The sports car travels along a straight road such
that its acceleration is described by the graph. Construct the
v-s graph for the same interval and specify the velocity of
the car when s = 10 m and s = 15 m.

Answer:

The volume is

Step-by-step explanation:

Volume of a sphere is given by

[tex]V = \frac{4}{3} \pi {r}^{ 3} [/tex]

where r is the radius

π = 3.14

From the question we were given the diameter and

radius = diameter/ 2

diameter = 2 feet

radius = 2/2 = 1 feet

So the volume of the sphere is

[tex]V = \frac{4}{3} (3.14)(1) ^{3} [/tex]

[tex] = \frac{4}{3} \times 3.14[/tex]

V = 4.186

We have the final answer as

V = 4 ft³ to the nearest hundredth

Hope this helps you

Answer:

B

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

-1 1/6 ÷ (-4 2/3)

Change to improper fractions

- ( 6*1 +1)/6 ÷ -(3*4 +2)/3

-7/6÷ -14/3

Copy dot flip

-7/6 * -3/14

Rewriting

-7/14 * -3/6

-1/2 * -1/2

1/4

Answer:

Step-by-step explanation:

18/60-12/60= 4 miles

just my guess

Answer:

SOLUTION SET ={a/a≥20}

Step-by-step explanation:

[tex]\frac{2a}{5}-2\geq\frac{a}{4}+1[/tex]

[tex]adding 2 on both sides[/tex]

[tex]\frac{2a}{5}-2+2\geq \frac{a}{4}+1+2[/tex]

[tex]now subtracting \frac{a}{4} on both sides[/tex]

[tex]\frac{2a}{5}-\frac{a}{4}\geq 3[/tex]

[tex]takig LCM as 20\\\frac{8a}{20}-\frac{5a}{20}\geq 3[/tex]

[tex]\frac{3a}{20}\geq 3[/tex]

[tex]by cross-multiplication[/tex]

3a≥3×20

3a≥60

dividing 3 on both sides

3a/3≥60/3

a≥20

SOLUTION SET ={a/a≥20} is the answer

i hope this will help you :)

Answer:

A

Step-by-step explanation:

The blue graph, g(x), is shifted down 8 units.

So the answer is f(x)-8 which is A

Answer:  C. g(x) = eˣ⁻¹ - 3

Step-by-step explanation:

g(x) is a vertical shift 8 units down (-8) from f(x)

f(x) = eˣ⁻¹ + 5

g(x) = (eˣ⁻¹ + 5) - 8

      = eˣ⁻¹ - 3

Answer:

C. The interquartile range is 55

Step-by-step explanation:

When you want to find the interquartile range you look at the box plot to see that it is everything from the upper interquartile range to the lower interquartile range is the interquartile range. So from 40 to 65. So there for the answer C. is incorrect.  

Answer:

A.

Step-by-step explanation:

Answer:

[tex]\sqrt[5]{x^7}[/tex]

or (x ^ 1/5) ^7

or ([tex]\sqrt[5]{x}[/tex])^7

Step-by-step explanation:

x ^ 1.4

Rewriting the decimal as an improper fraction

x ^ 14/10

x ^ 7/5

The top is the power and the bottom is the root

[tex]\sqrt[5]{x^7}[/tex]

or (x ^ 1/5) ^7

or ([tex]\sqrt[5]{x}[/tex])^7

Answer:

For two polygons to be similar, both of the following must be true: Corresponding angles are congruent. Corresponding sides are proportional.

Step-by-step explanation:

HOPE THIS HELPS AND PLSSS MARK AS BRAINLIEST]

THNXX :)

What must be true for two polygons to be similar?

Similar polygons: For two polygons to be similar, both of the following must be true: Corresponding angles are congruent. Corresponding sides are proportional.

Answer:512

Step-by-step explanation:

Let's solve your equation step-by-step.

3√x=3√512

3√x=67.882251

Step 1: Divide both sides by 3.

3√x

3

=

67.882251

3

√x=22.627417

Step 2: Solve Square Root.

√x=22.627417

x=22.6274172(Square both sides)

x=512

Check answers. (Plug them in to make sure they work.)

x=512(Works in original equation)

Answer:

x=512

Answer:

Hey there!

6x+6=7x-6

6=x-6

12=x

x=12

Hope this helps :)

Assuming both vertical lines are parallel and assuming I'm supposed to find all the unmarked angles...

Angle C:

Supplementary Angles.

x+36=180

180-36=x

x=144

Angle B:

Corresponding Angles.

