Find the sum of the infinite geometric series, if it exists.

4 - 1 + 1/4 - 1/16 + . . .

a. -1

b. 16/5

c. 3

d. does not exist

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.

Answer:

1 2/3 - 2/3

How to get it

5/3 simplifies into 1 and 2/3 and since you are doing addition and subtraction with x it cancels them out making it 1 and 2/3 minus 2/3, which would equal, 1, hope this helps!

Answer:

1 2/3 - 2/3

Step-by-step explanation:

You get this answer by canceling out the x's since they are the both the same with both the numbers: 5/3 and 2/3. So then you convert 5/3 into 1 2/3 and finish the rest of the equation which would end up being 1 2/3 - 2/3.

Answer: train A arrives first

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

The reason which allows him to write the statement could be reflexive property.

The reflexive property of congruence says that the considered geometric quantity, whether it be the angle, line segment, shape etc, is congruent to itself.

Michael writes, "Segment AC is congruent to segment AC."

The triangles in the figure are congruent by SSS Property.

This states that triangles are congruent if all the sides in one triangle are congruent to the corresponding sides of another.

The reason which allows him to write the statement could be reflexive property.

The three sides of triangle ABC is congruent to triangle CDA.

Learn more about triangles;

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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

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:

(x+1)^2+(y-7)^2=8

Step-by-step explanation:

You should try the next one and I can check work or tell you if it is right.  

The diameter length can be found be computing the distance that (-3,5) is to (1,9) which is sqrt(4^2+4^2)=sqrt(32).

The radius is half the diameter so it is sqrt(32)/2.

The center of the circle is the midpoint of a diameter. So compute the (Average of x, average of y)=(-1,7)

So plug into (x-h)^2+(y-k)^2=r^2 we get

(x+1)^2+(y-7)^2=32/4

simplifying gives

(x+1)^2+(y-7)^2=8

(I had to type this twice; my cat jump on my keyboard)

ANSWER

[tex]{(x + 1)}^{2} + {(y - 7)}^{2} = 8[/tex]

EXPLANATION

The given circle has P(-3,5) and Q(1,9) as its diameter.

The center can be obtained using the midpoint rule.

[tex]( \frac{ - 3 + 1}{2} , \frac{5 + 9}{2} )[/tex]

[tex]( - 1,7)[/tex]

The radius is obtained using the distance formula,

[tex]r = \sqrt{( - 1 - - 3 )^{2} + {(7 - 5)}^{2} } [/tex]

[tex]r = \sqrt{( 2)^{2} + {(2)}^{2} } = \sqrt{8} [/tex]

The equation is given by

[tex] {(x - h)}^{2} + {(y - h)}^{2} = {r}^{2} [/tex]

We substitute the center and radius to get:

[tex]{(x - - 1)}^{2} + {(y - 7)}^{2} = { (\sqrt{8}) }^{2} [/tex]

[tex]{(x + 1)}^{2} + {(y - 7)}^{2} = 8[/tex]

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!

First one has a general upward trend that will be a non-zero correlation

Second one shows a zero average slope, no upward or downward tendency;  NO CORRELATION

Third one has no slope, so NO CORRELATION

Fourth one, pronounced downward slope, strong negative correlation.

Fifth one, hard to tell but looks like no upward or downward average slope, so NO CORRELATION

Answer: B C E

Step-by-step explanation:

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:

x = 30t cos 20 or  x = 28.19t.

y = 30t sin 20 - 4.9t^2 + 2 or y =  -4.9t^2 + 10.26t + 2.

Step-by-step explanation:

The horizontal component of the velocity = 30 cos 20  m/s so the distance at time t seconds = 30t cos 20.

The vertical component  is obtained from the equation of motion

s = ut - 1/2* 9.8t^2 + 2

u = 30 sin 20

Vertical component  =  30t sin 20 - 4.9t^2 + 2.

Answer:

x(t) = 30t cos 20 or we can get x = 28.19t. y = 30t sin 20 – 4.9t^2 +2 or y= -4.9t^2 + 10.26t +2

Step-by-step explanation:

The path the rock took can be represented by the following equation x(t) = v0 * cos(θ) * t y (t) = v0 * sin (θ) * t – 0.5 * g * t^2 + h. v0 is the initial velocity (30 m/s), θ is the angle of launch (20 degrees), g is the acceleration due to gravity (9.8 m/s^2) , h is the initial height (2m ) , and t is time. When we switch the values, we get x(t) = 30t cos 20 or we can get x = 28.19t. y = 30t sin 20 – 4.9t^2 +2 or y= -4.9t^2 + 10.26t +2

First, lets focus on finding out the other two legs of the large triangle.

To do this, we use Pythagoras' Theorem.

So the left leg = √(16² + x²)

So the right leg = √(9² + x²)

Notice, the larger triangle is also a right angled triangle, that means the sum of the two legs squared = hypotenuse squared.

Since we have just worked out the two legs, we can substitute them into:

a² + b² = c²

(√(16² + x²) )²  +  (√(9² + x²) )² = (16 + 9)²

Notice that the power of two cancels out with the squareroots so we get:

(16² + x² ) + (9² + x² ) = (25)²     (simplify and collect like terms)

256 + x² + 81 + x² = 625    

337 + 2x² = 625     (subtract 337 from both sides to isolate the x )

2x² = 288                    (divide both sides by 2)

x² = 144                        (square root both sides)

x = √144

x = 12

_______________________________________

Answer:

x = 12

_______________________________________

Note: if you have any questions, please ask and I will be more than happy to help and give further explanations!

