century = x

                  there will be    2 (32) + 388 = 452 ppm

Answer:

ans = 6

Step-by-step explanation:

using pythoras theorem:

Hyp^2 = Opp^2 + Adj^2

10^2 = x^2 + 8^2

100 = x^2 + 64

x^2 = 100 - 64

x^2 = 36

x = √36

x = 6.

Hope this helps .

Answer:

7[tex]\frac{17}{49}[/tex]

Step-by-step explanation:

[tex]\frac{90}{7}[/tex]÷1 [tex]\frac{3}{4}[/tex]

= [tex]\frac{90}{7}[/tex]×[tex]\frac{7}{3}[/tex] ( keep change flip )

= [tex]\frac{360}{49}[/tex]

=7[tex]\frac{17}{49}[/tex]

Relative frequency is frequency relative to some quantity, usually the marginal or total frequency. The needed relative frequencies are: 14/50, 15/50, and 44/50 respectively.

Relative frequency is the ratio of the considered sub group's count to the total count. (so its frequency of the considered sub group relative to the total frequency).

The two way table given is:

                           Alaska                  Not Alaska               Total

Hawaiii                    6                            15                            21

Not Hawaii              8                            21                            29

Total                       14                            36                           50

Calculating the needed relative frequencies one by one:

Case 1: The relative frequency for students who have been to Alaska

Thus, the relative frequency for students who have been to Alaska (relative to total count) is 14/50

Case 2: The relative frequency for students who have been to Hawaii but not Alaska

Thus, the relative frequency for students who have been to Alaska (relative to total count) is 15/50

Case 3: The relative frequency for students who have not been to Alaska or Hawaii

Thus, the relative frequency for students who have been to Alaska (relative to total count) is 44/50

Thus, the needed relative frequencies are: 14/50, 15/50, and 44/50 respectively.

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Answer:

Yes

Step-by-step explanation:

y > 3x + 6

-8 > 3(-5) + 6

-8 > -15 +6

-8 > -9

-8 is greater than -9

Answer:

2 divided by 8

Step-by-step explanation:

2/8

/ means division sign

Answer:

When parallel light rays exit a concave lens, they

✔ diverge

.

When parallel light rays exit a convex lens, they

✔ converge

.

Step-by-step explanation:

The requried, parallel light rays diverge when passing through a concave lens, and converge when passing through a convex lens.

Refraction is the bending of light as it passes from one medium to another medium of different optical densities, such as from air to water or from air to a glass lens.

When parallel light rays exit a concave lens, they diverge as the concave lens is thinner at the center and thicker at the edges. This shape causes the light rays to bend away from the optical axis and spread apart from each other, resulting in a virtual image that is smaller than the object.

On the other hand, when parallel light rays exit a convex lens, they converge towards a focal point as the lens is thicker at the center and thinner at the edges. This shape causes the light rays to bend towards the optical axis and meet at a focal point, resulting in a real image that is inverted and can be larger or smaller than the object depending on the distance of the object from the lens.

Therefore, the behavior of parallel light rays upon exiting concave and convex lenses is quite different due to their distinct shapes and curvatures, resulting in opposite effects on the direction of light rays and the formation of images.

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Answer:

33 there you go

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

slope intercept form   slope = -2   y axis intercept = -2

y = -2x - 2      to graph this  pick two values of x   say -3   and  + 2

                        plug these values into the equation to find the corresponding y values, plot the points and then draw a line connecting them

Answer:

d

Step-by-step explanation:

Answer:

Step-by-step solving

Step-by-step explanation:

Looking at this problem you are going to need to divide the numbers already given to firgure out how many flower vases fit exactly 8 flowers-

1323 divided by 8= the answer I got was a decimal(165.375) you could always round or re-look at the problem, but you can't have a half of a vase so you would need to round to a whole number. Maybe insert a picture of the problem just incase you might of not added some things in the question. hope this helps.

Answer:

Step-by-step explanation:

The triangle is being reflected over the y-axis.

A(x, y) → (x, -y)

A(1, 4) → (1, -4)

A'(1, -4)

B(x, y) → (x, -y)

B(4, 3) → (4, -3)

B'(4, -3)

C(x, y) → (x, -y)

C(2, 1) → (2, -1)

C'(2, -1)

Hope this helps!

Answer:

$1305.91

Step-by-step explanation:

To solve this, we can use the geometric sequence formula

[tex]\alpha _n=a_1*r^n^-^1[/tex]

If we plug in our values we get [tex]\alpha _n=200*1.085^2^3[/tex]

Thus, leaving us with 1305.91

Hope this helps