What is the sum in simplest form?

4 1/2 + 1 3/5=

6 1/10

5 1/10

6 1/5

5 4/7

The logarithmic equation is:

log₂128 = x

So the correct option is the third one

Here we have the expression.

2ˣ = 128

Now, if we apply the natural logarithm to both sides, we can get:

ln(2ˣ) = ln(128)

Because of the property of natural logarithms, we can write the left side as:

ln(2ˣ) = x*ln(2) = ln(128)

Now, if we isolate x, we get:

x = ln(128)/ln(2)

And remember that:

ln(k)/ln(n) = logₙ(k)

Then we can rewrite the logarithmic equation as:

x = log₂(128)

Which is the third option.

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The plastic containers should be used by the company to minimize the cost because it will cost $5.40 more to use the wooden containers.

A mathematical word problem is a question that is stated as one or more sentences and calls on students to use their understanding of arithmetic operations to solve a "real-life" problem.

As you are aware, word problems can include almost any operation, including addition, subtraction, division, and even many operations at once.

From the given information:

If the company uses a wooden container shaped-liked rectangular prism, the will need to use (7560/180) containers.

= 42 containers of wooden containers.

If the company uses a plastic cylindrical container, they will need to use (7560/126) containers.

= 60 containers of plastic containers.

To determine the container that the company should use that will minimize the cost:

Therefore, we can conclude that the company should use plastic containers because it will cost $5.40 more to use wooden containers.

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Answer:

B. The plastic containers should be used because it will cost $5.40 more to use the wooden containers.

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

(10x + 25) / (3x + 12) = (5x) / (x + 4)

5(2x + 5) / 3(x + 4) = 5(x) / (x +4)

(2x + 5) / 3 = x

2x + 5 = 3x

x = 5

Check.

(10*5+ 25) / (3*5 + 12) = (5*5) / (5 + 4)

75/27 = 25/9

25/9 = 25/9

The probability of rolling a sum of six or two even numbers.

is P = 1/3

Here we are rolling two dice, and each dice has 6 possible outcomes, then the total number of outcomes is:

6*6 = 36

Now, the outcomes that given a sum of 6 are:

dice 1    dice 2.

1              5

5              1

2              4

4              2

3             3

We have 5 outcomes there.

The outcomes where both numbers are even are:

dice 1    dice 2.

2             2

2             4

4             2

4             4

4            6

6             2

6             4

6             6

We have 8 outcomes here (such that 2 are in the ones we counted before).

Then the total number of outcomes that either add to 6 or have both even numbers are:

5 + 8 - 2 = 12

Then 12 out of 36 outcomes either add to 6 or have both even numbers, this means that the probability is:

P = 12/36 = 1/3

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Using the total weight the number of red, green and yellow colour are 2, 4 and 3 respectively.

The total number of reds, yellows, and greens on a scale is 9.

The reds weighed 3 pounds each, the yellows weighed 6 pounds each, and the greens weighed 5 pounds each. The total weight is 44

pounds. There are 2 more greens than reds.

Therefore,

let

x = number of reds

number of greens = x + 2

y = number of yellow

Therefore,

x + x + 2 + y = 9

2x + y = 7

3x + 6y + 5(x + 2) = 44

3x + 6y + 5x + 10 = 44

8x + 6y = 34

Hence,

2x + y = 7

8x + 6y = 34

8x + 4y = 28

8x + 6y = 34

2y = 6

y = 6 / 2

y = 3

2x + 3 = 7

2x = 7 - 3

2x  = 4

x = 4 / 2

x = 2

Therefore,

the number red colour = 2

the number of green colour = 2 + 2 = 4

the number of yellow colour = 3

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The spherical coordinate that is converted from the given rectangular coordinate is (12.62, 46.67°, 35.3°).

Here, the given rectangular coordinate is (5, 5.3, 10.3).

Therefore, the value of 'x' is 5, the value of 'y' is 5.3 and the value of 'z' is 10.3.

We can convert the rectangular coordinate (x, y, z) into spherical coordinate (ρ, θ, Φ) by the below mentioned method.

