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The length of a rectangular frame is represented by the expression 3x + 6, and the width of the rectangular frame is represented by the expression 3x + 4. Write an equation to solve for the width of a rectangular frame that has a total area of 120 square inches.

Answer: 1010

Step-by-step explanation:

[tex]V=\frac{1}{3}(\pi)(8^{2})(15) \approx \boxed{\text{ } 1010 \text{ cm}^{3}}[/tex]

Answer:

D. 8

Step-by-step explanation:

32^(3/5) is the same as [tex]\sqrt[5]{32}[/tex]^3.

 [tex]\sqrt[5]{32}[/tex] = 2 because 2^5=32

2^3 = 8

Simplify the expression.

Rewrite 32 as 2⁵.

[tex]\bf{\left(2^{5}\right)^{\frac{3}{5} } }[/tex]

Apply the power rule and multiply exponents, (αᵐ)ⁿ=αᵐⁿ.

[tex]\bf{2^{5}^{(\frac{3}{5} )} }[/tex]

Cancel the common factor of 5.

Cancel the common factor.

[tex]\bf{2^{\not{5}}^{(\frac{3}{5} )} }[/tex]

Substitute the expression.

[tex]\bf{2^{3} \ \ \to \ Calculate \ power. }[/tex]

Raise 2 to the power of 3.

We conclude that the correct option is "D".

Answer:

Step-by-step explanation:

Perimeter is the sum of lengths of triangles. Hence it's unit in

c

m

. Area has unit

c

m

2

i.e., length squared. So if measurements are in the ratio

3

:

4

, areas are in the ratio

3

2

:

4

2

or

9

:

16

. This is because the two triangles are similar.

A total area is

75

square centimeters, we need to divide it by the ratio

9

:

16

Of which first will be the area of the smaller triangle.

Hence the area of the smaller triangle is

75

×

9

9

+

16

=

75

×

9

25

=

75

3

×

9

25

1

=

27

square centimeters

The area of larger triangle would be

75

×

16

9

+

16

=

3

×

16

=

48

square centimeters

Answer:

42 times

Step-by-step explanation:

Here,

4 hits = 7 times

1 hits= 7/4 times

24 hits = 7/4 × 24

= 42 times.

The number of times that the baseball player makes the hit if he hit 24 hits is 42 times, which is an option (a).

Given that:

A baseball player makes 4 hits every 7 times at bat.

It is required to find the number of times that the player hits if he hit 24 hits.

Number of times that 4 hits are made = 7

Number of times that 1 hit is made = 7/4

So, the number of times that 24 hits are made can be found by the following formula.

Using the proportional concept, the number of times, N, is:

[tex]N=\frac{7}{4} \times 24[/tex]

   [tex]=7\times6[/tex]

   [tex]=42[/tex]

Hence, the correct option is (a).

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In general, the greater the between-group variance compared to the within-group variance, the more likely you are to find statistical significance.

Unlike the inside group version, where the focus is on the differences among a population and its implication, the between-organization variant is concerned with finding how the method of corporations differ from each other.

Inside-organization version (on occasion referred to as mistakes organization or error variance) is a time period used in ANOVA tests. It refers to variations because of variations within individual businesses (or ranges). In other words, no longer all of the values within every group (e.g. method) are equal.

With the purpose to examine multiple groups right away, we can study the ANOVA, or analysis of Variance. not like the t-test, it compares the variance within every sample relative to the variance between the samples.

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Answer:

  213°

Step-by-step explanation:

Consider the angle measured at the lighthouse between North and the Boat. The lengths given in the problem statement are the lengths of the side opposite that angle, and the length of the hypotenuse of the right triangle shown. The trig function that relates the angle and those sides is ...

