The current on the Little River is 8 mph. Tom's
boat goes 15 mph in still water. How far upstream
can Tom's boat go on the Little River in 1.5 hours?
a) 12 miles
b) 25 miles
c) 10.5 miles
d) 34.5 miles

Answer:

8421/10000

Step-by-step explanation:

8421/10000

Answer: $402

Step-by-step explanation: I believe this answer is correct i did all the math

Answer:

i think it is 18

Step-by-step explanation:

because if he brought 6 for $18 and it was in sale for $3 that means there is no tax

Answer:

48 fl oz = 6 c

4 gal = 16 qt

Step-by-step explanation:

4 times 4 is 16

48 divided by 8 is 6

Considering the triangle given the variables are calculated to be

x = (5√6)/3

y = (10√6) / 3

Information given in the question

right angle triangle

The unknown variables is calculated using SOH CAH TOA

Definition of variables for the  right angle triangle

hypotenuse = y

opposite = 5√2

adjacent = x

The variable x is solved using tan, TOA, the angle is 60

tan 60 = Opposite / Adjacent

tan 60 = (5√2) / x

x = (5√2) / tan 60

x = (5√6)/3

The variable y is solved using sin, SOH, the angle is 60

sin 60 = Opposite / Hypotenuse

sin 60 = (5√2) / y

y = (5√2) / sin 60

y = (10√6) / 3

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The ratio of the areas of the similar figures is given as follows:

225/16.

Similar figures are figures that share these two features:

The ratio of the side lengths of the similar figures can be represented as follows:

(b/a).

The side length is measured in units, while the area is measured in units squared, hence the ratio of the areas of the similar figures is represented as follows:

(b/a)² = b²/a².

From the image of the right triangle shown at the end of the answer, the ratio of the side lengths is:

15/4.

Hence the ratio of the areas of the figures is given as follows:

(15/4)² = 225/16.

The figures are given by the image at the end of the answer.

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Answer:

Just add the 3 sides together

Step-by-step explanation:

if a triangle has the side values of 3, 4, 6. Then you would simply add them together!

3+4+6=13

therefor that triangles perimeter is 13

hope this helps!

Answer:

a) 1/11

b) 2/11

c) 0/11

d) 4/11

e) 9/11

Step-by-step explanation:

'MATHEMATICS' has 11 letters.

a) there is only one H out of the 11 letters meaning the probability is 1/11

b) there are two M s out of the 11 letters meaning the probability is 2/11

c) there is no B in the word meaning the probability is 0/11

d) there are four vowels (2 A s, 1 E and 1 I) out of the 11 letters meaning the probability is 4/11

e) there two A s in the word and 11-2=9 meaning the probability is 9/11

Hope this helps :)

The equations of both trees are Tree A = 38 + 6t and Tree B = 20 + 9t and the growth interval of tree A is t < 6

From the question, we have the following parameters that can be used in our computation:

Tree A

Tree B

The height after t years is

Tree = Initial height + rate * t

So, we have

Tree A = 38 + 6t

Tree B = 20 + 9t

Recall that

Tree A = 38 + 6t

Tree B = 20 + 9t

When Tree A is taller than Tree B, we have

38 + 6t > 20 + 9t

Evaluate the like terms

-3t > -18

Divide

t < 6

Hence, the interval is t < 6

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The required consecutive even integers are 66, 68, 70, and 72.

We have four integers. The integers are consecutive, that means the integers are one after the other. The integers are even, which means they are all divisible by two. The sum of these four even integers is 276.

Let the first even integer be represented by the variable "n". The next three consecutive integers are (n + 2), (n + 4), and (n + 6). Let the sum be denoted by "S".

S = n + (n + 2) + (n + 4) + (n + 6)

276 = 4n + 12

4n = 264

n = 66

Hence, the required integers are 66, 68, 70, and 72.

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The descending order to the list is 1, 4/5, 41%, -1.3, -7/4.

What us descending order?

When numbers are arranged from greatest to smallest or highest to lowest it is said to be in descending order.

Main Body:

To solve this question we need to convert all numbers into decimal system.

calculate:

1 can be written as 1.00

4/5 can be written as 0.8

-7/4 = -1.75

41% = 41/100 = 0.41

-1.3 can remain as it is because it itself is in decimal form.