Angle B ≅ Angle C

144

Angle A:

360 degrees in a quadrilateral

36+144+81+x=360

261+x=360

x = 99

Hope it helps <3

Answer:

D. all of the above

Step-by-step explanation:

All the letters from the options have a line of symmetry.

Hey there! I'm happy to help!

The surface area is just the area of this net. If you fold up the net it will give you a hollow 3-d shape.

On this net we have three congruent rectangles and two congruent triangles.

We see that each rectangle has a short side of 10 cm and a long side of 15 cm. The area of a rectangle is found by multiplying the long side by the short side.

15×10=150

So, each rectangle has an area of 150 cm².

Now, for the triangles. To find the area of a triangle you multiply the base by the height and then divide by two.

Each triangle has a base of 10 cm and a height 8 2/3 cm.

We multiply them.

10×8 2/3=86 2/3

And we divide by two.

86 2/3 ÷ 2 = 43 1/3

So, each triangle has an area of 43 1/3.  

Now, we add together the areas of our three rectangles and two triangles.

150+150+150+43 1/3+43 1/3=536 2/3

Therefore, the surface area is 536 2/3 cm².

Have a wonderful day!

Answer:

k = -18.

But See below.

Step-by-step explanation:

f(x) =  x^4 - 3x^3 - 6x^2 + kx - 16

If  x^2 + 3x + 2 is a factor then so is (x + 1) and (x + 2) as

x^2 + 3x + 2 = (x + 1)(x + 2)

So by the Factor Theorem f(-1) = 0:

f(-1) = (-1)^4 - 3(-1)^3 - 6(-1)^2 - 1k - 16 = 0

1 + 3 - 6 - k - 16 = 0

-18 - k = 0

k =  -18.

Checking:

f(-2) =   (-2)^4 - 3(-2)^3 - 6(-2)^2 - 18(-2) - 16

=  16 + 24 - 24 + 36 - 16 = 36   (NOT 0).

Answer:

k=11

explaination:

The average cost of weekly groceries is $124.50."  The statistical measurement are they most likely claiming is Mean

The correct option is (B)

The arithmetic mean of a given data is the sum of all observations divided by the number of observations.

For example, a cricketer's scores in five ODI matches are as follows: 12, 34, 45, 50, 24. To find his average score in a match, we calculate the arithmetic mean of data using the mean formula:

Mean = Sum of all observations/Number of observations

The value of the middlemost observation, obtained after arranging the data in ascending or descending order, is called the median of the data.

For example, consider the data: 4, 4, 6, 3, 2. Let's arrange this data in ascending order: 2, 3, 4, 4, 6. There are 5 observations. Thus, median = middle value i.e. 4.

The value which appears most often in the given data i.e. the observation with the highest frequency is called a mode of data.

As per the situation we have given average cost of groceries.

The mean is also the average sum of data divided by total number of data.

Hence, The statistical measurement is Mean.

Learn more about mean here:

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======================================================

Work Shown:

f ''' (x) = cos(x) .... third derivative

f '' (x) = sin(x)+C ... integrate both sides to get second derivative. Don't forget the +C at the end

We are given f '' (0) = 9, so we'll make use of this to find C

f '' (x) = sin(x)+C

f '' (0) = sin(0)+C

9 = sin(0) + C

9 = 0 + C

9 = C

C = 9

Therefore, f '' (x) = sin(x)+C turns into f '' (x) = sin(x)+9

------------

Integrate both sides of the second derivative to get the first derivative function

f '' (x) = sin(x)+9

f ' (x) = -cos(x)+9x+D ... D is some constant

Make use of f ' (0) = 4 to find D

f ' (x) = -cos(x)+9x+D

f ' (0) = -cos(0)+9(0)+D

4 = -1 + 0 + D

D = 5

So we have f ' (x) = -cos(x)+9x+D turn into f ' (x) = -cos(x)+9x+5

------------

Lastly, apply another round of integrals and substitutions to find the f(x) function. We'll use f(0) = 8.

f ' (x) = -cos(x)+9x+5

f(x) = -sin(x) + (9/2)x^2 + 5x + E .... E is some constant

f(0) = -sin(0) + (9/2)(0)^2 + 5(0) + E

8 = 0 + 0 + 0 = E

E = 8

------------

We have

f(x) = -sin(x) + (9/2)x^2 + 5x + E

turn into

f(x) = -sin(x) + (9/2)x^2 + 5x + 8

Answer:

[tex]h=30[/tex]

Step-by-step explanation:

Volume of a cone=1540[tex]cm^{3}[/tex], Radius=7cm.

