Math 7 Review:Question 4
A car used 15 gallons of gasoline when driven 315 miles. Based on this
information, which expression should be used to determine the unit rate of
miles per gallon of gasoline?
Select one:
15 gallons
315 miles
O
315 miles x 15 gallons
O
315 miles
15 gallons
O
315 miles - 15 gallons

Answer:

96.25%

Step-by-step explanation:

The empirical rule regarding mean and standard deviation is that

Therefore between mean and +2 standard deviation or between mean and -2 standard deviation you will find  approximately 95/2 = 47.5% of the values

Between mean and ± 3 standard deviations you will find approximately 97.5/2 = 48.75% of the values

Therefore between 2 standard deviations above and 3 standard deviations below you will find approximately 47.5 + 48.75 = 96.25% of values

The probability of a prime number or a number greater than 3 coming up is given as follows:

5/6.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

When a dice is thrown, there are six possible outcomes, ranging from 1 to 6, and the desired outcomes are given as follows:

Hence the probability is given as follows:

5/6.

Learn more about the concept of probability at https://brainly.com/question/24756209

#SPJ1

Answer:

Step-by-step explanation:

21 : 14

Both have 7 in common

3 : 2

So Option C 21 : 14 is the correct answer

The approximate value of the solution to the equation e' = 120 is e ≈ 120.the value of e by rounding it to a Reasonable number of Decimal places.

The given equation is e' = 120, where e represents some variable.

To solve for e, we can start by dividing both sides of the equation by the coefficient of e, which is 1:

e' / 1 = 120 / 1

Simplifying the right-hand side, we get:

e' = 120

This means that the value of e is equal to 120. So the solution to the equation e' = 120 is e = 120.

To find the approximate value of e, we can use a calculator to evaluate the expression. Since e is a variable, we cannot substitute it directly into the calculator. However, we can estimate the value of e by rounding it to a reasonable number of decimal places.

In this case, since e' is given as 120, we can assume that e is also in the same units. So we can round e to the nearest whole number:

e ≈ 120

Therefore, the approximate value of the solution to the equation e' = 120 is e ≈ 120.

To know more about Decimal places.

https://brainly.com/question/28393353

#SPJ11

Answer:

bru i can barely do my own work right fr

Step-by-step explanation:

The function f ( x ) = 2 x² + 5 will have the value 23 for f (- 3).

We are given the function:

f ( x ) = 2 x² + 5

We need to find the value of f ( -3 ).

We will do this by substituting the value of x = - 3 in the function and then evaluating the expression.

Putting x = -3 in the function, we get that:

f ( x = - 3 ) = 2 (- 3)² + 5

Solving the square, we get that:

f (- 3) = 2 ( 9 ) + 5

Simplifying the expression, we get that:

f (- 3) = 18 + 5

f (- 3) = 23

Therefore, we get that, the function f ( x ) = 2 x² + 5 will have the value 23 for f (- 3).

Learn more about function here:

https://brainly.com/question/4025726

#SPJ9

Answer:

$67.932

Step-by-step explanation:

6.8% of $999 is $67.932. The total would be $1066.932 Pls Brainly Thx!

Answer:

We can use the formula for compound interest to solve this problem. The formula is:

A = P * (1 + r/n)^(n*t)

where:

A = the amount of money after t years

P = the principal amount (the initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, P = $5000, r = 0.03, n = 12 (since the interest is compounded monthly), and t = 10. Plugging these values into the formula, we get:

A = 5000 * (1 + 0.03/12)^(12*10)

A = 5000 * (1.0025)^120

A ≈ $6,621.36

So the investment will be worth approximately $6,621.36 after 10 years.

Answer:

vertical

Step-by-step explanation:

When two lines intersect, 4 angles are formed. Two non-adjacent angles are called vertical angles.

