On a bicycle, Misty rides for 4 hours and is 30 miles from her house. After riding for 6 hours, she is
44 miles away.
What is Misty's rate?

Answer:

9.24 m to 2 DP's.

Step-by-step explanation:

Consider the right triangle formed from a side , altitude and 1/2 the base.

By pythagoras:

x^2 = 8^2 + (0.5x)^2     where x is the length of each side.

x^2 - 0.25x^2 = 64

0.75x^2 = 64

x^2 = 64/0.75 =  85.3333.

x = 9.2376 m.

Answer:

-53

Step-by-step explanation:

-60 -13

you would divide -> 51/68  and you would get .75. move the 2 first numbers after the dot to the front and you get 75%

Answer:

I the diagram, 17  represents 25% of the total  games. Since 17 times 3 equals 51, you use the first 3 columns to find the answer of 75%.  

Just took test that was the answer they gave.

Step-by-step explanation:

Answer:

c = 28 m

Step-by-step explanation:

Here we have a right triangle with shortest side (a) of length 17 m and smallest angle (A) equal to 37 degrees and positioned opposite side (a).  The sine function is applicable here:

 17 m

---------- = opp / hyp = sin 37 degrees = approximately 0.602.

    c

Then 17 m / c = 0.602, or (after inverting both sides)

  c             1

-------- = -----------

17 m      0.602

Solve for c.  Cross-multipying, we get 0.602c = 17 m.

Dividing both sidees by 0.602 yields c = 28.24 m, which should be rounded off to the nearest whole number:  c = 28 m

The interest is 16% compounded semi-annually, is Rs. 121,179.10.

To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.

Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)

So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:

Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.

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No, the expression (x^3 - 1) / (x^2 - 1) does not simplify to x.

To simplify the expression, let's first factorize both the numerator and denominator.

The numerator can be factorized using the difference of cubes formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2). So, we have (x^3 - 1) = (x - 1)(x^2 + x + 1).

The denominator is a difference of squares: a^2 - b^2 = (a - b)(a + b). Therefore, (x^2 - 1) = (x - 1)(x + 1).

Now, we can simplify the expression by canceling out the common factors in the numerator and denominator:

[(x - 1)(x^2 + x + 1)] / [(x - 1)(x + 1)]

The (x - 1) terms cancel out, leaving us with:

x^2 + x + 1 / (x + 1)

So, the simplified form of the expression is (x^2 + x + 1) / (x + 1), which is not equal to x.

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Answer:

The answer is in the image.

Answer:

x ≥ 18

Step-by-step explanation:

This can be simplified by changing the sign on the 12 value. This is because you are subtracting a negative number and two negatives make a positive (- - = +):

x (--12) ≥ 30

x + 12 ≥ 30

Subtract 12 from both sides:

x + 12 - 12 ≥ 30 - 12

x ≥ 18

Hope this helps!

Answer:

1/2 mile

Step-by-step explanation:

its 2 1/2 miles right? so u just have to find the difference.

2.5-0.25=2.25

2.25-1.75=0.5

0.5 miles is left

Answer:

11 buses

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Answer:

a. Z = 1.99

b. 97.67%

c. Z = 2.56

d. 0.52%

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

a. If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)?

The heights of adult men in America are normally distributed, with a mean of 69.7 inches and a standard deviation of 2.66 inches, and thus, we have \(\mu = 69.7, \sigma = 2.66\)

6 feet 3 inches = 6*12 + 3 = 75 inches, which means that we have to find z when X = 75. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{75 - 69.7}{2.66}\)

\(Z = 1.99\)

b. What percentage of men are SHORTER than 6 feet 3 inches?

The proportion is the p-value of Z = 1.99.

Looking at the z-table, Z = 1.99 has a p-value of 0.9767.

0.9767*100% = 97.67%, which is the answer.

c. If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)?