The height of a cone=h

When we need to find the height of a cone, we can use the formula of the volume of a cone, which is [tex]\frac{1}{3} \pi r^{2} h[/tex] to find the height of a cone.

[tex]1540cm^{3} =\frac{1}{3}\pi r^{2} h[/tex]

Put the pi value=22/7 and the value of radius which is 7 cm into the formula.

[tex]1540cm^{3}=\frac{1}{3}*\frac{22}{7} 7^{2}h[/tex]

[tex]1540cm^{3} =\frac{154}{3}h[/tex]

Move [tex]\frac{154}{3}[/tex] to another side. 1540 divided by  [tex]\frac{154}{3}[/tex] to calculate what is the value of h, h is the height of a cone. Like this.

[tex]\frac{1540cm^{3} }{\frac{154}{3} } =h[/tex]

[tex]30=h[/tex]

Rearrange the h.

[tex]h=30[/tex]

I hope you will understand my solution and explanation. If you still cannot get the point, you can ask me anytime! Thank you!

Answer:

The height of the cone is h = 30 cm.

Step-by-step explanation:

The formula for a cone is:

[tex] \\ V = \frac{1}{3}*\pi*r^2*h[/tex]

We have (without using units) and using pi = 22/7:

[tex] \\ 1540 = \frac{1}{3}*\frac{22}{7}*(7)^2*h[/tex]

Which is equals to:

[tex] \\ 1540 = \frac{1}{3}*\frac{22}{7}*(7)*h[/tex]

[tex] \\ 1540 = \frac{1}{3}*22*7*h[/tex]

Well, we have to solve the equation for h:

[tex] \\ \frac{1540*3}{22*7} = h[/tex]

[tex] \\ 30 = h[/tex]

Therefore, the height of the cone is 30 cm.

Answer:

d- Mode

Step-by-step explanation:

Mean is 7

Range is 11

Median is 2.5

Mode is the most repeated no... which is 5

Answer:

(a) The point estimate for the population mean travel tax is $ 83.36.

(b) The lower bound is $73.70 and the upper bound is $93.02 One can be [95]% confident that the mean travel tax for all cities is between these values.

(c) The researcher could decrease the level of confidence.

Step-by-step explanation:

We are given that a normal probability plot suggests the data could come from a population that is normally distributed.

X: 68.87, 78.25, 70.44, 84.67, 79.79, 86.33, 100.24, 98.26.

(a) A point estimate for the population mean travel tax is the sample mean of the data. i.e;

      Point estimate, [tex]\bar X[/tex] =  [tex]\frac{\sum X}{n}[/tex]

                                     =  [tex]\frac{68.87+ 78.25+ 70.44+ 84.67+ 79.79+ 86.33+ 100.24+ 98.26}{8}[/tex]

                                     =  [tex]\frac{666.85}{8}[/tex]  = $83.36

So, the point estimate for the population mean travel tax is $ 83.36.

(b) Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                             P.Q.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean travel tax = $83.36

             s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex]  = $11.55

             n = sample size = 8

             [tex]\mu[/tex] = population mean travel tax

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-2.365 < N(0,1) < 2.365) = 0.95  {As the critical value of t at 7 degrees of

                                                 freedom are -2.365 & 2.365 with P = 2.5%}  

P(-2.365 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.365) = 0.95

P( [tex]-2.365 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.365 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-2.365 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.365 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.365 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.365 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                        = [ [tex]\$83.36-2.365 \times {\frac{\$11.55}{\sqrt{8} } }[/tex] , [tex]\$83.36+2.365 \times {\frac{\$11.55}{\sqrt{8} } }[/tex] ]

                        = [$73.70, $93.02]

Therefore, a 95% confidence interval for the population average debt load of graduating students with a bachelor's degree is [$73.70, $93.02].

The lower bound is $73.70 and the upper bound is $93.02 One can be [95]% confident that the mean travel tax for all cities is between these values.

(c) The researcher could decrease the level of confidence who wants to increase the precision of the interval but does not have access to additional data.

Answer:

Step-by-step explanation:

[tex]tan^{-1} (\frac{\sqrt{3} }{3} )=x\\tan x=\frac{\sqrt{3} }{3} =tan (\frac{\pi}{6} )\\x=\frac{\pi}{6}[/tex]

Answer:

52 students

Step-by-step explanation:

From the question above, we have the following information:

a) Vidya ranks 7th from the top.

