Anjali was keeping track of how far she walked. She walked 1 1/10 miles on Monday, 4 4/5 miles on Wednesday, and 2 1/4 on Friday. What was the total distance she walked? show your work using decimals. pls help

We have the sum of cubes identity

[tex]a^3 + b^3 = (a + b) (a^2 - ab + b^2)[/tex]

and observing that 1 + 4 = 2 + 3, we have

[tex]1^3 + 4^3 = (1 + 4) (1^2 - 4 + 4^2) = 5 \times 13[/tex]

and

[tex]2^3 + 3^3 = (2 + 3) (2^2 - 6 + 3^2) = 5 \times 7[/tex]

Then

[tex]\sqrt{1^3+2^3+3^3+4^3+5^3} = \sqrt{5\times13 + 5\times7 + 5\times5^2} = \sqrt{5 \times (20 + 25)} \\\\ ~~~~~~~~ = \sqrt{5^2 \times (4 + 5)} = \sqrt{5^2\times9} = \sqrt{5^2\times3^2} = 5\times3 = \boxed{15}[/tex]

Alternatively, we have the well-known sum of cubes formula

[tex]\displaystyle \sum_{i=1}^n i^3 = \frac{n^2(n+1)^2}4[/tex]

The sum under the square root is this sum with [tex]n=5[/tex]. Then

[tex]1^3+2^3+3^3+4^3+5^3 = \dfrac{5^2\times6^2}4 = 225 = 15^2[/tex]

and so the square root again reduces to 15.

Answer:

C = 29.7

Step-by-step explanation:

Remember to use a^2 + b^2 = c^2

21^2+ 21^2 = c^2

441 + 441 = c^2

882 = c^2

you square root both sides

c= 29.6984

Round it

C = 29.7

The exponential equation for the growth is f(x)=57[tex]e^{0.51x}[/tex] where x is the number of days and the population on 21st march is 2069983.5 of microbes.

Given:

Days                   population

0                                57

1                                 95

5                               700

10                               8525

We have to form exponential equation which shows the growth of microbes.

We know that exponential equation which shows the sum is as under:

f(x)=P[tex]e^{rt}[/tex] where r is the rate of growth and x is the number of days, months or years depending on how things grows.

In the question when x=0 population is 57.

f(0)=57

P[tex]e^{0}[/tex]=57

P=57

When x=1, population is 95.

f(1)=95

P[tex]e^{r}[/tex]=95

57 [tex]e^{r}[/tex]=95

57=95/[tex]e^{r}[/tex]----1

when x=5,population is 700.

f(5)=700

P[tex]e^{5r}[/tex]=700

57[tex]e^{5r}[/tex]=700

57=700/[tex]e^{5r}[/tex]-----2

Equating 1&2

95/[tex]e^{r}[/tex]=700/[tex]e^{5r}[/tex]

[tex]e^{5x} /e^{x} =700/95[/tex]

[tex]e^{5r-r}[/tex]=7.36

[tex]e^{4r}[/tex]=7.36

[tex](2.7182)^{4r}[/tex]=[tex](2.7182)^{2}[/tex]

equating both sides

4r=2

r=0.5

put the value of t=21 in the exponential equation

f(21)=57[tex]e^{0.5*21}[/tex]

=57[tex]e^{10.5}[/tex]

=57*36315.5

=2069983.5

Hence the population on 21st march is 2069983.5.

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The inverse of the given function is y = [tex]\rm \sqrt {x/2}[/tex].

A function is a mathematical statement used to relate a dependent and an independent variable.

The function given is

y = 2x²

To find the Inverse of a function ,

The x and y are interchanged and the function is again written in terms of x

Here

x = 2y²

y² = x/2

y = [tex]\rm \sqrt {x/2}[/tex]

Therefore the inverse of the given function is y = [tex]\rm \sqrt {x/2}[/tex].

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The approximate depth of water for a tsunami traveling at 200 kilometers per hour, given the equation S=356√d, where S is the speed in kilometers per hour and d is the average depth of the water in kilometers, is 0.32 km. Hence, option A is the correct choice.

To solve for the average depth of water, when the water is traveling at 200 kilometers per hour, we substitute speed S = 200, in the relation S = 356√d.

