Write the ratio as a fraction in lowest terms.
46 minutes to 3 hours

The displacement of Maurice from his starting point is 232 miles.

The displacement of an object is the change in the position of the object. Displacement measures how far an object is from its initial position or starting point.

The displacement of Maurice from his starting point is calculated as follows;

|B

|

|                         |A

|                         |

|--------------------- |

A line connecting point A and B will form the displacement of Maurice from his staring point.

line connecting AB = hypotenuse side of the right

Base of the triangle = 168 miles

Height of the triangle = 422 - 262 = 160 miles

AB = √(168² + 160²)

AB = 232  miles

Thus, the displacement of Maurice from his starting point is 232 miles.

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[Mathematical Situation]

Simplify [tex]0.042[/tex] × [tex]0.8[/tex].

Solution:

[tex]0.0336[/tex]

Hope this helps!

The value of x in 5 - x < 4/7 based on the information given will be x < 4 3/7.

It should be noted that based on the information given in the question, the expression will be:

5 - x < 4/7

Therefore, collect like terms

5 - x <4/7

x < 5 - 4/7

x < 4 3/7

Therefore, the value of x is less than 4 3/7.

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Answer:

x < 18 and x > −72

Step-by-step explanation:

The equations which represent the standard form are:

A) 3x+12y=-6

D) -10x+7y=13

F) 3/4x+y=8

G) 5x+14y=3

Given we have a set of equations.

A technique for expressing linear equations is the standard form. The standard form, the slope-intercept form, and the point-slope form are some of the numerous ways that a linear equation can be expressed. Ax + By = C is a representation of the general form, commonly referred to as the standard form, of linear equations.

A) 3x+12y=-6

the above equation is in the form of Ax + By = C

B) x-y = 1

the above equation is not in the form of Ax + By = C

C) 2x=9

the above equation is not in the form of Ax + By = C

D)  -10x+7y=13

the above equation is in the form of Ax + By = C

E) 6y=11

the above equation is not in the form of Ax + By = C

F)  3/4x+y=8

the above equation is in the form of Ax + By = C

where A=3/4 and B=1

G)  5x+14y=3

the above equation is in the form of Ax + By = C

Hence  we get the required equations in the standard form.

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The sum of a geometric series with a first term of 3 and a common ratio of 10/9 is;

∑ [tex]3 (\frac{10}{9} )^k^-^1[/tex]  where, K = 1 to n.

What is Geometric series?

A geometric series is a list of numbers having a common ratio. Each term after the first is gotten by multiplying the previous one by the common ratio.

Given that;

The first term is 3 and the common ratio is 10/9.

Now, A geometric sequence has the form:

a, ar , ar², ar³, . . .

Hence, The nth term of a geometric sequence is;

⇒ ∑ [tex](ar^k^-^1)[/tex]     where, k = 1 to n.

Therefore, the sum of geometric series with a first term of 3 and a common ratio of 10/9 is:

⇒ ∑ [tex]3 (\frac{10}{9} )^k^-^1[/tex]  where, k = 1 to n.

So, The sum of a geometric series with a first term of 3 and a common ratio of 10/9 is;

⇒ ∑ [tex]3 (\frac{10}{9} )^k^-^1[/tex]  where, k = 1 to n.

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Applying the triangle sum theorem, the value of x is: 4.

When we add the three interior angles of a triangle together, the sum must be equal to 180 degrees according to the triangle sum theorem.

Given the triangle with the following interior angles, 35°, (22x - 3)°, and 60°. Therefore:

35 + (22x - 3) + 60 = 180 [triangle sum theorem]

Solve for x

35 + 22x - 3 + 60 = 180

Combine like terms

92 + 22x = 180

Subtract 92 from each side of the equation

92 + 22x - 92 = 180 - 92

22x = 88

Divide both sides by 22

22x/22 = 88/22

x = 4

Thus, applying the triangle sum theorem, the value of x is: 4.

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The measure of the central angle m∠VWU is 69 degrees

Central angle is the angle formed by two arms and having the vertex at the centre of a circle.

The diameter of a circle runs from the centre of a circle.

The diameter SU and RT intersect each other at point Q.

Therefore,

m∠VWS = m∠TWU (Vertically opposite angles)

m∠VWU = m∠SWT (Vertically opposite angles)

Hence,

m∠TWU = 111 degrees.

Therefore,

m∠VWU = 360 - 111 - 111  /2

m∠VWU = 360 - 222 / 2

m∠VWU = 138 / 2

m∠VWU = 69 degrees

Therefore, the measure of the central angle m∠VWU is 69 degrees

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Answer: The answer in exact form would be 1/100 or 0.01

Answer:

1/100

Step-by-step explanation:

1/10^2 = 1/10 x 1/10 = 1/100

Answer:

The value of x is -√3/2 and the value of y = -1/2.

Step-by-step explanation:

It is given that t = π/6 and we need to find the point (x y) on the unit circle that corresponds to the real number t.

Now,

Let us suppose that the real number 't' is to be of an arc length from the positive X-axis.