  Sin = Opposite/Hypotenuse

The sine of the angle at the lighthouse is ...

  sin(bearing to boat) = (13.5 km)/(24.6 km) = 45/82

The value of the angle is found using the inverse sine function, called the arcsine function:

  bearing to boat = arcsin(45/82) ≈ 33°

The bearing from the boat to the lighthouse is in the opposite direction. It can be found by adding 180° to this angle:

  bearing to lighthouse = 33° +180° = 213°

__

Additional comment

The attached image shows a calculator making this calculation. Note that the angle mode is set to DEG (lower left corner). The arcsine function is usually found as the 2nd function of the Sin key.

Answer:

[tex]\begin{cases}x=-6\\y=-10\end[/tex]

Step-by-step explanation:

[tex]\begin{cases}-x+3y=-24 \left(1)\right\\-4x+2y=4 \left(2)\right\end[/tex]

Make x the subject in (1)

[tex]x=3y+24 \left(3)\right[/tex]

Sub into (2)

[tex]-4(3y+24)+2y=4\\\\\implies-12y-96+2y=4\\\\\implies10y=-100\\\\y=-10[/tex]

Sub into (3)

[tex]x=-30+24\\\\x=-6[/tex]

Hence

[tex]\begin{cases}x=-6\\y=-10\end[/tex]

Answer:

[tex]\left \{ {{x=-6} \atop {y=-10}} \right. .[/tex]

Step-by-step explanation:

[tex]\left \{ {{-x+3y=-24\ \ (1)} \atop {-4x+2y=4\ \ \ (2)}} \right. \ \ \ \ \\[/tex]

We multiply equation (1) by -4:

-x+3y=-24 |*(-4)

-x*(-4)+3y*(-4)=-24*-(-4)

4x-12y=96.  (3)        ⇒

[tex]\left \{ {{4x-12y=96\ \ (3)} \atop {-4x+2y=4\ \ \ (2)}} \right.[/tex]

We summarize equations (2) and (3):

[tex]-10y=100\ |:(-10)\\y=-10.\\Make\ y \ the\ subject\ in\ (1):\\-x+3*(-10)=-24\\-x-30=-24\\-x=-24+30\\-x=6\ |*(-1)\\x=-6.[/tex]

f(x)=y=√x looks something like this:

(4,2)

(9,3)

(16,4)

Whilst your graph is much higher slope, for lack of better term

Rules of transformation

f(x)+b - function is shifted b units upward (up y-axis)

f(x)-b - function is shifted b units downward (down y-axis)

f(x+b) - function is shifted b units to the left (negative x-axis)

f(x-b) - function is shifted b units to the right (positive x-axis)

-f(x) - function is reflected over x-axis

f(-x) - function is reflected over y-axis

bf(x) - vertical stretch for |b| > 1, vertical shrink for 0< |b| <1

f(bx) - horizontal shrink for |b| > 1, horizontal stretch for 0< |b| <1
**INVALIDATE my answer, as statements were given 10 mins after posted**

Answer:

The graph is translated to the left by 3

Step-by-step explanation:

the equation would be y= sqrt(x)+3

Answer:

PART A

length of foot = y

length of forearm = x = 17

Equation: y = 0.860x + 3.302

Plug in 17 for x in the equation, and simplify. Remember to follow PEMDAS, first multiply, then combine like terms:

y = (0.860)(17) + 3.302

y = 14.62 + 3.302

y = 17.922

length of foot = y = 17.922 inches long

Answer:

  D.  all three figures

Step-by-step explanation:

A cube is a rectangular prism that has every edge equal in length to every other edge. This ratio of edge lengths holds for all cubes. Every cube is similar to every other cube.

Cubes with edge lengths of 5 ft, 7 ft, and 10 ft will all be similar. Any pair of corresponding edges of different cubes will have the same ratio.