I can confirm that the other person is right, the answer is 12.

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:

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:

  (-7, 5)

Step-by-step explanation:

Comparing the equation to the standard form equation of a circle of radius r centered at (h, k):

  (x -h)² +(y -k)² = r²

you see that h=-7 and k=5.

The center of the circle has coordinates (-7, 5).

_____

Like a lot of math, it's about pattern matching.

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

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.

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%

Final answer:

To find the height of the 7th bounce of a bouncy ball, where each bounce is 64% of the height of the previous one, use the geometric sequence formula. For the first bounce's height of 5.5 feet and a common ratio of 0.64, calculate the 6th power of 0.64, then multiply by 5.5 and round to the nearest tenth.

Explanation:

The student is asking about finding the height of the seventh bounce of a bouncy ball, which follows a geometric sequence in which each term is 64% of the previous one. To find the height of the 7th bounce, we will use the formula for the nth term of a geometric sequence, which is an = a1 × r(n-1), where a1 is the first term, r is the common ratio, and n is the term number.

The first term a1 is the height of the first bounce, which is 5.5 feet, and the common ratio r is 0.64 (since 64% is 0.64 in decimal form). Using this information, the height of the 7th bounce is calculated as follows:

Calculate the 6th power of the common ratio: 0.646

Multiply this value by the height of the first bounce: 5.5 × 0.646

Round the result to the nearest tenth

Calculating the exact value and rounding to the nearest tenth gives us the height of the seventh bounce.

ANSWER

[tex]{7x}^{3} - 2 {x}^{2} - 5[/tex]

EXPLANATION

A simplified polynomial is said to be in standard form if it is in descending powers of x.

The polynomial expression is

[tex](6 {x}^{3} + 3 {x}^{2} - 2) + ( {x}^{3} - 5 {x}^{2} - 3)[/tex]

We group similar terms to get;

[tex]6 {x}^{3} + {x}^{3} + 3 {x}^{2} - 5 {x}^{2} - 3 - 2[/tex]

Combine similar terms

[tex]{7x}^{3} - 2 {x}^{2} - 5[/tex]

The polynomial above is in standard form.

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.

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Answer:

127% markup

Step-by-step explanation:

So we need to plug in 31 into each

R(31)=160(31)=4960

C(31)=71(31)-.02(31)^2=2181.78

So the selling price is 4960 for 31 stereos.

The total cost for making 31 stereos is 2181.78.

So that is a markup for sure.

So you find the difference and then divide it by the total cost.

(4960-2181.78)/2181.78=1.27 approximately

so there is 127% markup

Answer:

914 and 916

Step-by-step explanation:

let the first integer be x

The next largest consecutive even integer is hence x+2

given that the 2 integers add up to 1830,

x + (x+2) = 1830

2x + 2 = 1830

2x = 1828

x = 914

Hence the first number is 914

the second number is 914 + 2 = 916

Check Answer:

914 + 916 = 1830 (verified)

[tex]2n+2n+2=1830\\4n=1828\\n=457\\\\2n=914\\2n+2=916[/tex]

914 and 916

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:

  {±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24}

Step-by-step explanation:

Since the leading coefficient is 1, any rational zeros will be divisors of -24.

_____

Comment on rational zeros

If the leading coefficient is not one, then rational zeros will be the ratio of a divisor of 24 to a divisor of the leading coefficient.

Check the picture below.

Answer:

180.07 rev / min

Step-by-step explanation:

Diameter (D) of each wheel =28 inches

Circumference (C) =  π x 28 = 28π inches

Conversions:

1 mile = 63,360 inches

1 hour = 60 min

Hence 15 miles / hour

= (15)(63,360) inches / hour

= (15)(63,360) / 60  inches / min

= 15,840 inches per min

Number of revolutions per min = Number of inches per min ÷ circumference in inches

=15,840 inches/min ÷ 28π inches

= 180.07 revolutions per min

To find the number of revolutions per minute a bicycle's wheels make, convert the speed from miles per hour to inches per minute, calculate the wheel's circumference, and divide the traveling speed in inches per minute by the circumference. A bicycle with 28-inch diameter wheels going 15 miles per hour makes approximately 180 revolutions per minute.

To determine how many revolutions per minute the wheels of a bicycle with a 28-inch diameter are turning when traveling at 15 miles per hour, we first need to convert the speed to inches per minute. There are 5280 feet in a mile and 12 inches in a foot, so first we calculate:

15 miles/hour * 5280 feet/mile * 12 inches/foot = 950400 inches/hour

Since there are 60 minutes in an hour, we then convert to inches per minute:

950400 inches/hour / 60 minutes/hour = 15840 inches/minute

Next, we need to find out the circumference of the bicycle wheel, as this will tell us how far the bike travels with each revolution. The formula for the circumference (C) of a circle using the diameter (d) is:

C = π * d

For a wheel with a diameter of 28 inches:

C = π * 28 inches ≈ 87.96 inches

Now, to find the number of revolutions per minute, we divide the traveling speed in inches per minute by the circumference:

15840 inches/minute / 87.96 inches/revolution ≈ 180 revolutions per minute (rounded to the nearest whole number).

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