Visitors to a museum each hour during operating hours: 35. 42, 65, 59,84.62.46.
52,24
Lowest value:
Highest value:
Spread:
Center value:

Answer:

Step-by-step explanation:

To graph an exponential function f(x) = [tex]2^{x-1}[/tex],

Step - 1 :

Find the value of x that makes the exponent 0.

x - 1 = 0

x = 1

f(1) = 2⁰ = 1

Similarly, for other input values (x- values),

For x = 2,

f(2) = [tex]2^{2-1}[/tex]

     = 2¹

     = 2

For x = 3

f(3) = [tex]2^{3-1}[/tex]

     = 2²

     = 4

For x = 4

f(4) = [tex]2^{4-1}[/tex]  

     = 2³

     = 8

Therefore, table for input - output values will be,

x        1            2            3          4

f(x)     1            2            4          8

Answer:

:>

Step-by-step explanation:

Answer:

Question 8 should be 25.6 hours

Step-by-step explanation:

Since time = distance/speed.

We just replace the words with the appropriate numbers.

time =

[tex] \frac{ 3.84 \times {10}^{5} }{1.5 \times {10}^{4} } [/tex]

which equals 25.6

Answer:

So your answer is  d = -1/4 = -0.250

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    6*d-11/2-(2*d-13/2)=0

           13

Simplify   ——

           2

        11            13

 (6d -  ——) -  (2d -  ——)  = 0

        2             2

2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  2  as the denominator :

          2d     2d • 2

    2d =  ——  =  ——————

          1        2  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

2d • 2 - (13)     4d - 13

—————————————  =  ———————

      2              2  

        11     (4d - 13)

 (6d -  ——) -  —————————  = 0

        2          2    

           11

Simplify   ——

           2

4.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  2  as the denominator :

          6d     6d • 2

    6d =  ——  =  ——————

          1        2  

4.2       Adding up the two equivalent fractions

6d • 2 - (11)     12d - 11

—————————————  =  ————————

      2              2    

5.1       Adding fractions which have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(12d-11) - ((4d-13))     8d + 2

————————————————————  =  ——————

         2                 2  

6.1     Pull out like factors :

  8d + 2  =   2 • (4d + 1)

 4d + 1  = 0

 4d + 1  = 0

7.1      Solve  :    4d+1 = 0

Subtract  1  from both sides of the equation :

                     4d = -1

Divide both sides of the equation by 4:

                    d = -1/4 = -0.250

Answer:

d = -1/4 = -0.250

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

add up all of the angles correct ft im not sure but i think its C.

Answer:

4/25

Step-by-step explanation:

Answer:

260% of 420=1092

166 2/3%of 60= 100

Answer: The number one occurs 300 times while writing the numbers from 1 to 999.

Step-by-step explanation:

Answer:

The graph of the function f( (1/2)x ) will expand across x-axis

Step-by-step explanation:

We have been given the function:

f(x) = x⁴

If we substitute x = (1/2)x into the given equation, we get:

f((1/2)x) = ( (1/2)x )⁴

We can simplify the equation

f((1/2)x) = = (1/2)⁴ x⁴

f((1/2)x) = = (1/16) x⁴

Graph of both of the functions is shown below. We can clearly see that that the graph of the function f((1/2)x) = = (1/16) x⁴ expands horizontally on x-axis as compared to the graph of f(x) = x⁴

Answer:   £ 81.38

Step-by-step explanation:

Given: On Monday,

5 builders took [tex]3\dfrac{1}{2}[/tex] hours  ( i.e. [tex]\dfrac{7}{2}[/tex] hours )  to build a wall.

On Tuesday, only 2 builders were available.

As workers are inversely proportional to the time if the job remains constant.

Inverse variation equation : [tex]x_1y_1=x_2y_2[/tex]

Let x be the time taken by 2 builders, then

[tex]2\times x =5\times \dfrac{7}{2}[/tex]

[tex]\Rightarrow\ x=\dfrac{35}{2}\times\dfrac{1}{2}=\dfrac{35}{4}=8.75[/tex]

So, 2 builders will take 8.75 hours.