We know, ρ² = (x²+y²+z²)

Therefore, ρ

= √(x²+y²+z²)

= √[(5)²+(5.3)²+(10.3)²]

= √(25+28.09+106.09)

= √(159.18)

= 12.62

Again, tan θ = (y/x)

Therefore, θ = tan⁻¹(y/x) = tan⁻¹(5.3/5) = tan⁻¹(1.06) = 46.67°

Similarly, cos Φ = (z/ρ)

Therefore, Φ = cos⁻¹(z/ρ) = cos⁻¹(10.3/12.62) = cos⁻¹(0.816) = 35.3°

Here, the spherical coordinate is (ρ, θ, Φ).

Therefore, the required spherical coordinate for the given rectangular coordinate is (12.62, 46.67°, 35.3°).

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Answer:

13

Step-by-step explanation:

w^2 = -2^2 = 4

-v = -1*-8 = 8

Put it together: w^2-v+1 --> 4+8+1 = 13

The equation of [tex]f(x) = e^{-6x}[/tex] by maclaurin series is [tex]f(x)=\sum_{i=0}^{\infty} \frac{(-6.x)^{i} }{i!}[/tex].

The maclaurin series for f(x) is defined by the following formula:

[tex]f(x) = \sum_{i=0}^{\infty} \frac{f^{(i)} (0)}{i!} .x^{i}[/tex]--------------(1)

Where [tex]f^{i}[/tex] is the i - th derivative of the function

If f(x) = [tex]e^{-6x}[/tex], then the formula of the i - th derivative of the function is:

[tex]f^{i} =(-6)^{i} .e^{-6x}[/tex]----------------------(2)

Then,

[tex]f^{i}(0) = (-6)^{i}[/tex]

Lastly, the equation of the trascendental function by Maclaurin series is: [tex]f(x)=\sum_{i=0}^{\infty} \frac{(-6)^{i}.x^{i} }{i!} \\f(x)=\sum_{i=0}^{\infty} \frac{(-6.x)^{i} }{i!}[/tex]---------------(3)

Hence,

The equation of [tex]f(x) = e^{-6x}[/tex] by maclaurin series is [tex]f(x)=\sum_{i=0}^{\infty} \frac{(-6.x)^{i} }{i!}[/tex].

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Answer:

7 people are going in the minivan.

Step-by-step explanation:

Since Chris AND the other 18 people are going, add 1 to 18 (19).

There are 3 cars, which have 4 each. We can use multiplication to determine that there are a total of 3 x 4 people in the cars, which is equivalent to 12.

Since the remaining party people are going in the minivan, we will subtract 12 from 19 to get 7.

Therefore, 7 people are going in the minivan.

Hope this helps!

The secant of circle D is the 'line GH'. Where the line segment EF is the diameter of the circle, line segment DC is the radius, and the ray AB is the tangent of the given circle.

The line that passes through the circle and touches the circle at two points is said to be a secant line of the circle.

The given circle D has a center at D.

The radius of the circle is given by the line segment CD

The diameter (or) the longest chord of the circle is given by the line segment EF

The ray AB passes touches the circle at point B, which is called the tangent of the circle.

Where the line GH passes through the circle and touches at two points. So, this line GH is said to be the secant of the circle.

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Disclaimer: The given question is incomplete(needs a diagram). Here is the required diagram attached.

Question: In circle D, which is a secant?

a) EF

b) DC

c) Line segment AB

d) Line GH

Answer:

ray ab

Step-by-step explanation:

Answer:

angle a = [tex]\boxed{154}^{\circ}[/tex]

Step-by-step explanation:

The angles in a triangle add up to 180°.

∴ ∠a + 13° + 13° = 180°

⇒ ∠a + 26° = 180°

⇒ ∠a = 180° - 26°

⇒ ∠a = 154°

Answer:

Angle a equals= 154°

Step-by-step explanation:

you have two angles which add up to 26°

remember that triangle always adds up to 180°

so you calculate 180-26 and you get 154

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.

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Answer:

The slope is -3.

Step-by-step explanation:

The slope is the Rise/Run between the two points.  The change in y for every change in x.  Take the two points and calculate the:

RISE = (-6 - 3) = -9

RUN = (8 - 5) = 3

Rise/Run, or slope, is = -9/3 or -3

I graphed a line with slope of -3 and then added 18 to force the line to intersect the two given points.

Answer:

11.8 units

Step-by-step explanation:

The circle equation is given as:

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2Where

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2r

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we have

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sides

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sidesr = 5.9

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sidesr = 5.9Multiply by 2

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sidesr = 5.9Multiply by 22r = 11.8

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sidesr = 5.9Multiply by 22r = 11.8Hence, the diameter of the circle is 11.8 units

Answer: 8,9.