Answer:

A

Step-by-step explanation:

So whenever you're finding the difference between two numbers you generally use the equation: |a-b| since a-b may or may not be negative, but |a-b| will always equal |b-a|. Since the only thing that differs is the sign. So when you have: [tex]|-\frac{2}{3}-\frac{5}{3}|[/tex], in this case a=-2/3 and b=5/3 (b is positive since you're subtracting b, so if b appeared positive in the equation, it's actually negative, since the negative sign in |a-b|, which would make the two negatives cancel out). This means A is the correct answer. You could also calculate what the value is. Calculating gives you: [tex]|-\frac{7}{3}| = \frac{7}{3}[/tex]. And as you can see the top one, has two numbers separated by 7 one thirds.

Answer:

A

Step-by-step explanation:

It is absolute value and when it is absolute value, it is positive.

The numbers which are the means of the proportion as given in the task content are in; Choice D; 3 and 20

It follows from the task content that the proportion whose mean is to be evaluated in the task content is; 2/3 = 20/30.

On this note, it follows that the numbers 2 and 30 are the lower and upper extremes of the property and hence, 3 and 20 are the mean of the proportion.

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Answer:

vertex = (2, - 32 )

Step-by-step explanation:

given a quadratic function in standard form

y = ax² + bx + c ( a ≠ 0 ) , then the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

given

y = 2(x + 2)(x - 6) ← expand factors using FOIL

   = 2(x² - 4x - 12 ) ← distribute parenthesis

y   = 2x² - 8x - 24 ← in standard form

with a = 2, b = - 8 , then

x = - [tex]\frac{-8}{4}[/tex] = 2

substitute x = 2 into the function for corresponding y- coordinate

y = 2(2 + 2)(2 - 6) = 2(4)(- 4) = 8 × - 4 = - 32

vertex = (2, - 32 )

The area of the space under the slide is 2.10 square meters

The diagram in the question is added as an attachment

The vertical distance is represented by h.

So, we have:

sin(70) = h/2

Solve for h

h = 2 * sin(70)

Evaluate

h = 1.88 m

Hence, the vertical distance is 1.88 m

This is calculated using

sin(40) = h/Slide

This gives

sin(40) = 1.88/Slide

Solve for Slide

Slide = 1.88/sin(40)

Evaluate

Slide = 2.92

Hence, the length of the slide is 2.92 m

This is calculated using:

A = 0.5 * h * slide * sin(∅)

Where

∅ = 90 - 40 = 50

So, we have:

A = 0.5 * 1.88 * 2.92 * sin(50)

Evaluate

A = 2.10

Hence, the area of the space under the slide is 2.10 square meters

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Answer:

B

Step-by-step explanation:

since the slope is 5, 1/5x or -1/5x cannot be the slope. since the slope isn't negative it also cancels out -5x. 5x can be your only slope and that is in answer B.

Answer:

The answer is 6.2

Step-by-step explanation:

The factors of 16 are 1,2,4,8, and 16.

get the sum of the factors which is 31, then divide it to number of the addends which is 5.

31/5 = 6.2

Answer:

Second option 1.6x10^14

Step-by-step explanation:

[tex](x - a)(x - b)(x - c) \\ (x {}^{2} - bx - ax + ab)(x - c) \\ x {}^{3} - bx {}^{2} - ax {}^{2} + abx - cx {}^{2} + cbx + cax - abc[/tex]

[tex]x {}^{3} + ( - a - b - c)x {}^{2} + (ab + cb + ca)x - abc [/tex]

[tex] - a - b - c = - 7 \\ ab + ac + bc = 16 \\ - abc = - 12 \: \: \: \: \: abc = 12[/tex]

The formula for Classical Probability.

The probability of a simple event happening is the number of times the event can happen, divided by the number of possible events. The “math” way of writing the formula is P(A) = f / N.

Without replacing drawn marbles:

Probability of drawing 3 green:

3/10*2/9*1/8=1/120

Probability of drawing 3 black:

4/10*3/9*2/8=1/30

Probability of drawing 3 green:

3/10*2/9*1/8=1/120

Adding these three: 6/120 =5%

If replacing marbles after each draw

Probability of drawing 3 black:

(3/10)^3=9/1000

Probability of drawing 3 green:

(4/10)^3=16/10000

Probability of drawing 3 black:

(3/10)^3=9/1000

Adding these three: 34/1000= 3.4%.