Each paid  £9.30 for each hour.

Then, each builder will be paid for the work completed on Tuesday = £9.30 x  8.75

≈ £ 81.38

Hence, each builder will be paid £ 81.38 for the work completed on Tuesday .

Answer:

300 degrees

Step-by-step explanation:

we know that [tex]\pi = 360 degrees[/tex][tex]\pi = 360 \ degrees[/tex]

we have to find value of [tex]5\pi /6[/tex]

for that we have to multiply 5/6 to [tex]\pi[/tex] and 360 degrees

[tex]\pi = 360 \ degrees\\5\pi /6 = 5/6 *360 = 300[/tex]

Thus,  [tex]5\pi /6[/tex] = 300 degrees.

Answer:

150

Step-by-step explanation:

Answer:

21.94

Step-by-step explanation:

Convert the percentage to a decimal.

23.7% = 0.237

Divide the number the decimal.

5.2/0.237 = 21.94

The answer is 21.94.

(i) AB and DC are parallel, so the lines containing these sides have the same slope.

The line containing AB has slope (2 - (-1))/(10 - 4) = 3/6 = 1/2.

Use the point-slope formula to find the equation of the line containing CD:

[tex]y-8=\dfrac12(x-12)\implies y=\dfrac x2+2\implies\boxed{2y=x+4}[/tex]

AP is perpendicular to both AB and CD, and perpendicular lines have slopes that are negative reciprocals of one another. This means the line containing AP has slope -1/(1/2) = -2. Using the point-slope formula again, the equation of the line containing AP is

[tex]y-(-1) = -2(x-4)\implies \boxed{y=-2x+7}[/tex]

(ii) D lies on the x axis, so its y-coordinate is 0. Find the x-coordinate by plugging y = 0 into the equation for the line containing CD:

[tex]2\cdot0=x+4\implies x=-4[/tex]

So D is the point (-4, 0).

P is the intersection of the lines containing CD and AP, so set them equal and solve for x and y :

[tex]y=\dfrac x2+2\text{ and }y=-2x+7[/tex]

[tex]\implies\dfrac x2+2=-2x+7\implies 5x=10\implies x=2[/tex]

[tex]\implies y=-2\cdot2+7\implies y=3[/tex]

So P is the point (2, 3).

(iii) For ASBC to be a parallelogram, we need to find the coordinates of S such that the line containing AS is parallel to the line containing BC, and the line containing SC is parallel to the line containing AB.

BC has slope (8 - 2)/(12 - 10) = 6/2 = 3. Then the line containing AS has equation

[tex]y-(-1)=3(x-4)\implies y=3x-13[/tex]

We already know AB has slope 1/2. Then the line containing SC has equation

[tex]y-8=\dfrac12(x-12)\implies y=\dfrac x2+2[/tex]

S is the intersection of these two lines:

[tex]3x-13=\dfrac x2+2\implies\dfrac{5x}2=15\implies5x=30\implies x=6[/tex]

[tex]\implies y=3\cdot6-13\implies y=5[/tex]

So S is the point (6, 5), and *not* (2, -7) as the answer key suggests. In fact, (2, -7) is located lower than the point A and slightly to the left; if you draw that point and connect it to the other three, there's no way to get a parallelogram.

(iv) Find the lengths of AB, CD, and AP. Then the area is (AB + CD)*AP/2.

[tex]AB=\sqrt{(4-10)^2+(-1-2)^2}=3\sqrt5[/tex]

[tex]CD=\sqrt{(12-(-4))^2+(8-0)^2}=8\sqrt5[/tex]

[tex]AP=\sqrt{(4-2)^2+(-1-3)^2}=2\sqrt5[/tex]

so the area is

[tex]\dfrac{(3\sqrt5+8\sqrt5)2\sqrt5}2=\boxed{55}[/tex]

Answer:

40% spent. 60% left.