This will be solved in the following way:

S = 356√d,

or, 200 = 356√d {Substituting S = 200},

or, 200/356 = (356√d)/356 {Dividing both sides by 356},

or, √d = 0.5618 {Simplifying},

or, d = 0.32 kilometers.

Therefore, the approximate depth of water for a tsunami traveling at 200 kilometers per hour, given the equation S=356√d, where S is the speed in kilometers per hour and d is the average depth of the water in kilometers, is 0.32 km. Hence, option A is the correct choice.

The provided question is incomplete.

The complete question is:

"The speed that a tsunami can travel is modeled by the equation S=356√d, where S is the speed in kilometers per hour and d is the average depth of the water in kilometers. What is the approximate depth of water for a tsunami traveling at 200 kilometers per hour?

A. 0.32 km

B. 0.75 km

C. 1.12 km

D. 3.17 km"

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Answer:c

Step-by-step explanation:

c

Answer:

D.

Step-by-step explanation:

The equation must be true to have a proportion.

12/20 = 0.6

21/34 = 0.62

A. No

10/15 = 0.666666...

34/60 = 0.566666...

B. No

13/23 = 0.565217...

26/56 = 0.46428...

C. No

25/15 = 1.6666...

85/51 = 1.6666...

D. Yes

Answer: D

Answer:

probably B

Step-by-step explanation:

Using the formula pi*r^2, we plug in our values
pi*49=49pi mi^2
but, we still have one more step, as we are calculating for three quarters of a circle, not a full circle.
To find the area for 3/4 of a circle, we just multiply 3/4 by the area of the circle

49pi*3/4=147pi/4

A quick way (though not always accurate) to guess the answer in a multiple choice like this is to see that someone might find the area of the full circle as their final answer, not multiplying by 3/4, so there's a good chance that 49pi mi^2 would be an answer in the multiple choice. since we know that there is a correct answer that is exactly 3/4 of that answer, we can take the ratios of the answers and check if any of them equal 3/4. indeed, after checking a bit, answer B divided by answer A equals 3/4 exactly, and no other answer combination equals 3/4 (D/B is about equal to 4/5). So, we can guess that B is the answer.

Still better to actually do the problem though

The function y = x + 1 has a slope (rate of change) of 1 as well as an y intercept of 1.

An equation is an expression that shows the relationship between two or more numbers and variables.

The standard form for a linear function is:

y = mx + b

Where m is the slope and b is the y intercept.

Given the function y = x + 1

The function y = x + 1 has a slope (rate of change) of 1 as well as an y intercept of 1.

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Answer:

The linear equation modeling the given function is P(t)=1700t+45000.

Step-by-step explanation:

In the question it is given that a town's population has been growing linearly. In 2003, the population was 45000, and the population has been growing by 1700 people each year.

It is required to write an equation P(t), for the population t years after 2003.

To solve this question, substitute the given slope , or change in population in the equation with the initial population . Thus, formulate the equation modeling the given function.

Step 1 of 1

Formulate the equation in the slope-intercept form.

[tex]$$\begin{aligned}&y=m x+b \\&P(t)=1700 t+45000\end{aligned}$$[/tex]

Theo should expect the spinner to land on "Action" 12 times.

Probability refers to a possibility that deals with the occurrence of random events.

Given: A spinner with 5 sections labeled action, drama, sci-fi, horror, and comedy.

Theo spins the spinner 60 times.

We need to find the number of times, out of 60, the spinner lands on "Action".

Here, a total number of outcomes= 5

A number of favorable outcomes = 1

So, the probability that the spinner lands on "Action" = 1/5

Theo spins the spinner 60 times.

So, the number of times the spinner lands on "Action"

= 1/5 x 60 = 12

Hence, Theo should expect the spinner to land on "Action" 12 times.

