Use the formula to evaluate the infinite series. Round to the nearest hundredth if necessary.

Answer:

A. [tex]\text{sin}^{-1}(\frac{2}{3})\approx 42^{\circ}[/tex]

B. [tex]\text{tan}^{-1}(4)\approx 76^{\circ}[/tex]

C. [tex]\text{cos}^{-1}(0.1)\approx 84^{\circ}[/tex]

Step-by-step explanation:

We have been given inverse trigonometric functions. We are asked to find the value of each function.

A. [tex]\text{sin}^{-1}(\frac{2}{3})[/tex]

We will use inverse sin to solve our given equation as:

[tex]\text{sin}^{-1}(\frac{2}{3})=41.81^{\circ}[/tex]

Round to nearest degree:

[tex]\text{sin}^{-1}(\frac{2}{3})\approx 42^{\circ}[/tex]

B. [tex]\text{tan}^{-1}(4)[/tex]

We will use inverse tann to solve our given equation as:

[tex]\text{tan}^{-1}(4)=75.963756^{\circ}[/tex]

Round to nearest degree:

[tex]\text{tan}^{-1}(4)\approx 76^{\circ}[/tex]

C. [tex]\text{cos}^{-1}(0.1)[/tex]

We will use inverse cosine to solve our given equation as:

[tex]\text{cos}^{-1}(0.1)=84.2608295^{\circ}[/tex]

Round to nearest degree:

[tex]\text{cos}^{-1}(0.1)\approx 84^{\circ}[/tex]

To solve the problem we must know about the concept of trigonometry.

The value of  [tex]\rm sin^{-1} (2/3), tan^{-1}(4), and\ cos^{-1}(0.1)[/tex] is 42, 76, and 85 degrees respectively.

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

Given

[tex]\rm sin^{-1} (2/3), tan^{-1}(4), and\ cos^{-1}(0.1)[/tex] are the trigonometric function.

To find

The value of the [tex]\rm sin^{-1} (2/3), tan^{-1}(4), and\ cos^{-1}(0.1)[/tex].

[tex]\rm 1. \ \ sin^{-1} (2/3) = 41.81^o = 42^o\\\\ 2. \ \ \ \ \ tan^{-1}(4) = 75.96^o = 76^o \\\\3. \ \ cos{-1}(0.1)= 84.26^o = 85^o[/tex]

The value of  [tex]\rm sin^{-1} (2/3), tan^{-1}(4), and\ cos^{-1}(0.1)[/tex] is 42, 76, and 85 degrees respectively.

More about the trigonometry link is given below.

https://brainly.com/question/22698523

Which display can be used to find how many days had a high temperature above 15 deg?

Answer: A  The dot plot

In the dot plot, you can see each temperature since each temperature is represented by 1 dot.

Which display makes it easier to see that the first quartile is 9 deg?

Answer: B  The box plot

The box plot shows where the upper and lower quartiles are.

Answer:

First question: A . The dot plot

Second question: B . The box plot

Step-by-step explanation:

In the dot plot it is easy to count 7 values above 15.

In the box plot are shown (in this order): the minimum value; the lower quartile, called Q1; the median, the upper quartile, also called Q3; and the maximum value. As can be seen in the graph, the the first quartile is 9 °C

Answer:

255

Step-by-step explanation:

(2+2+3+10) × (8+9+-9+7)

First, remove the brackets:

2 + 2 + 3 + 10 × 8 + 9 + -9 + 7

Now calculate like so:

2 + 2 + 3 + 10 = 17

8 + 9 + -9 + 7 = 15

(17) × (15) = 17 × 15 = 255

PLEASE DO MARK ME AS BRAINLIEST UWU

Answer:

Your answer for this question is 255.

Step-by-step explanation:

To solve this problem, we must remember how to use PEMDAS.  This tells us that we must simplify what is in parentheses first, exponents next, then multiplication and division, and finally addition and subtraction.  In this case, this means that we must first perform the operations inside of the parentheses before the multiplication of the two groups of parentheses.

If we simplify within both groups of parentheses, we get:

(2+2+3+10) * (8+9+-9+7)

= (17) * (15)

We get the above simplification by performing the addition of all of the constants in the first group of parentheses and performing the addition and subtraction in the second group (notice that the +9 and -9 cancel each other out).