Step-by-step explanation:

[tex](x-2)^2+(y+6)^2=20\\Circle \ equation\\\boxed {(x-a)^2+(y-b)^2=r^2}\\r^2=20\\r*r=\sqrt{20}*\sqrt{20}\\ r=\sqrt{20}\\ r=\sqrt{4*5}\\ r=2\sqrt{5} \\ D=2r\\D=2*2\sqrt{5}\\ D=4\sqrt{5}\\ D\approx8,9.[/tex]

At any value of x, Bruce would have always used 3 tiles less than Felicia.

Calculate to explain:

So, there is no solution.

Any value of x, Bruce would have always used 3 tiles less than Felicia.

Therefore, at any value of x, Bruce would have always used 3 tiles less than Felicia.

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The complete question is given below:
Is it possible for Bruce and Felicia to have used the same number of tiles? Use complete sentences to explain your reasoning.

Number of tiles Bruce used: 5x + 2

Number of tiles Felicia used: 5x + 5

Slope can be found from two points using the equation [tex]\frac{y_{2}- y_{1}}{x_{2}- x_{1}}[/tex].

Take any two points to substitute in. In this example, I'll use the first two points, (-4, 15), and (-2, 9). Put these into the equation and you'll get

[tex]\frac{(9-15)}{(-2-(-4))}[/tex]. Simplify further to get [tex]\frac{-6}{2}[/tex]. Divide this and you'll get the slope, -3!

hope this helps!

By the ratio test, the series converges for

[tex]\displaystyle \lim_{k\to\infty} \left|\frac{(x+2)^{k+1}}{\sqrt{k+1}} \cdots \frac{\sqrt k}{(x+2)^k}\right| = |x+2| \lim_{k\to\infty} \sqrt{\frac k{k+1}} = |x+2| < 1[/tex]

so that the radius of convergence is 1, and the interval of convergence is

|x + 2| < 1   ⇒   -1 < x + 2 < 1   ⇒   -3 < x < -1

The radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series. This can be obtained by using ratio test.  

Ratio test is the test that is used to find the convergence of the given power series.  

First aₙ is noted and then aₙ₊₁ is noted.

For  ∑ aₙ,  aₙ and aₙ₊₁ is noted.

[tex]\lim_{n \to \infty} |\frac{a_{n+1}}{a_{n} }|[/tex] = β

Here [tex]a_{k}[/tex] = [tex]\frac{(x+2)^{k}}{\sqrt{k} }[/tex]  and  [tex]a_{k+1}[/tex] = [tex]\frac{(x+2)^{k+1}}{\sqrt{k+1} }[/tex]

Now limit is taken,

[tex]\lim_{n \to \infty} |\frac{a_{n+1}}{a_{n} }|[/tex] = [tex]\lim_{n \to \infty} |\frac{(x+2)^{k+1} }{\sqrt{k+1} }/\frac{(x+2)^{k} }{\sqrt{k} }|[/tex]

= [tex]\lim_{n \to \infty} |\frac{(x+2)^{k+1} }{\sqrt{k+1} }\frac{\sqrt{k} }{(x+2)^{k}}|[/tex]

= [tex]\lim_{n \to \infty} |{(x+2) } }{\sqrt{\frac{k}{k+1} } }}|[/tex]

= [tex]|{x+2 }|\lim_{n \to \infty}}{\sqrt{\frac{k}{k+1} } }}[/tex]

= [tex]|{x+2 }|[/tex] < 1

- 1 < [tex]{x+2 }[/tex] < 1

- 1 - 2 < x < 1 - 2

- 3 < x < - 1

We get that,

interval of convergence = (-3, -1)

radius of convergence R = 1

Hence the radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series.

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Answer:

4

Step-by-step explanation:

18 + 18 = 36

So you got 36 cuz you times by two so you times the same for x

which is

2 x 2 = 4

Answer:

4

Step-by-step explanation:

We can set up a proportion.

18:2 = 36: x

If we multiply 18 by 2, and multiply 2 by 2, we can get 18:2 = 36:4, so x is equal to 4

Answer:

-41

Step-by-step explanation:

5(14-23)+8 ÷ 2

=5(-9)+4

=-45+4

=-41

The solution of the given expression 5(14-23)+8 ÷ 2 is -41.

Usually, simplification involves proceeding with the pending operations in the expression.