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Answer:

3072

Step-by-step explanation:

General form of a geometric sequence:

  [tex]a_n=ar^{n-1}[/tex]

where:

Given values:

Substitute the given values into the formula to create an equation for the nth term:

[tex]\implies a_n=3(4)^{n-1}[/tex]

To find the 6th term, substitute n = 6 into the equation:

[tex]\implies a_6=3(4)^{6-1}[/tex]

[tex]\implies a_6=3(4)^{5}[/tex]

[tex]\implies a_6=3(1024)[/tex]

[tex]\implies a_6=3072[/tex]

Therefore, the 6th term of a geometric sequence whose 1st term is 3 and whose common ratio is 4 is 3072.

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Answer:

(d) y≥-5

Step-by-step explanation:

first, we find the equation for the blue line:

a doesn't work as it goes diagonally, so as b, e, or f.

so it must be y≥-5 or y<-5

since the graph is shaded above the line, it must be greater than or greater than or equal to, so it must be D) y≥-5.

You can tell it must be D as greater or less than is dotted while greater equal or less equal would be a solid line.

Answer:

[tex]x = - 4[/tex]

[tex]y = - 4[/tex]

Step-by-step explanation:

Looking at these equations, we can see neither x or y have the same coefficient. Therefore, we need to multiply or divide, to make either the x or the y the same. It's less of a hassle to make the Xs the same, so let's do that. Taking the top equation and multiplying it by 4, we get:

[tex]4x - 20y = 64[/tex]

Now let's subtract the top equation from the bottom equation, leaving us with a third equation:

[tex] - 18y = 72[/tex]

Divide 72 by -18 to get

[tex]y = - 4[/tex]

Now let's substitute into our first equation to find X:

[tex]x + 20 = 16[/tex]

Leaving us with:

[tex]x = - 4[/tex]

Now let's substitute into the second equation to check our solution is correct:

[tex] - 16 + 8 = - 8[/tex]

This is correct, so the answer is X and Y are both equal to -4

Answer:

Step-by-step explanation:

Comments

AE = AT = 7                                                  Given

AT is a perpendicular bisector of OS        Property of a circle

AE is a perpendicular bisector of BR        Property of a circle

ER = 1/2 BR = 48/2 = 24                              Property of a bisector

TS = ER                                                        Property of a bisector and chord

TS = 24                                                        ER = 24 so TS = 24

AS^2 = TS^2 + TA^2                                   Pythagorean Theorem + rt angle

AS^2 = 24^2 + 7^2                                      Substitute values

AS^2 = 576 + 49                                         Combine

AS^2 = 625                                                 Take sqrt of both sides

√AS^2 = √625                                  

AS = 25

Answer

AS = 25

Answer:

y = - 6x + 7.5

Step-by-step explanation:

the perpendicular bisector of BC passes through the midpoint of BC at right angles to BC.

calculate the slope m of BC using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = B (- 2, 1 ) and (x₂, y₂ ) = C (4, 2 )

[tex]m_{BC}[/tex] = [tex]\frac{2-1}{4-(-2)}[/tex] = [tex]\frac{1}{4+2}[/tex] = [tex]\frac{1}{6}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{6} }[/tex] = - 6

the midpoint of BC is the average of the x and y coordinates

midpoint = ( [tex]\frac{-2+4}{2}[/tex] , [tex]\frac{1+2}{2}[/tex] ) = ( [tex]\frac{2}{2}[/tex] , [tex]\frac{3}{2}[/tex] ) = ( 1, 1.5 )

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 6 , then

y = - 6x + c ← is the partial equation

to find c substitute (1, 1.5 ) into the partial equation

1.5 = - 6 + c ⇒ c = 1.5 + 6 = 7.5

y = - 6x + 7.5 ← equation of perpendicular bisector of BC

Answer:

its 3 grapes

Step-by-step explanation:

6-3=3 therefore the answer is 3

Answer:

3 grapes are left

Step-by-step explanation:

if you subtract 3 from 6 (6 - 3) you will find the answer you need to find how many grapes you have left.

The equivalent equations to [tex]\frac{3}{5}(30x - 15) = 72[/tex] are given as follows:

Equivalent equations are equations that have the same solution.

First, we have to check the solution to [tex]\frac{3}{5}(30x - 15) = 72[/tex], hence:

[tex]\frac{3}{5}(30x - 15) = 72[/tex]

Applying the fraction:

18x - 9 = 72 -> first equivalent equation

Simplifying by 3:

3(6x - 3) = 72 -> second equivalent equation

The solution is:

18x - 9 = 72

18x = 81

x = 81/18

x = 4.5 -> third equivalent equation.