Step-by-step explanation:

To find the percentage spent, divide the two values, then multiply by 100.

$32 / $80 = 0.40    0.40 x 100 = 40% spent.

To find the percentage of money left, subtract the two values.

$80 -$32 = $48

Then, divide the two values and multiply by 100.

$48 / $80 = 0.60   0.60 x 100 = 60% left.

Answer:

the lines are perpendicular

Step-by-step explanation:

the first step to this question will be to find the slope intercept form of each of these lines. to do this we will first:

find the slope-

(-3,-1) and (1,-9)

y2-y1 / x2- x1

-9 - (-1)  / 1 - (-3)  (negative - negative = positive)

-8 / 4

therefore the slope is:

-2

we know that slope intercept form is y=mx+b

so.. y= -2x +______

I left the last part blank, because we only have the first half of the equation, now we will substitute the value of x and y into the equation from one of the coordinate points given above.

(-9) = -2(1) + _____

now we can simplify:

-9 = -2

this equation (-9 = -2) is not true, therefore we need to determine what we have to do to -2 to make it equal to -9.

-9 = -2 - 7 is true

therefore the answer is :

y= -2x-7

therefore the slope intercept form is y= -2x - 7

now that you know how to find the slope intercept form, you can find the other slope intercept form, and i'll provide the answer:

the slope intercept form you should find is

y= [tex]\frac{1}{2}[/tex]x + [tex]\frac{7}{2}[/tex]

now when we plot both of these lines we can see that:

the lines are perpendicular, meaning the lines pass through each other.

Answer:

the two lines are perpendicular to one another

Step-by-step explanation:

Find the slopes of the two lines and then compare them.

If the slopes are the same, the lines are parallel.

If the slopes are negative reciprocals, the lines are perpendicular.

If neither of these conditions hold, then the lines are neither parallel nor perpendicular.

(−3,−1) and (1,−9):  As we go from the first point to the second, x (the "run") increases by 4 and y (the "rise") decreases by 8.  Thus, the slope of the line through (−3,−1) and (1,−9) is m = rise / run = -8/4, or m = -2.

(1,4) and (5,6):  As we go from the first to the second, x increeases by 4 and y increases by 2.  Thus, the slope of the line through (1,4) and (5,6) is

m = rise / run = 2/4 = 1/2.

Because 1/2 is the negative reciprocal of -2, we know that the two lines are perpendicular to one another.

Answer:

41°

Step-by-step explanation:

Looking at the attached diagram

A central angle of a circle is always congruent to its intercepted arc.

Therefore, m arc BC = m∠BZC

Again, m∠BAC is one-half m arc BC, as the measure of an inscribed angle is half the measure of its intercepted arc.

This gives us the following results:

= m∠BZC = 82°

= m arc BC = m∠BZC

= m arc BC = 82°

= m∠BAC = 1/2 × 82°

= m∠BAC = 41°

Note that:

∠DCA ≅ ∠BAC because alternate interior angles are congruent.

So m∠DCA = m∠BAC.

Hence, m∠DCA = 41°.

Answer:

double: 1%

year6%

6 year: 36%

Step-by-step explanation:

Answer:

last three questions are statistical question

Answer:

The last three questions

Step-by-step explanation:

Answer:

Step-by-step explanation:

Total number of cards = 48

Red cards/black cards = 1/1

(so, 24 each of read and black cards)

8 red cards are removed.

Now, there will be (24-8) number of cards left in the pack which equals to 16 cards.

So, now the number of red cards in the pack= 16

Number of black cards = 24

Ratio of red card/ black card

[tex] = \frac{16}{24} [/tex]

[tex] = \frac{2}{3} [/tex]

Hope this helps...

Good luck on your assignment...