Hence the order from greatest to smallest is as

1 > 0.8 > 0.41 > -1.3 > -1.75

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a) The current bond price (present value) is $420.03.

b) The percentage by which the price of bonds will increase between now (current) and maturity (18 years) is 138%.

The current bond price represents its present value.

The present value is the discounted future cash inflows.

We can compute the present value using an online finance calculator as follows:

N (# of periods) = 18 years

I/Y (Interest per year) = 12$

PMT (Periodic Payment) = $40 ($1,000 x 4%)

FV (Future Value) = $1,000

Results:

PV = $420.03

Sum of all periodic payments = $720.00

Total Interest = $1,299.97

Percentage increase in bond price = [(Future value - Present value)/Present value x 100]

= 138% [($1,000 - $420.03)/$420.03 x 100]

Thus, the present value of the bonds $420.03 will grow by 138% at maturity.

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The frequency distribution based on the information given is illustrated below.

What is the frequency distribution of table?

A frequency distribution table is the chart that summarizes all the data under two columns - variables/categories, and their frequency.

It should be noted that the distribution table has two or three columns and the first column lists all the outcomes as individual values or in the form of class intervals, depending upon the size of the data set.

Given the above information the frequency distribution table is:

Cost of living[tex]\begin{table}[]\begin{tabular}{ll}Cost of living & Number of States \\85.0 - 94.9 & 9 \\95.0 - 104.9 & 5 \\105.0 - 114.9 & 0 \\115.0 - 124.9 & 2 \\125.0 - 134.9 & 2 \\135.0 - 144.9 & 1 \\145.0 = 154.9 & 1 \end{tabular}\end{table}[/tex]   Number of states

85.0 - 94.9             9

95.0 - 104.9         5

105.0 - 114.9         0

115.0 - 124.9         2

125.0 - 134.9         2

135.0 - 144.9         1

145.0 - 154.9         1

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Answer: 78 ÷ 3 = 26

Step-by-step explanation:

     We are given that there are 3 groups shown. This means we will be dividing by 3.

     We are given that each group has 2 ten rods (20) and 6 ones cubes (6). This means the answer is 26.

     Lastly, 26 * 3 = 78, meaning we are dividing 78 by 3.

This gives us:

     78 ÷ 3 = 26

The function operation (f + g)(x) of the functions f(x) = √( 16x⁴ ) and g(x) = 3x² - 3x - 5 is -5x² + 5x - 7.

A function is simply a relationship that maps one input to one output.

Given the functions in the question;

To determine the function operation (f + g)(x), replace the function designators with the functions and simplify.

(f + g)(x) = f(x) + g(x)

(f + g)(x) = √( 16x⁴ ) + ( 3x² - 3x - 5 )

Replace √( 16x⁴ ) with 4x²

(f + g)(x) = 4x² +  3x² - 3x - 5

Collect and add like terms

(f + g)(x) = 7x² - 3x - 5

Therefore, the function operation (f + g)(x) is 7x² - 3x - 5.

Option A is the correct answer.

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Answer: $323,050

Step-by-step explanation:

355,000 over 1 x 9 over 100 = 3195000 over 100 (31950)

355,000- 31,950 = 323,050 which is your answer, hope this helped <3

The statement that shows the correct relationship between production cost and the number of golf balls produced is that the minimum production cost of 17.5 occurs when 35 golf balls are produced.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

Then the minimum is represented by the formula;

c - b² / 4a

We have given equation C(x) = 0.1x² - 7x + 140

a = 0.1

b = -7

c = 140

Now plugging in values to c - b² / 2a

= 140 - 7² / (4 * 0.1)

=  17.5

The minimum production cost will be; 17.5

Now plugging 35 into the given equation;

C(x) = 0.1x² - 7x + 140

C(x) = 0.1 ( 35)² - 7 (35) + 140

C(x) = 17.5

Therefore, 35 golf balls produce the minimum cost.

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Answer:

that the minimum production cost of 17.5 occurs when 35 golf balls are produced.

Step-by-step explanation:

Potential rational solution(s) to the above polynomial equation is ±1, ±2.