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Answer:

In the SAS congruence criterion, you must show that two pairs of sides are equal and their included angles are equal as well. But In the SAS similarity criterion, you must show that two pairs of sides are proportional and their included angles are equal.

Step-by-step explanation:

Solution: In the SAS congruence criterion, you must show that two pairs of sides are equal and their included angles are equal as well. But In the SAS similarity criterion, you must show that two pairs of sides are proportional and their included angles are equal.

The system of inequalities that correctly represents this scenario is given by:

A system of inequalities is when two or more variables are related, and inequalities are built to find the values of each variable.

In this problem, the variables are given as follows:

The manager of the stand expects sales of a minimum of 100 items, hence:

[tex]x + y \geq 100[/tex].

The concession stand at a local high school sells nachos for $4 each and popcorn for $2 each. The manager wants a total of at least $225, hence:

[tex]4x + 2y \geq 225[/tex]

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The correct option is to show that the ratios HL/JL = IL/KL = HI/JK are equivalent. Option A is correct.

For two triangles to be similar, the ratio of the measure of similar sides of the triangle must be equal to a constant known as a scale factor.

From the given figures, the expression that can be used to prove that the triangles are similar is as shown;

HL/JL = IL/KL = HI/JK

Hence the correct option is to show that the ratios HL/JL = IL/KL = HI/JK are equivalent

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I can Confirm A is correct

Step-by-step explanation:

The attached graph represents the line plot of the dataset

The frequency table is given as:

Amount        3   3.5    4  4.5  5

Frequency   1      2     3   3    1

To create the line plot, we represent the frequency by dots.

Take for instance:

See attachment for the line plot

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The required probability is 0.45

We have total 26 letters in english, of which 21 are consonants and 5 are vowels.

According to the question, we have to select 5 of them of which 4 will be consonants and 1 will be vowel.

Suppose we want to have the vowel in the first selection, so the probability of picking a vowel is equal to the quotient between the number of vowels and the number of total number of letters.

So the probability is 5/26

Now, a letter has been selected, so in the set, we have 25 letters left.

In the next 4 selections, we must select consonants.

In the second selection the probability is 21/25

In the third selection the probability is 20/24

In the fourth selection the probability is 19/23

In the last selection the probability is 18/22

So, the probability is (5/26)×(21/25)×(20/24)×(19/23)×(18/22)

Now, remember that we take that the vowel must be in the first place, but it can be in any five places, so if we add the permutations of the vowel letter we have,

P = 5×(5/26)×(21/25)×(20/24)×(19/23)×(18/22) = 0.45

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For question 1 option C is the correct answer and for question 2 option A is the correct answer.

We need to find which transformation from the graph of a function f(x) describes the graph of 10f(x).

Here the transformation that describes the graph of g(x) is a vertical dilation of scale factor k = 10 of f(x).

We can start by defining the general vertical dilation.

For a given function f(x), a vertical dilation stretches or contracts the graph vertically, depending on the scale factor k.

And it is written as:

g(x) = k*f(x).

Then here we have:

g(x) = 10*f(x)

It is easy to see that this is a vertical dilation of scale factor k = 10. Therefore, option C is the correct answer.

We need to check from the given options which information is sufficient to prove that quadrilateral ABCD is a parallelogram.

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Therefore, option A is the correct answer.

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The amount in pounds of Type A coffee used is 36 pounds.

Type A coffee costs Susan $5.45 per pound, and type B coffee

costs $4.05 per pound.

Therefore,

Let x = the number of pounds of Type A coffee.

total pounds = x + 3x

total cost = 5.45(x) + 3x(4.05)

633.60 =  5.45(x) + 3x(4.05)

633.60 =   5.45x + 12.15x

633.60 = 17.6x

divide both sides by 17.6

x = 633.60 / 17.6

x = 36

Pounds of Type A coffee used = 36 pounds

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Answer:

2x-9=0

2x-9+9=0+9.add the inverse of subtraction /addition/ (+9)

2x=9....then divide by 2

x=9/2

x=4.5. will the final answer

Steps 4 and 5 describe the errors Stephen made.