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Answer:

a) Call-more is cheaper

b) 60 minutes

Step-by-step explanation:

Call-More: C = 0.40t + 25

Talk-Now:  C = 0.15t + 40

a) Substitute t =  50 minutes in the above equations.

Call-More:

         C = 0.40*50 + 25

            = 20 + 25

        C = 45

 Talk-Now:

          C = 0.15*50 + 40

              = 7.5 + 40

          C  = 47.40

Company Call-more is cheaper than Talk-now.

b) We have to find the conditions under what condition the two companies charge the same.

    Charge of company Call-more = charge of company Talk-now.

                  0.40t + 25 = 0.15t + 40

                            0.40t = 0.15t + 40 -25

                            0.40t = 0.15t + 15

                 0.40t - 0.15t = 15

                             0.25t = 15

                                     [tex]\sf t = \dfrac{15}{0.25}\\\\ t = \dfrac{15*100}{25}\\\\[/tex]

                                     t = 15*4

                                     t = 60 minutes

Two companies charge the same for 60 minutes.

The value of (g-f)(X) is 2x - 6x³ +6.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given:

f(x)= 6x³-4, g(x)= 2x+2

Now,

(g-f)(x)= g(x)-f(x)

= 2x+2-( 6x³-4)

=2x+2- 6x³+4

=2x - 6x³ +6

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Answer:

Step-by-step explanation:

The Matching for each transformation is

1. (x,y) → (3x, y)

horizontal stretch by factor 3.

2. (x,y) → (x + 3, y)

translation 3 unit right

3. (x,y) → (x, 3y)

Vertical stretch by factor 3.

4. (x,y) → (x, y + 3)

translation 3 unit up.

5. (x,y) → (3x, 3y)

dilation with Scale factor 3.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

1. (x,y) → (3x, y)

It is horizontal stretch by factor 3.

2. (x,y) → (x + 3, y)

It is translation 3 unit right because the rule for translation for 3 unit right is x - > x + a

3. (x,y) → (x, 3y)

It is Vertical stretch by factor 3.

4. (x,y) → (x, y + 3)

It is translation 3 unit up.

5. (x,y) → (3x, 3y)

It is dilation with Scale factor 3.

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is that 2.11 I think so

Step-by-step explanation:

I don't know explain it to you and

In order to draw a perpendicular bisector you must have ruler , compass and a pencil.

Given nothing and we have to show the steps to draw a perpendicular bisector.

Perpendicular bisector is the line which divides the line into two equal parts and makes 90° angle on other line.

If we want to make a perpendicular bisector on a line then we have to follow the following steps:

1) First draw a line with the help of ruler on which we want to make perpendicular bisector.

2) Now take a compass and a pencil.

3) Put the pencil in the compass and strech the compass equal to half or little more of the length of the line.

4) Now put the compass on one end of the line and draw an arc on the line or may be just upward.

5) Now repeat the step 4 from other end.

6) Now draw a line from the point where two arcs intersects on the line.

7) It is the perpendicular bisector of the line.

Hence to draw a perpendicular bisector we require compass, ruler and a pencil.

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Answer: If she waits on 13 tables than she should expect to earn $220

Step-by-step explanation:

15*13=195

195+25=220

Answer: A=48 squared centimeters

Step-by-step explanation: First you need to find the area of the whole rectangle. Area equals length times width (9*8), which is 72. Next you find the area of the white region: 4*6=24. Finally, you subtract the smaller region from the whole: 72-24=48. BOOM: you got the exact right answer :)

Answer: 1

Step-by-step explanation:

When [tex]x=0[/tex], [tex]y=\boxed{1}[/tex]