Now, we must simply multiply together our final two values to obtain our final answer.

17 * 15 = 255

Therefore, your answer is 255.

Hope this helps!

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount \underline{for the first 3 years}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$20000\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases}[/tex]

[tex]\bf A=20000\left(1+\frac{0.06}{1}\right)^{1\cdot 3}\implies A=20000(1.06)^3\implies \boxed{A=2382.032} \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \textit{Compound Interest Earned Amount \underline{for the next 4 years}}[/tex]

[tex]\bf A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2382.032\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]\bf A=2382.032\left(1+\frac{0.08}{1}\right)^{1\cdot 4}\implies A=2382.032(1.08)^4\implies \boxed{A\approx 3240.73} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{amount for this period}}{2382.032+3240.73}\implies 5622.762[/tex]

Answer:

8

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Answer: train A arrives first

Step-by-step explanation:

Answer:

60°

Step-by-step explanation:

Here we are given that the number of convertibles cars. Total number of cars owned by the dealers is 90. We have to draw the pie graph for above ratio. The pie chart is a circular statistical graph , where the different portion in form of sectors on the circle showing the amount of different entities.

The angle covered by an entity is in the same proportion as its number is in ration to the total number of all the entities.

Hence

[tex]\frac{15}{90}=\frac{\theta}{360}\\\\\theta=\frac{15*360}{90}\\\theta=\frac{15*4}{1}\\\theta=60\\[/tex]

Hence we will represent 60 degrees in order to represent 15 cars in our chart.

To represent convertibles on the pie graph, calculate the proportion of convertibles sold to the total number of cars sold (15/90) and multiply by the total degrees in a circle (360). Convertibles should be represented by a 60-degree slice on the pie graph.

The question is asking how to calculate the degree measure for the convertibles slice in a pie chart based on the total sales in a month. We know that a pie chart represents 100% of a data set, with the entire chart being a 360-degree circle. To find the degree measure for the convertibles, we would perform a proportion calculation based on the number of convertibles sold (15) out of the total number of cars sold (90). The calculation is as follows:

Proportion of convertibles to total sales = (Number of convertibles sold / Total cars sold) = 15 / 90

Now, multiply this proportion by the total degrees in a circle to get the degree measure for convertibles:

Degree measure for convertibles = Proportion of convertibles imes Total degrees in a circle = (15 / 90) * 360 = 1/6 * 360 = 60 degrees

Therefore, the convertibles should be represented by a 60-degree slice on the Pie Graph.

Answer: I think it is A.

Step-by-step explanation:

Answer:

The real zero is between 1 and 2.

Step-by-step explanation:

The given function is:

[tex]f(x)=x^3-2[/tex]

To find the zeros of this function, we set f(x)=0.

[tex]\implies x^3-2=0[/tex]

Add 2 to both sides to obtain:

[tex]\implies x^3=2[/tex]

Take the cube root of both sides

[tex]\implies x=\sqrt[3]{2}[/tex]

[tex]\implies x=1.26[/tex]

Therefore the real zero is between 1 and 2.

9680 yards. Miles biked a total of 9680 yards.

The key to solve this problem is coverting the Mixed Fraction to Improper Fraction, and make the conversion from miles to yards.

Convert the Mixed Fraction 5 1/2 to an Improper Fraction:

- Multiply the whole number 5 by the denominator

5 x 2 = 10

- Add the result to the numerator

1 + 10 = 11

- Write the Improper Fraction with the same denominator of the Mixed Fraction, and the numerator with the result above

5  1/2 miles ---------->  11/2 miles

To convert miles to yard with mile = 1760 yards:

11/2 * 1760 yards = 19360 yards/2 = 9680 yards

Final answer:

Miles biked for a total of 5 1/2 miles. By converting miles to yards using the fact that there are 1,760 yards in one mile, Miles biked a total of 9,680 yards.

Explanation:

The student has asked how many yards Miles biked if he rode a total of 5 1/2 miles. To find the answer, we need to convert miles to yards. Since there are 1,760 yards in a mile, we can multiply the number of miles by this conversion factor.