=> t = π/6

Further, if we look at the graph given below;

We observe that the reference angle π/6 is one of the standard angles with the ratio of opposite to adjacent sides as indicated above.

=> x, y = -√3/2, -1/2

Therefore, it can be inferred from the graph that the value of x is -√3/2 and the value of y = -1/2.

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I THINK X IS 5/4 ANY ANSWER CHOISES ??

Answer: 6.47

Step-by-step explanation:

a hundredth is .01 so 3 of those would be .03, and 6.5 - .03 is 6.47

Answer:

A is the answer of the question

Answer:

x = 3 ± √23

Step-by-step explanation:

Simplify the quadratic equation.

[tex]3x^2-18x+5 = 473x^2-18x+5-47 = 0\\3x^2-18x-42 = 0\\\\a = 3\\b = -18\\c = -42\\\\x = (-(-18)\pm\sqrt{ (-18)^2-4(3)(-42) )} \div 2(3)\\x = (18\pm\sqrt{ 324+504)} \div 6\\x = (18\pm\sqrt{ 828}) \div 6[/tex]

Simplify further.

[tex]x = (18\pm\sqrt{ 23\times 36}) \div 6\\x = (18\pm6\sqrt{ 23}) \div 6\\x = 6(3\pm\sqrt{23}) \div 6[/tex]

Thus, the solution is

x = 3 ± √23

Hope this helps.

x = 3 + √23 and x = 3 - √23 are the two solutions of the given quadratic equation.

ax²+bx+c=0, with a not equals to 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

To solve for x in the equation 3x^2 - 18x + 5 = 47, we can begin by simplifying the equation:

[tex]3x^2 - 18x - 42 = 0[/tex]

Next, we can divide both sides of the equation by 3 to get:

[tex]x^2 - 6x - 14 = 0[/tex]

To solve for x, we can use the quadratic formula:

[tex]x =\frac{ (-b \pm \sqrt{(b^2 - 4ac))} }{ 2a}[/tex]

In this case, a = 1, b = -6, and c = -14, so we have:

[tex]x = \frac{(-(-6) \pm \sqrt{((-6)^2 - 4(1)(-14)))}}{2(1)} \\x = \frac{(6 \pm \sqrt{(36 + 56))}}{ 2} \\x = (6 \pm \sqrt{92}) / 2[/tex]

Simplifying the radical, we get:

x = (6 ± 2√23) / 2

Dividing both the numerator and denominator by 2, we get:

x = 3 ± √23

Therefore, the two solutions to the equation [tex]3x^2 - 18x + 5 = 47[/tex] are x = 3 + √23 and x = 3 - √23.

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The number of 2 bedroom apartments that are there is 10.

Let the number of one bedroom = b

Since there are 5 more 2-bedroom apartments than 1- bedroom apartments. This will be b+5.

There are 15 apartments. Therefore, the expression will be:.

b + b + 5 = 15

2b + 5 = 15.

2b = 15 - 5.

2b = 10

b = 10 / 2

b = 5

Number of 2 bedroom = b + 5 = 5+5 = 10.

Therefore, the number of 2 bedroom apartments that are there is 10.

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[tex]f(x) = ae {}^{bx} \\ f(2) = 5 \: \: \: \: \: f(3) = 4[/tex]

[tex]5 = ae {}^{2b} \: \: \: \: \: \: \: 4 = ae {}^{3b} \\ divide \: both \: systems \\ e {}^{b} = \frac{4}{5} \: \: \: \: so \: \: \: b = ln(0.8) \\ solving \: for \: a \: we \: get \: that \: a = \frac{125}{16} [/tex]

[tex]f(x) = \frac{125}{16} e {}^{ln(0.8)x} [/tex]

[tex]f(10) = \frac{125}{16} e {}^{10ln(0.8)} = \frac{65536}{78125} \approx0.838861 \\ f(100) = \frac{125}{16} e {}^{100ln(0.8)} = \frac{4 {}^{98} }{5 {}^{97} } \approx1.59 \times 10 {}^{ - 9} [/tex]

Answer:the answer is 56.1 m

Step-by-step explanation:56.1 m

Answer:

22/10

=2.2

22-2.2=19.8

Stephanie pays £19.8

Answer: Thus, the number with the larger value of 8 is 184.36 and it is 100 times larger.

Step-by-step explanation:

First we can find out the place value,

Then we can write,

Define Place value :

Place value is the basis of our entire number system. This is the system in which the position of a digit in a number determines its value. The number 42,316 is different from 61,432 because the digits are in different positions.

                     [or]

Place value of a digit can be defined as the position of the particular digit in a given number.

For Example :

The place value of 7 in 1870 is  70

Given the data,

First we use digit is :    184.36

Second we use digit is : 9027.83

Place value of 8 in First digit is  ⇒ 184.36 is 80

Place value of 8 in Second digit is ⇒ 9027.83  is 0. 8

We can solve the Ratio is :

                      Ratio = 80/ 0.8

                       Ratio = 100 times

Therefore,

Thus, the number with the larger value of 8 is 184.36 and it is 100 times larger.