Answer: vertical

Answer:

Vertical

Step-by-step explanation:

Just did the lesson and checked the answer key :D

Let y be a solution to the given differential equation,

\(y' = xy\)

where

\(\displaystyle y = \sum_{n=0}^\infty c_n x^n \\\\ y' = \sum_{n=0}^\infty nc_nx^{n-1} = \sum_{n=1}^\infty nc_nx^{n-1} = \sum_{n=0}^\infty (n+1)c_{n+1}x^n\)

Substituting these series into the DE gives

\(\displaystyle \sum_{n=0}^\infty (n+1)c_{n+1}x^n = x\sum_{n=0}^\infty c_nx^n \\\\ \sum_{n=0}^\infty (n+1)c_{n+1}x^n = \sum_{n=0}^\infty c_nx^{n+1} \\\\ \sum_{n=0}^\infty (n+1)c_{n+1}x^n = \sum_{n=1}^\infty c_{n-1}x^n \\\\ c_1 + \sum_{n=1}^\infty (n+1)c_{n+1}x^n = \sum_{n=1}^\infty c_{n-1}x^n \\\\ c_1 + \sum_{n=1}^\infty \bigg((n+1)c_{n+1}-c_{n-1}\bigg)x^n = 0\)

Then the coefficients \(c_n\) in the series solution are governed by the recurrence,

\(\begin{cases}c_0 = c_0 \\ c_1 = 0 \\ (n+1)c_{n+1}-c_{n-1} = 0&\text{for }n\ge1\end{cases}\)

We have

\((n+1)c_{n+1}-c_{n-1} = 0 \implies nc_n - c_{n-2} = 0 \implies c_n = \dfrac{c_{n-2}}n\)

so it follows that \(c_1=c_3=c_5=\cdots = 0\), while

\(c_0 = \dfrac{c_0}1 = \dfrac{c_0}{2^0\times0!} \\\\ c_2 = \dfrac{c_0}2 = \dfrac{c_0}{2^1\times1!}\\\\ c_4 = \dfrac{c_2}4 = \dfrac{c_0}{2\times4} = \dfrac{c_0}{2^2\times2!}\\\\ c_6 = \dfrac{c_4}6 = \dfrac{c_0}{2\times4\times6} = \dfrac{c_0}{2^3\times3!}\)

and so on, with the general n-th coefficient being

\(c_n = \begin{cases}0&\text{if }n\text{ is odd} \\ \dfrac{c_0}{2^{n/2}\left(\frac n2\right)!} &\text{if }n\text{ is even}\end{cases}\)

Then the power series solution is

\(\displaystyle y(x) = c_0 \sum_{n=0}^\infty \frac{x^n}{2^{n/2}\left(\frac n2\right)!} = c_0 \sum_{n=0}^\infty \frac1{\left(\frac n2\right)!} \left(\frac x{\sqrt2}\right)^n\)

but this doesn't tell the whole story because it doesn't capture the odd-index-is-zero case.

More concisely: let n = 2k for integers k ≥ 0. Then

\(\displaystyle y(x) = c_0 \sum_{k=0}^\infty \frac{x^{2k}}{2^k k!} = c_0 \sum_{k=0}^\infty \frac1{k!} \left(\frac{x^2}2\right)^k\)

and as a bonus, it's easier to get an exact solution for this DE,

\(y(x) = c_0e^{x^2/2}\)

Answer:

No. it's less than. The bigger the negative number is, the lesser it is.

Answer:

Step-by-step explanation:

$2,350

30% of $2,350 is $705

$2,350-$705=$1,645

After the first year, you can sell it for $1,645

$1,645

30% of $1,645 is $493.5

$1,645-$493.5=$1151.5

After the second year, you can sell it for $1151.5

$1151.5

30% of $1151.5=$345.45

$1151.5-$345.45=$806.05

After the third year, you can sell it for $806.05

$806.05

30% of $806.05=$241.815

$806.05-$241.815=$564.235

After four years, you can sell it for $564.235

Round it up to the nearest dollar:

$564.

Answer:

$43.87

Step-by-step explanation:

Elijah has decided to lease her car for  years. She will be earning lease rental on the car along with interest. The interest charges on the lease rentals is amortized at the lease interest rate. The lease interest rate for the vehicle is decided to be 41%.

Year 1 : $20,000 * 41% * 0.045 * .025 = $18.20

Year 2 : ($20,000 - $18.20) * 41% * 0.045 * 0.25 = $25.67

The sum of year 1 and year 2 is $43.87.