First, let's represent 5 1/2 miles as an improper fraction: 5 1/2 = 11/2 miles. Next, we multiply 11/2 by 1,760:

11/2 miles
= 11/2
* 1760 yards/mile
= 11*880 yards
= 9,680 yards.

Therefore, Miles biked a total of 9,680 yards.

Temperature can relate to how cold the ice cream cone is.

The ice cream cone(s) can relate to all the buildings in the city.

Step-by-step explanation:

Answer:

b.

Step-by-step explanation:

We have to look at sign changes in f(x) to determine the possible positive real roots.

[tex]f(x)=-3x^4-5x^3-x^2-8x+4[/tex]

There is only one sign change here, between the -8x and the +4.  So that means there is only 1 possible real positive root.

Now we have to look at sign changes in f(-x) to determine the possible negative real roots.

[tex]f(-x)=-3x^4+5x^3-x^2+8x+4[/tex]

There are 3 sign changes here.  That means there are either 3 negative roots or 3-2 = 1 negative root.  So we have:

1 positive

3 or 1 negative

We need to pair them up now with all the possible combinations.

If we have 1 positive and 1 negative, we have to have 2 imaginary

If we have 1 positive and 3 negative, we have to have 0 imaginary

Keep in mind that the total number or roots--positive, negative, imaginary--have to add up to equal the degree of the polynomial.  This is a 4th degree polynomial, so we will have 4 roots.

1. The first step to solving this problem is to find the values of x and y. This can be done in a multitude of different ways, however I will go with the method of substitution.

Thus, the first thing we must do is write out both equations and rearrange one of them so that either x or y is the subject of the equation. Looking at the two equations, I can see that in the second equation this would be easier, and that we could also simplify the first equation a little further. Thus:

a) Collecting like terms to simplify equation 1:

4x + 3y = 14 - y

4x + 4y = 14 (Add y to both sides)

b) Rearranging equation 2 to make x the subject:

x - 5y = 2

x = 2 + 5y (Add 5y to both sides)

Now, we can substitute x = 2 + 5y into the first equation:

4x + 4y = 14

if x = 2 + 5y:

4(2 + 5y) + 4y = 14

8 + 20y + 4y = 14 (Expand 4(2 + 5y))

8 + 24y = 14 (Add 20y and 4y)

24y = 6 (Subtract 8 from both sides)

y = 1/4 (Divide both sides by 24)

Now that we know that y = 1/4, we can substitute this back into x = 2 + 5y:

x = 2 + 5y

if y = 1/4: x = 2 + 5(1/4)

x = 2 + 5/4

x = 13/4

2. So now we know that x = 13/4 and y = 1/4. Given these values, we can now solve x - y as such:

x - y = 13/4 - 1/4

= 12/4

= 3

Thus, the value of x - y is 3 (answer C).

Answer:

2xy∧²√13xy

Step-by-step explanation:

Answer:

The solution is x = 6 and y =1

Explanation :

In the substitution method we solve a system of equation by substituting the value of one variable from an equation to the another equation,

Given system of equations,

x-y = 5  ⇒ y = x - 5.......(1)

2x+y = 13.......(2)

Substitute the value of y from equation (1) to equation (2),

2x+x-5=13

3x-5=13

3x=18

x = 6

Again from equation (1),

y = 6 - 5 = 1

Answer:

[tex]82=3x+22[/tex]

The temperature in Bangor is [tex]x=20\°[/tex]

Step-by-step explanation:

Let

x -----> the temperature in Bangor

y ----> the temperature in Miami

we know that

The linear equation that represent this situation is

[tex]y=3x+22[/tex] ----> equation A

[tex]y=82[/tex] ----> equation B

substitute equation B in equation A and solve for x

[tex]82=3x+22[/tex]

[tex]3x=82-22[/tex]

[tex]3x=60[/tex]

[tex]x=20\°[/tex]

Answer:

3x + 22 = 82

Step-by-step explanation:

I am positive its correct

Answer:

x² + 8x + 16

Step-by-step explanation:

You can draft the Pascal's Triangle as below;

                                             Exponent

                  1-----------------------0

               1     1  -------------------1

             1   2    1 ------------------2

            1  3   3   1 -----------------3

According to the question, we use values for exponent 2 because (a+b)²

Given  (x+4)²...................................expand

x² × 4⁰ + x¹ × 4¹+ x⁰ × 4²

x² × 1 + x × 4 + 1 × 16

x² + 4x + 16---------------------------------introduce values in exponential 2 of the table which are 1  2  1

x² × 1 + 2 × 4x + 16 × 1

⇒ x² + 8x + 16

Check the picture below.