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Answer:

Step-by-step explanation:

54, because 135/5 = 2727x2 = 54 Ibs.

Answer: you will be 54 pounds

Step-by-step explanation:

The area of the triangle with the given dimensions are 77cm.

According to the statement

We have to find that the area of the triangle.

So, For this purpose, we know that the

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle.

From the given information:

15 cm

7 cm

22 cm

Then

The base of the triangle is 7 cm and the height of the triangle is a 22cm.

Then

A = 1/2 × b × h.

A = 1/2 × 7 × 22.

Now solve it then

A = 154/2

A = 77cm.

So, The area of the triangle with the given dimensions are 77cm.

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The length of the sides AB and B'C' will be 2.7 units and 16.2 units, and the measure of the angles ∠A, ∠B, and ∠C are 77.5°, 54.2°, and 48.3°, respectively.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

Triangle ABC is dilated with a scale factor of 3. Then the scale factor will be 3.

If the side BC is 5.4 units long, then the length of the side B'C' will be

B'C' = 3 x BC

B'C' = 3 x 5.4

B'C' = 16.2 units

If the side A'B' is 8.2 units long, then the length of the side AB will be

AB = A'B' / 3

AB = 8.2 / 3

AB = 2.7 units

If the measure of the angles ∠A, ∠B, and ∠C are 77.5°, 54.2°, and 48.3°, respectively.

There is no effect of dilation on the angle. Then the angles will remain the same.

The length of the sides AB and B'C' will be 2.7 units and 16.2 units, and the measure of the angles ∠A, ∠B, and ∠C are 77.5°, 54.2°, and 48.3°, respectively.

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It should be noted that simplifying 5¹⁰ × 5² will be 5^12.

It should be noted that these values have to do with powers. In this case, since that have same base and we want to multiply, we will add their powers.

Therefore, 5¹⁰ × 5² will be:

= 5¹⁰ × 5²

= 5^12

In conclusion, the value will be 5 raise to power 12

Therefore, based on the information, it should be noted that the value of 5¹⁰ × 5² will be 5^12.

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Simplify 5¹⁰ × 5²

The statement that, "Volume can be measured in liters or cubic meters" is True.

There are several units used for measuring the volume of a liquid or other substance or object but the international unit of measurement for volume is the cubic meter or m³.

Volume is also common measured in the very popular unit known as liters. Smaller measures of liters include milliliters. For the cubic meter, there are also cubic millimeters and cubic decimeters.

In conclusion, it is true that volume can be measured in liters or cubic meters.

Options for this question include:

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Answer:

-4920.75 or 18

Step-by-step explanation:

I'm not quite sure if this is correct because I got two diffrent soultions for a.

In a1=3 I got a=3

In a8= -6561 I got a= -820.125

So i plugged my two solutions in to find a6

I got

18

or

-4920.75

That doesn't really seem correct, but I tried!!

The radiactive decay equation in terms of t that models the situation is 32 = 1024e^{(-0.0239/s)t}

Radioactive decay is the spontaneous disintegration of atoms with the emission of radiation.

The half life of a radioactive isotope is the time it takes for half the number of atoms in a given sample to disintegrate.

To model the situation, we use the equation for radioactive decay which is given below

[tex]N = N_{0}e^{-{\lambda}t}[/tex] where

Given that the half life of the isotope dubnium-263 is 29 seconds and  sample of dubnium-263 was first measured to have 1024 atoms. Then, after t seconds, there were only 32 atoms of the isotope remaining. we have that

So, λ = 0.693/29 s = 0.0239 /s

So, susbtituting the values of the variables into the equation, we have

[tex]N = N_{0}e^{-{\lambda}t}[/tex]

[tex]32 = 1024e^{-(0.0239/s)t}[/tex]

So, the radiactive decay equation in terms of t that models the situation is 32 = 1024e^{(-0.0239/s)t}

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Answer:

a 1760.

b 32.1

c 8.5 × 10^8

d 5.09×10^-5

In combination, 56 ways can Nick choose topping can only be chosen .

What is permutation and combination?

given that Nick choose pizza = 5

menu of toppings if each topping =8

chosen once  = 8c5

                        =>   8! / (5!(8−5)!)

                         =>  56

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Answer:

None of these

Step-by-step explanation:

We can estimate f'(9) by finding the slope of the secant through the two points closest to (9, f(9)).

[tex]\frac{f(10)-f(8)}{10-8}=\frac{16-10}{2}=3[/tex]

The sequence is an arithmetic sequence due to the presence of a common difference.

An arithmetic sequence is a sequence that has a common difference while a geometric sequence is a sequence with a common ratio. For instance, given the sequence below:

a, b, c, d...

The sequence is an arithmetic sequence if;

common difference = b - a = c - b = d - c

The sequence is a geometric progression if;

common ratio = b/a = c/b = d/c

Given the sequence 17, 13, 9, ...

d = 13 - 17 = 9 - 13

d = -4

Since the sequence has a common difference, hence the given sequence is an arithmetic progression.

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