Stephen evaluated [tex](6.34\times 10^{-7})(4.5\times 10^3)[/tex].  

His work is shown below.

Step 1 - [tex](6.34\times 10^{-7})(4.5\times 10^3)[/tex]

Step 2 - [tex]=(6.34\times 4.5)(10^{-7} \times 10^3)[/tex]

Step 3 - [tex]=(28.53)(10^{-4})[/tex]

Step 4 - [tex]20.53\times 10^4[/tex]

Error is the step as 4 sign is negative.

So correct step is [tex]=(28.53)(10^{-4})[/tex]

Step 5 - [tex]=(28.53)(10^{-4})[/tex]

Error is the step as there are 4 in place of 3.

So correct step is [tex]=(28.53)(10^{-4})[/tex]

Steps 4 and 5 describe the errors Stephen made.

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By inclusion/exclusion,

[tex]n(P' \cup Q) = n(P') + n(Q) - n(P' \cap Q)[/tex]

We have

[tex]n(\xi) = n(P) + n(P') \implies n(P') = 28 - n(P)[/tex]

so that

[tex]n(P'  \cup Q) = (28 - n(P)) + n(Q) - 2n(P) = 28 - 3n(P) + n(Q)[/tex]

Now,

[tex]n(\xi) = 28 \implies n(P \cup Q) = 28 - 7 = 21[/tex]

and by inclusion/exclusion,

[tex]n(P \cup Q) = n(P) + n(Q) - n(P \cap Q)[/tex]

Decompose [tex]Q[/tex] into the union of two disjoint sets:

[tex]Q = (P \cap Q) \cup (P' \cap Q)[/tex]

Since they're disjoint,

[tex]n(Q) = n(P\cap Q) + n(P'\cap Q) \implies n(Q) = n(P\cap Q) + 2n(P)[/tex]

[tex]\implies n(P \cup Q) = n(P) + (n(P\cap Q) + 2n(P)) - n(P \cap Q)[/tex]

[tex]\implies 21 = 3n(P)[/tex]

[tex]\implies n(P) = 7[/tex]

From the Venn diagram, we see there are 3 elements unique to [tex]P[/tex] - by the way, this is the set [tex]P \cap Q'[/tex] - so [tex]n(P\cap Q) = 7-3 = 4[/tex], and it follows that

[tex]n(Q) = n(P\cap Q) + 2n(P) = 4 + 2\times7 = 18[/tex]

Finally, we get for (a)

[tex]n(P' \cup Q) = 28 - 3n(P) + n(Q) = 28 - 3\times7 + 18 = \boxed{25}[/tex]

For (b), we have by inclusion/exclusion that

[tex]n(P \cup Q') = n(P) + n(Q) - n(P \cap Q') = 7 + 18 - 3 = \boxed{22}[/tex]

Answer: Infinite

Step-by-step explanation:

Answer:

one solution, r = - 2

Step-by-step explanation:

4(2r - 1) = - 2(3r + 16) ← distribute parenthesis on both sides

8r - 4 = - 6r - 32 ( add 6r to both sides )

14r - 4 = - 32 ( add 4 to both sides )

14r = - 28 ( divide both sides by 14 )

r = - 2

Answer:

1400000

Step-by-step explanation:

This is very simple,

multiply the total tickets with this fraction which is

= 2/5x 3500000

= 1400000

Answer:

14,000,000.

Step-by-step explanation:

2 out 5  tickets are winners.

So number of winning tickets = 3,500,000 * 2/5

= 2 * 7,000,000

= 14,000,000

-0.5244 will separates the highest 70% of the scores in a normal distribution from the lowest 30%

Normal Distribution is bell shaped and symmetrical in nature.

We use standard normal to find probabilities of normal distribution.

Fig 1 represents Graph of standard normal

and Fig 2 is % points Table for standard normal distribution.

From % points Table the value separates the highest 70% of the scores in a normal distribution from the lowest 30% is 0.5244 since 30% lies left side from 0 it will be negative

⇒  value separates the highest 70% of the scores in a normal distribution from the lowest 30% is -0.5244

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