Example; 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form.

Simplification usually involves making the expression simple and easy to use later.

WE have given an expression as;

5(14-23)+8 ÷ 2

Solve the bracket then division;

=5(-9) + 4

=-45+4

=-41

Therefore, the solution of the given expression is -41.

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Answer:

B

Step-by-step explanation:

Answer:

x = 11

Step-by-step explanation:

A segment parallel to a side of a triangle cuts off proportional segments on the sides.

48/6 = (3x + 7)/5

8 = (3x + 7)/5

3x + 7 = 40

3x = 33

x = 11

The area of the region cleaned by the 7-in wiper blade with the angle subtended being 92⁰ as described in the task content is; 39.32in².

According to the task content, it follows that the wiper blade is 7-in long and subtends an angle of 92°.

Consequently, the area swept by the blade in discuss can be determined by the Area of sector formula and hence, is;

Area = (92/360) × (22/7) × 7².

Area = 39.32 in².

Ultimately, it follows from the solving steps above that the area of the region cleaned by the 7-in wiper blade with the angle subtended being, 92⁰ is; Area = 39.32 in².

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The solutions for the given system are (3,2), (3,-2), (-3,2) and (-3,-2).

The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

The solution of these equations represents the points at which the parabolas intersect.

2x²+8y²=50 (1)

x²  + y²= 13 (2)

Multiplying the equation 2 by -2, you have:

2x²+8y²=50 (1)

-2x² -2 y²= -26(2)

Sum both equations, you have: 6y²= 24. Now, you can find y.

6y²= 24

y²=4

y=±2

If y=2, from equation 2, you have

x²  + y²= 13

x²  + 2²= 13

x²  + 4= 13

x² =13-4

x² =9

x=±3

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Answer:

b

Step-by-step explanation:

Answer:

B. Monday

Step-by-step explanation:

Monday, Tuesday, Wednesday, Monday, Tuesday, Wednesday, Monday

hope it helps

[tex]\\ \tt{:}\dashrightarrow \ell=\dfrac{\Theta}{180}\pi r[/tex]

[tex]\\ \tt{:}\dashrightarrow \Theta=\dfrac{180\ell}{\pi r}[/tex]

[tex]\\ \tt{:}\dashrightarrow \Theta=\dfrac{180(13)}{5\pi}[/tex]

[tex]\\ \tt{:}\dashrightarrow \Theta=149^{\circ}[/tex]

[tex]\\ \tt{:}\dashrightarrow \Theta=149(60)[/tex]

[tex]\\ \tt{:}\dashrightarrow \Theta=8940'[/tex]

The angle subtended at the center of a circle of radius 5 cm by a length of 13 cm is 149.1°.

Given that,

The angle is subtended at the center of a circle of radius 5 cm by a length of 13 cm.

Here, Lenght of an arc = 13 cm

The radius of an arc = 5 cm

Used the formula for the angles (θ);

Length of an arc = 2πrθ / 360°

Substitute all the values, we get;

13 = 2 × 3.14 × 5 × θ / 360°

Solve for θ;

13 × 360° = 31.4 × θ

4,680° = 31.4 × θ

θ = 4,680°/31.4

θ = 149.1°

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Answer:

36

Step-by-step explanation:

don't know but let me check right quick

The area of a circle with a circumference that equals the perimeter of the square is 9.62 units².

What is circle ?

the side measurements of the square is 2.75 units.

the perimeter of this square, we must multiply 2.75 by 4 because a square has four equal side measurements.

2.75 × 4 = 11

Let's use the formula for finding radius given the circumference.

[tex]Radius = \frac{circumference}{2\pi }[/tex]

the circumference because our circumference is 11 units.

Radius = [tex]\frac{11}{2pi }[/tex]

put π = 3.14 * 2

radius =  11 / 2 * 3.14

radius = 11/  6.28 ⇒ 1.75

the area of the circle = [tex]\pi r^{2}[/tex]

area = 3.14 * (1.75)²  ⇒9.61325

Lastly, we round this number to the nearest hundredth as it is asked of us in the problem.

9.61325 = 9. 62

Therefore, the area of the circle is 9.62 units².

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The five number summary and interquartile range for the data-set is given by:

In this problem, we have that:

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Answer:

-2/3

Step-by-step explanation:

A rational number is a number that can be expressed as a fraction so when you add 2 fractions it’s a rational number