Mathematically,

Vidya = 7th student

b) Divya 3 ranks behind Vidya.

Divya = Vidya + 3

Hence, Mathematically:

Divya = 7 + 3 = 10

Divya = 10th student

c) Also, Divya is 7 ranks ahead of Medha.

Mathematically,

Medha = 10 + 7= 17

Medha= 17th student

d)Sushma is 32 ranks behind Medha

Mathematically,

Sushma = Medha + 32

= 17 + 32 = 49

Sushma is the 49th student

Therefore, since, Sushma is 4th from the bottom, total number of students is:

49 + 3 = 52 students

Answer:

The rise is -6.

Step-by-step explanation:

For this problem, the direction of the vector gives the indication of a negative slope.  We know that the equation to find slope = rise/run meaning y/x values.  So for this, we can see the y-value of the blue triangle (the rise) to be 6, and the x-value of the blue triangle (the run) to be 3.  And as stated before, this is a negative slope, in the y-direction.  Hence, the rise is -6 for the blue triangle.

Answer:

sqroot 16/49 A

Step-by-step explanation:

The expression  [tex]\frac{\sqrt{16}}{\sqrt{49}}[/tex] is equivalent to expression [tex]\sqrt{\frac{16}{49}}[/tex] because by property  [tex]\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b} }[/tex].

The expression [tex]\frac{\sqrt{16}}{\sqrt{49}}[/tex] can be simplified by taking the square root of 16 and the square root of 49 separately.

√16 equals 4 because the square root of 16 is the number that, when multiplied by itself, gives 16.

Similarly, √49 equals 7 because the square root of 49 is the number that, when multiplied by itself, gives 49.

So, the expression [tex]\frac{\sqrt{16}}{\sqrt{49}}[/tex] simplifies to 4/7.

and we know that [tex]\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b} }[/tex]

[tex]\sqrt{\frac{16}{49}}[/tex] is equivalent to  [tex]\frac{\sqrt{16}}{\sqrt{49}}[/tex] , which simplifies to 4/7.

Therefore, [tex]\sqrt{\frac{16}{49}}[/tex] is equivalent to  [tex]\frac{\sqrt{16}}{\sqrt{49}}[/tex] .

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Answer:

Given,

Volume of a cone = 1540 cm[tex] {}^{3} [/tex]

Radius ( r ) = 7 cm

π ( pi ) = [tex] \frac{22}{7} [/tex]

Height of cone ( h ) = ?

Now, let's find the height of cone:

Volume of cone = [tex]\pi \: {r}^{2} \frac{h}{3} [/tex]

plug the values

[tex]1540 = \frac{22}{7} \times {(7)}^{2} \times \frac{h}{3} [/tex]

Evaluate

[tex]1540 = \frac{22}{7} \times 49 \times \frac{h}{3} [/tex]

Calculate

[tex]1540 = \frac{154 \: h}{3} [/tex]

Apply cross product property

[tex]154 \: h = 1540 \times 3[/tex]

Calculate the product

[tex]154 \: h = 4620[/tex]

Divide both sides of the equation by 154

[tex] \frac{154 \: h}{154} = \frac{4620}{154} [/tex]

Calculate

[tex]h \: = 30 \: cm[/tex]

Hope this helps...

Best regards!!

Step-by-step explanation:

mean is always equal to additon of total no.s by total no.s

2 + 4 + 6 + 8 + 10 + 12

=42

total no.s = 6 no.s

42/6

=7

therefore 7 is the answer which is the mean deviation of the following no.s .

Answer:

Here,

initial price (p)=$6500

Time from 2007 to 2020 (t)= 13yrs.

rate (r)=14.3%

now,

[tex]present \: price \: (pt) = p(1 - \frac{r}{100} )[/tex]

or, pt = $6500(1-14.3/100)

by simplifying it we get,

The, present price is $5570.5.

now, if you are searching for depreciated amount only then,

depreciated amount =$6500-$5570.5

=$929.5.

Hope it helps...

Answer:

48 degrees

Step-by-step explanation:

A straight line measures up to 180 degrees so take what we know which is 138 and subtract that from 180 to get your answer 48

Answer:

48

Step-by-step explanation:

Sum of angles On a straight line = 180

Given angle = 132

O, x is the remaining angle that must join 132 to form 180, which is

180-132 = 48 degrees.

Hope this helps

Good luck

Answer:

When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x). the line y = -x is the point (-y, -x).

Step-by-step explanation:

Hope you understand