Actual rational solution are ±1, +2.

What is  polynomial equation?

Polynomial equations are those created using exponents, coefficients, and variables. The greater of its possible exponents is referred to as the equation's degree.

Main Body:

Given:

x³ - 2x² - x +2 = 0

We will use the Rational Root Theorem:

If the rational number r/s is a root of a polynomial whose coefficients are integers, then the integer r is a factor of the constant term, and the integer s is a factor of the leading coefficient.

So, if the constant therm is 2 and the leading factor is 1, candidates for roots are:

±1,±2

Dividing x³ - 2x² - x +2 = 0 by x-1, we get

x²-x-2 as quotient.

Splitting the middle term ,

⇒x² - 2x + x - 2

⇒x(x- 2) + 1(x-2)

⇒(x+1)(x-2)

so x= -1 , 2

Hence the rational solution to the equation are ±1, 2.

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Answer: 324

Step-by-step explanation: 10% is the same as 1/10

360/10 is 36

360-36= 324

meaning 324 students now attend Haley elementary school <3

hope this helps <33

In the equation 2[(4m * 3.5) / 400] = 171.5, the value of m is 2450

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation. It will be considered as an expression.

In the equation given;

2[(4m * 3.5) / 400] = 171.5

To solve for m, we have to expand the bracket and make m the subject of formula.

2[(4m * 3.5) / 400] = 171.5

2[14m/400] = 171.5

28m / 400 = 171.5

28m = 400 * 171.5

28m = 68600

m = 68600 / 28

m = 2450

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The minimum temperature in Salt Lake City in December is 5 degrees Fahrenheit.

The average December temperature in Salt Lake City, Utah, is 10 degrees Fahrenheit. The actual December temperature can vary in Salt Lake City by 5 degrees Fahrenheit either above or below the average.

We need to find out the minimum temperature in Salt Lake City in December. Let the temperature be denoted by the variable "M". The minimum temperature is the difference between the average temperature and the variation in the temperature.

M = 10 - 5

M = 5

Hence, the minimum temperature in Salt Lake City in December is 5 degrees Fahrenheit.

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By solving a linear equation, it can be calculated that

The space station is at a distance of 144000 miles from NASA headquarters

What is linear equation?

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Here, a linear equation needs to be solved

Let the space station be d miles from NASA headquarters

Speed of the first rocket = 19200 miles/hour

Speed of the second rocket = 18000 miles /hour

Time taken by the first rocket to reach the space station = [tex]\frac{d}{19200}[/tex]

Time taken by the second rocket to reach the space station = [tex]\frac{d}{18000}[/tex]

By the problem,

[tex]\frac{d}{18000} - \frac{d}{19200} = 0.5\\\\\frac{16d - 15d}{288000} = 0.5\\\\\frac{d}{288000} = 0.5\\\\d = 288000 \times 0.5\\\\d = 144000 \ miles[/tex]

The space station is at a distance of 144000 miles from NASA headquarters

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Simon bought a $48 table on sale. The price of the table can be estimated by $50.

The sale propose 30% off, then an estimate for the discount can be calculated using proportion:

$50 -- 100%,

$x -- 30%

that is mathematically

Find x:

Answer: correct choice is B

The markup price on the table would be $32.

So, we have:

Now, calculate the makeup price:

Mark-up price = Discount * Selling Price

Mark-up price = (28/100) * 114

Mark-up price  = 31.92

Mark-up price ≈ 32.

Hence, the markup price on the table would be $32.

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Answer: 15√11z

Step-by-step explanation:

The coordinate of point C will be (5, 5). Then the correct option is A.

Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have

x = (mx₂ + nx₁) / (m + n)

y = (my₂ + ny₁) / (m + n)

On a direction plane, the place of two companions can be characterized by the focuses A(1,3) and B(7,6). Their instructor is remaining at point C, and the educator's separation from point An is two times the separation from Point B.

The ratio is given as 2:1.

x = (7 × 2 + 1 × 1) / (2 + 1)

x = 15 / 3

x = 5

y = (6 × 2 + 1 × 3) / (2 + 1)

y = 15 / 3

y = 5

The coordinate of point C will be (5, 5). Then the correct option is A.

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