Answer:

1/2 is the answer (actually, it's ±1/2)

Step-by-step explanation:

The identity you need here is for a half angle of tangent.  That identity is as follows:

[tex]tan(\frac{\theta }{2})=[/tex]±[tex]\sqrt{\frac{1-cos\theta }{1+cos\theta } }[/tex]

If we need the cos of that angle, we need to find the missing hypotenuse.  Applying Pythagorean's Theorem to that right triangle, we get that the hypotenuse is 5.  The cos of the angle is 3/5.  Filling in the formula, using only the principle root since you have not allowed for the negative in the choices you gave:

[tex]tan(\frac{\theta }{2})=\sqrt{\frac{1-\frac{3}{5} }{1+\frac{3}{5} } }[/tex]

Turning each one of those 1's into 5/5 we combine the fractions to simplify to:

[tex]tan(\frac{\theta }{2})=\sqrt{\frac{\frac{2}{5} }{\frac{8}{5} } }[/tex]

Bringing up the lower fraction and flipping to multiply gives us:

[tex]tan(\frac{\theta }{2})=\sqrt{\frac{2}{5}*\frac{5}{8}  }[/tex]

Canceling out the 5's and reducing the remaining fraction gives us

[tex]tan(\frac{\theta }{2})=\sqrt{\frac{1}{4} }[/tex]

and since the square root of 4 is 2, we end with a solution of 1/2

Answer: 2l+2w

Step-by-step explanation:

Answer:21 plus 2w

Step-by-step explanation:

Answer:

108 miles

Step-by-step explanation:

you multiply the 18 miles he can go on one mile of gas by 6, and you reach 108 miles

Answer:

Vertical stretch by a factor of 5.8 , reflection across x-axis ⇒ answer B

Step-by-step explanation:

* Lets revise the vertical and horizontal stretch with reflection

- A vertical stretching is the stretching of the graph away from the

 x-axis

- If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched

 by multiplying each of its y-coordinates by k.

- If k should be negative, the vertical stretch is followed by a reflection

 across the x-axis  

- A horizontal stretching is the stretching of the graph away from

 the y-axis

- If 0 < k < 1 (a fraction), the graph of y = f(k•x) is f(x) horizontally

 stretched by dividing each of its x-coordinates by k.

- If k should be negative, the horizontal stretch or shrink is followed

 by a reflection in the y-axis

* Lets solve the problem

∵ G(x) = sin x

∵ F(x) = -5.8 sin x

∴ F(x) = -5.8 G(x)

- From the rule above

∴ G(x) is stretched vertically by scale factor -5.8

∵ The scale factor is negative

∴ The vertical stretch is followed by a reflection across the x-axis  

* The transformation is:

  Vertical stretch by a factor of 5.8 , reflection across x-axis

To obtain the graph of f(x) = -5.8sin x from g(x) = sin x, a vertical stretch by a factor of 5.8 and a reflection across the x-axis are required.

To transform the graph of the function g(x) = sin x into the graph of f(x) = -5.8sin x, two main transformations are required:

Option B (vertical stretch by a factor of 5.8 and reflection across the x-axis) correctly describes the required transformations to obtain the graph of f(x) from the graph of g(x).

Answer:

x=-1

Step-by-step explanation:

General equation of line is y=mx+n where m is slope. So, if we use point (-4, 8) and slope in equation we have 8= 2/3.(-4)+n

Then we have n=8+8/3, that is n=32/3

Therefore equation of our line is y=2/3.x + 32/3

For the point (x,10) in equation 10=2/3.x + 32/3

Then we have 2/3.x = - 2/3 then x= -1

Answer:

x = - 1

Step-by-step explanation:

Using the slope formula to find the slope m

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (x , 10) and (x₂, y₂ ) = (- 4, 8)

m = [tex]\frac{8-10}{-4-x}[/tex] = [tex]\frac{2}{3}[/tex], that is

[tex]\frac{-2}{-4-x}[/tex] = [tex]\frac{2}{3}[/tex] ( cross- multiply )

2(- 4 - x) = - 6 ( divide both sides by 2 )

- 4 - x = - 3 ( add 4 to both sides )

- x = 1 ( multiply both sides by - 1 )

x = - 1

Answer:

  (-2, 2)

Step-by-step explanation:

You can graph the equations and points and see which points fall into the doubly-shaded area. The only one that does is (-2, 2).