Answer:

x = 135

Step-by-step explanation:

Use the right triangle altitude theorem and similar triangles.

x/81 = 225/x

x^2 = 81 * 225

x = 9 * 15

x = 135

Answer:

135

Step-by-step explanation:

Answer:

=434.86

Step-by-step explanation:

The radius = 4.7cm

this means that using the equation that is given (V=4/

3πr^3)

add the radius where it says r

it also says you are allowed to use a calculator so put the equation into your calculator to give you the answer.

i hope this helped :)

Answer:

volume of sphere is 4 thirds pie r squared. Google it!

Step-by-step explanation:

Answer:

[tex](x+10)^2-186[/tex]

Step-by-step explanation:

Answer:

3 1/2 (in fraction form but 11.2... something) hope this helps

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

2x^2-3x+

Factor out 2

2( x^2 -3/2x)

Take the coefficient of x

-3/2

Divide by 2

-3/4

Square it

(-3/4) ^2 = 9/16

This is the number inside the square

2( x^2 -3/2x + 9/16)

Multiply by 2 since that is factored on the outside

9/16 *2 = 9/8

Add to the equation

2x^2-3x+9/8

Answer:

Leftmost box: Graph, because it has zero x intercepts

Middle box: Function f with a vertex at 2, 0

Rightmost box: g(x)=x^2+x-2

Answer:

g(x)=x^2+x-2

Step-by-step explanation:

Answer: 0, −5, 4

Step-by-step explanation:

The given function is

[tex]f(x)=x^3+x^2-20x[/tex]

One of the zero of the given polynomial function is x=0.

To find other zeroes put f(x)=0

[tex]x^3 + x^2 - 20x=0\\\\\Rightarrow\ x(x^2+x-20)=0\ \ \ [\text{Taking x as common}][/tex]

That is

[tex]x^2+x-20=0[/tex] or [tex]x=0[/tex]

if [tex]x^2+x-20=0[/tex]

then [tex]x^2+5x-4x-20=0\ \ \ [\text{By using middle term splitting method}][/tex]

[tex]\Rightarrow\ x(x+5)-4(x+5)=0\\\\\Rightarrow\ (x+5)(x-4)=0\\\\\Rightarrow\ x=-5, 4[/tex]

So, the zeroes of f(x) are 0, −5, 4 .

Hence, the correct option is 0, −5, 4.

Answer: Ok for the second one because I don't really get the wording in the first one (thats cuz i SUCK at vocabulary) the answer is 756,100 and a number greater is any number from 756,073-756,149

Step-by-step explanation:

ok so 756072 rounds to 756100 because 72 is closer to 100 than it is to 0

from 50 on, you would round up so to round up to 756100 the smallest possible number is 756050 since the 50 will round up

the highest number is 756149 because from 50 onwards it will round to 756200 instead.

so you can choose any number from 756050-756149

Answer:

The percentage of  volumes that are within 3 standard deviation of the mean is 99.73%.

Step-by-step explanation:

We want to calculate the area under the curve within 3 standard deviations from the mean.

If we use the standard normal distribution, this probability can be calculated as the diference between P(z<3) and P(z<-3).

[tex]P(-3<X<3)=P(z<3)-P(z<-3)\\\\P(-3<X<3)=0.9987-0.0013=0.9973[/tex]

The area under the curve for the standard distribution and for any normal distribution within 3 standard deviation from the mean is 0.9973.

The percentage of  volumes that are within 3 standard deviation of the mean is 99.73%.

Answer:

B. 120°

Step-by-step explanation:

If two tangents intersect in the exterior of a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs.

m∠A° = 1/2(300 - 60)

m∠A° = 1/2(240)

m∠A° = 120

Answer: A

Step-by-step explanation:

The domain of a function is the minimum and maximum value of independent variable (x).

The domain of the function according to the given graph will be the starting point of the line of best fit to the end point of the line.

Trace the starting point and the end point to the x - axis.

If you do so, the starting point is 2 and the end point is 10.

The domain is therefore, 2< = x <= 10. The correct answer is A