The heights of adult women in America are also normally distributed, but with a mean of 64.5 inches and a standard deviation of 2.54 inches, and thus, we have \(\mu = 64.5, \sigma = 2.54\). We have to find Z when X = 5*12 + 11 = 71. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{71 - 64.5}{2.54}\)

\(Z = 2.56\)

d. What percentage of women are TALLER than 5 feet 11 inches?

The proportion is 1 subtracted by the p-value of Z = 2.56.

Looking at the z-table, Z = 2.56 has a p-value of 0.9948.

1 - 0.9948 = 0.0052

0.0052*100% = 0.52%, which is the answer.

We get the length of QS as 102 units.

We are given two equations:

QR = 4 x +7, and RS = 8 x - 37

We are also told that R is the mid point of QS.

This means that R will divide QS in two equal halves.

This also implies that:

QR = RS

Substituting the values, we get that:

4 x + 7 = 8 x - 37

Solving for x, we get that:

8 x - 4 x = 7 + 37

4 x = 44

x = 44 / 4

x = 11

Now substituting the value of x in QR and RS to find the length of QS:

QR = 4 x + 7 = 4 ( 11 ) + 7 = 44 + 7 = 51

RS = 8 x - 37 = 8 ( 11 ) - 37 = 88 - 37 = 51

QS = QR + RS

QS = 51 + 51 = 102

Therefore, we get the length of QS as 102 units.

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Answer:

5

Step-by-step explanation:

Answer:

k = -2

j = 5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

j + k = 3

j - k = 7

Step 2: Rewrite Systems

j - k = 7

Step 3: Redefine Systems

j + k = 3

j = 7 + k

Step 4: Solve for k

Substitution

Step 5: Solve for k

Answer:

1 kg = 1000 grams

15,000 grams = 15kg

The statement; "I drank 0.7 liters of water today" makes sense

We know that we can say that a statement is reasonable when the statement does make a logical sense. The implication of that is that the statement can be seen to have meaning. In the example we have been told that nobody can be 15 feet tall thus the statement is not reasonable.

It is possible for someone to drink as much as  0.7 liters of water in a day since people could even has as much as five liters of water in a  day.

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The values into the slope-intercept form, we have y = -5x - 6

The slope-intercept form of a linear equation is given by:

y = mx + b

where 'm' represents the slope of the line, and 'b' represents the y-intercept.

In this case, the y-intercept is (0, -6), which means that the line crosses the y-axis at the point (0, -6).

The slope is given as -5.

Therefore, substituting the values into the slope-intercept form, we have:

y = -5x - 6

This equation represents the line with a y-intercept of (0, -6) and a slope of -5.

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Answer:

26

Step-by-step explanation:

17 + 22 + x = 65

39 + x = 65

65 - 39 = x

26 = x

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The solution to the equation given by M * M * M = 729 is 9

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

Given the equation:

M.M.M = 729

This gives:

M * M * M = 729

M³ = 729

Taking the cube root of both sides:

∛M³ = ∛729

M = 9

The solution to the equation is 9

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Answer:  

can u be more specific so i can properly help u  

Explanation:  

pls explain and i will edit my answer  

The ideal congressional district size (Standard Divisor) in 1790 was 34437.33.

The number of persons each House of Representatives seat represents is known as the "Standard Divisor" (SD). By dividing the total population of all the states by the total number of seats available for voting, the SD is determined. SD is calculated as Total U.S. Population / Total Number of Voting Seats.

The ratio of the entire population to the available seats (or other allocations) is known as the standard divisor. • The Hamilton system divides up any extra seats among the states with the largest fractional parts after allocating each state its lower quota initially.

Given,

population in 1790 was 3,615,920,

number of objects = 105

⇒ Standard divisor = total population / number of objects

⇒ Standard divisor = 3,615,920 / 105

⇒ Standard Divisor = 34437.33

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Answer:

  (8 terms) 9, 3, 5, 4, 1, (3 terms)

Step-by-step explanation:

Assuming your sequence is ...