___

You can also evaluate the inequalities at the given points to see which might work. The inequality y > x is the simplest to evaluate, and it immediately eliminates the last two choices:

  -3 > -1 . . . not true

  -1 > 0 . . . not true

So, we can check the first two choices in the first inequality:

  -(-3) +1 > 5 . . . not true

  -(-2) +1 > 2 . . . TRUE

The ordered pair (-2, 2) makes both inequalities true.

Answer:

2nd Option is correct.

Step-by-step explanation:

Given Inequalities are,

y < x + 1  .....................(1)

y > x .....................(2)

To find: Ordered pair which makes he inequalities true.

Pair 1:

x = -3 , y = 5

Inequality (1),

LHS = 5

RHS = -(-3) + 1 = 4

⇒ LHS > RHS

Thus, this pair does not satisfy the pair of inequalities.

Pair 2:

x = -2 , y = 2

Inequality (1),

LHS = 2

RHS = -(-2) + 1 = 3

⇒ LHS < RHS

Inequality (2),

LHS = 2

RHS = -2

⇒ LHS > RHS

Thus, this pair satisfies the pair of inequalities.

Pair 3:

x = -1 , y = -3

Inequality (1),

LHS = -3

RHS = -(-1) + 1 = 0

⇒ LHS < RHS

Inequality (2),

LHS = -3

RHS = -1

⇒ LHS < RHS

Thus, this pair does not satisfy the pair of inequalities.

Pair 4:

x = 0 , y = -1

Inequality (1),

LHS = -1

RHS = -(0) + 1 = 1

⇒ LHS < RHS

Inequality (2),

LHS = -1

RHS = 0

⇒ LHS < RHS

Thus, this pair does not satisfy the pair of inequalities.

Therefore, 2nd Option is correct.

Answer:

the first one is 350 inches (350 in) and the second on is 350 square inches (350 in2)

Step-by-step explanation:

Answer:

y=(3/2)x+4

Step-by-step explanation:

step 1

Find the slope m

we have

the points (4, 10) and (2, 7)

The slope is equal to

m=(7-10)/(2-4)

m=3/2

step 2

Find the equation into slope point form

y-y1=m(x-x1)

we have

m=3/2

(x1,y1)=(2,7)

substitute

y-7=(3/2)(x-2)

y=(3/2)x-3+7

y=(3/2)x+4

Answer:

B.

Step-by-step explanation:

The function is positive when it is above the x-axis

The following x values are where the function has positive y coordinates:

(-2,0)

(4,inf)

The function is negative when it is below the x-axis

The following x values are where the function has negative y coordinates:

(-inf,-2)

(0,4)

So you should see all of these intervals listed in choice B

Answer:

B

Step-by-step explanation:

Answer:

(m-5) (n-4)

Step-by-step explanation:

mn - 4m - 5n + 20

We will factor by grouping

mn -5n  -4m +20

Factor an n out of the first 2 terms and a -4 out of the last 2 terms

n (m-5) -4(m-5)

Now factor out a m-5

(m-5) (n-4)

The average for the 5 tests is a 74.

The total of the 5 grades needs to equal 5 x 74 = 370

The total of the 4 graded tests is : 76 +80 + 69 + 71 = 296

Subtract that from the first total: 370 - 296 = 74

The grade needs to be a 74

Answer:

57%

Step-by-step explanation:

We are given the results of survey of one thousand families to determine the distribution of families by their size.

We are to find the probability (to the near percent) that a given family has 3, 4 or 5 people.

Frequency of families with 3, 4 or 5 people = 200 + 245 + 125 = 570

Total frequency = 1000

P (families with 3, 4 or 5 people) = (570 / 1000) × 100 = 57%