Answer:

Below

Step-by-step explanation:

Find unit rate (since it starts at 0,0)

at 45 seconds  it is 900 bottles

             900 bottles / 45 seconds = 20 bottle / sec

20 bottles / sec * 80 sec = 1600 bottles

The statements that are true are:

When a class interval is expressed as "100 - 199," the following statements are true:

The class interval is equal to 99: False

The class interval "100 - 199" represents a range of values from 100 to 199. The difference between the upper and lower limits of the interval is 199 - 100 = 99, not equal to 99.

The number 100 is included in this class interval: True

The lower limit of the class interval is 100, and the interval includes all values greater than or equal to 100. Therefore, 100 is included in this class interval.

The number 200 is included in this interval: False

The upper limit of the class interval is 199, and the interval includes all values less than 199. Therefore, 200 is not included in this class interval.

The class interval is equal to 100: False

The class interval "100 - 199" represents a range of values from 100 to 199. The interval spans a range of 100 units (199 - 100 = 99), but it is not equal to 100 itself.

Learn more about normal distribution here:

https://brainly.com/question/29509087

#SPJ1

The value of g(h(10)) is 2√2. the correct option is A.

Given that the functions are g(x)=√x-4 and h(x)=2x-8.

A function is defined as the relationship between a set of inputs where each input has an output.

Firstly, we will find the value of h(10) by substituting x=10 in the function h(x)=2x-8.

h(10)=2(10)-8

h(10)=20-8

h(10)=12

Now, we will find g(h(10)) where h(10)=12.

By substituting h(10)=12 in g(h(10)), we get

g(h(10))=g(12).

Further, we will find g(12) by substituting x=12 in the function g(x)=√x-4, we get

g(12)=√(12-4)

g(12)=√8

g(12)=2√2

Hence, the value of function g(h(10)) when g(x)=√x-4 and h(x)=2x-8 is 2√2.

Learn more about the function from here brainly.com/question/24160317.

#SPJ9

Answer:

r = 8

Step-by-step explanation:

Solve for r:

r + 4 = 12

Subtract 4 from both sides:

r + (4 - 4) = 12 - 4

4 - 4 = 0:

r = 12 - 4

12 - 4 = 8:

Answer: r = 8

Answer:

73

Step-by-step explanation:

on a numberline, 25 is in the negative place so add 25 to get it to 0. you wanna get to 48 so you add 48. add 25 with 48 and you get 73

The polynomial of degree 3 with zeros at x = 3, x = -4, and x = 5 is P(x) = x^3 - 4x^2 - 17x + 60.  

To construct a polynomial of degree 3 with zeros at x = 3, x = -4, and x = 5, we can use the fact that the polynomial can be written as a product of linear factors corresponding to each zero.

The factor corresponding to x = 3 is (x - 3).

The factor corresponding to x = -4 is (x + 4).

The factor corresponding to x = 5 is (x - 5).

To obtain the polynomial, we multiply these factors together:

P(x) = (x - 3)(x + 4)(x - 5)

Expanding this expression gives us:

\(P(x) = (x^2 - 3x + 4x - 12)(x - 5)\)

\(= (x^2 + x - 12)(x - 5)\)

\(= x^3 - 5x^2 + x^2 - 5x - 12x + 60\)

\(= x^3 - 4x^2 - 17x + 60\).

For similar question on polynomial.

https://brainly.com/question/2833285  

#SPJ11

The total surface area of the square based solid pyramid is 384 sq.cm.

A square pyramid in geometry is a pyramid with a square base. It is a right square pyramid with C4v symmetry if the apex is perpendicular to and above the square's center. It is an equilateral square pyramid if all edge lengths are equal.

Given that, the area of the base is = 144 sq. cm.

Then the length of the side of the square base is:

a = √144 = 12 cm.

The vertical heigh = 8 cm.