  7, 3, 9, 6, 4, 1, 3, 7, 9, 3, 5, 4, 1, 7, 6, 5

The proposed sequence must have an even number of odd terms, so must be one of ...

  4 +1 +3 +7 +9 = 24

  7 +9 +3 +5 +4 = 28

  9 +3 +5 +4 +1 = 22

  3 +5 +4 +1 +7 = 20

The 5-number sequence you're looking for is 9, 3, 5, 4, 1.

Answer:

look it up

Step-by-step explanation:

Answer:

21x^4 + 8x + 7

Step-by-step explanation:

This is the answer because:

1) Simplify each term and multiply like terms and multiply them because in order to find the area we have to multiply the height and width.

2) Since we have to multiply like terms, 7x^2 and 3x^2 are the only like terms. Therefore, we multiply 7x^2 * 3x^2 = 21x^4.

3) The rest of the numbers are not like terms.

4) Therefore, the answer is 21x^4 + 8x + 7

Hope this helps!

Answer:

Zeros: 0, 1, and 7

Step-by-step explanation:

Given function: f(x) = 3x(x - 1)²(x - 7)²

To find the zeros (also known as the x-intercepts) of the function, first substitute f(x) = 0 into the equation and simplify.

1. Substitute f(x) = 0:

\(\sf f(x) = 3x(x - 1)^2(x - 7)^2\\\\\Rightarrow 0 = 3x(x - 1)^2(x - 7)^2\)

2. Divide both sides by 3:

\(\sf \dfrac{0}{3} = \dfrac{3x(x - 1)^2(x - 7)^2}{3}\\\\\Rightarrow 0=x(x-1)^2(x-7)^2\)

3. Separate into possible cases:

\(\sf a)\ x = 0\\b)\ (x - 1)^2 = 0\\c)\ (x - 7)^2 = 0\)

4. Simplify:

\(\sf a)\ x = 0\ \textsf{[ already simplified ]}\)

\(\sf b)\ (x - 1)^2=0\ \textsf{[ take the square root of both sides ]}\\\\\sqrt{(x - 1)^2}=\sqrt{0}\\\\\Rightarrow x-1=0\ \textsf{[ add 1 to both sides ]}\\\\x-1+1=0+1\\\\\Rightarrow x=1\)

\(\sf c)\ (x - 7)^2=0\ \textsf{[ take the square root of both sides ]}\\\\\sqrt{(x - 7)^2}=\sqrt{0}\\\\\Rightarrow x-7=0\ \textsf{[ add 7 to both sides ]}\\\\x-7+7=0+7\\\\\Rightarrow x=7\)

Therefore, the zeros of this function are: 0, 1, and 7.

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Answer:

1. 11

2. 1

3. 4

4. 16

Step-by-step explanation:

Start with the number visiting all 3 spots, i.e. 10, this goes in the middle (the triple overlap zone);

Then, the number of those visiting two of the 3 spots less 10 will go into each dual overlap zone;

Finally, the total number of those visiting a single spot less anything in any overlap zone of that circle needs to go in the singular outer zone;

What this means is:

In the case of Coron:

10 visited Coron and the other 2 spots;

11 visited Coron and El Nido, but 10 of these also visited the Reef as well, leaving only 1 who visited just Coron and El Nido;

Similarly, 12 went to Coron and the Reef, 10 of these went to El Nido as well so just 2 visited only Coron and the Reef;

Then 24 in total visited Coron, 10 of these visited the two other spots as well, 1 visited Coron and El Nido and 2 visited Coron and the Reef;

So 13 (= 10 + 1 + 2) visited Coron and one or more of the other two spots, leaving 11 (=24 - 13) who visited Coron alone;

Do the same thing with El Nido and the Reef to get the answers to the other questions;

This is all represented in the Venn diagram shown;

The last question is calculated by summing all the values in each zone and subtracting the total from 50, which is the total number of students;

This gives 16.