Then the slant height is calculated using the Pythagoras Theorem:

c² = a² + b²

l² = b² + h²

Here, b = 1/2 a = 1/2(12) = 6cm

l = √(6)² + (8)²

l = 10 cm

The total surface area of the square pyramid is given as:

SA = a² + 2al

Substituting the values we have:

SA = 144 + 2(12)(10)

SA = 384 sq.cm

Hence, the total surface area of the square based solid pyramid is 384 sq.cm.

Learn more about pyramid here:

https://brainly.com/question/17615619

#SPJ1

Answer:

0.0319

Step-by-step explanation:

To approximate this probability, we shall be using the Bernoulli approximation of the Binomial distribution.

Let p = probability of selecting a reference book = 65% = 0.65

Let q = probability of selecting other books= 1-p = 1-0.65 = 0.35

Now, we want to find the probability that all of these 8 books to be re-shelved are reference book.

We set up the probability as follows;

P(X = 8) = 8C8 •p^8•q^0

P(X = 8) = 1 * (0.65)^8 * (0.35)^0

P(X = 8) = 0.031864481289 which is 0.0319 to 4 decimal places

three receivers Jerry Rice Larry Fitzgerald Randy Moss are comparing catch yards at the end of their careers. Jerry Rice has 5,476 more yd than Larry Fitzgerald. Moss has 2127 less yards than Larry Fitzgerald. the three receivers combined have 55,606 yards. how many yards does Jerry Rice have?​

Let

x -----> the number of yards that Jerry Rice has

y -----> the number of yards that Larry Fitzgerald has

z ----> the number of yards that Randy Moss has

we have that

x=y+5,476 ------> equation A

z=y-2,127 ------> equation B

x+y+z=55,606 -------> equation C

substitute equation A and equation B in equation C

(y+5,476)+y+(y-2,127)=55,606

solve for y

3y+3,349=55,606

3y=52,257

y=17,419 yds

Find the value of x

x=y+5,476

x=17,419+5,476=22,895

therefore

the answer is

The sequence is decreasing as n increases and sequence converges to the value 0.

The given sequence is defined as aₙ = 1 / (7n + 3).

To determine if the sequence converges or diverges, we need to analyze its behavior as n approaches infinity.

As n increases, the denominator 7n + 3 also increases which means that the values of aₙ will get smaller and smaller, approaching zero as n becomes larger.

The sequence converges to the value 0.

The sequence is decreasing as n increases.

The sequence converges to the value 0.

To learn more on Sequence click:

https://brainly.com/question/21961097

#SPJ1

Answer:

1. x = 4.5

2. x = 0.75 or x = -4.5

Explanation:

The quadratic formula says the solutions of the equation with the form ax² + bx + c are:

So, if the equation is 4x² - 36x + 81, the value of each constant is

a = 4

b = -36

c = 81

Then, the solutions are

It means that this equation has a unique solution x = 4.5

In the same way, if we have the equation 8x² + 30x = 27, we first need to subtract 27 from both sides, so:

8x² + 30x - 27 = 27 - 27

8x² + 30x - 27 = 0

Now, we can identify the values of a, b, and c.

a = 8

b = 30

c = -27

Therefore, the solutions of the equation are

So, the solutions for each quadratic equation are:

1. x = 4.5

2. x = 0.75 or x = -4.5

Answer:

18%, 0.18, .24, 2/7

Step-by-step explanation:

It's quite simple actually. Try to put them in one format.

For example, decimals:

18% - .18

2/7 - .28 (or 0.28571428571)

.24 - .24

.18 - .1818  (or .1818181818...)

Put them together:

.18, .28, .24, .1818

And re-arrange them.

.18, .1818, .24, .28

From here you can revert them to their original format.

18%, .18, 0.24, 2/7

Hoped this helped!

Answer:

76 cm cubed

Step-by-step explanation:

2 x 2 x 4 = 16 cm cubed

3 x 4 x 5 = 60 cm cubed

The given expression is

1. The expression has three terms. 3y, -5x, and 4. Remember that terms are those expressions separated by a sign.

2. The coefficients of the expressions are 3, and -5. Remember that a coefficient is a number that multiplies a variable.

Answer:

y-4x-7.

HOPE ITS HELPSS

Answer:

length+ width=36

length×width=323

length=19cm

width=17cm

19×17=323

19+17=36