Write a unit rate for the situation.
Situation: 87 students in 3 classrooms
Unit rate:
students per classroom

Answer:

7^{2} + x^{2} = 16^{2}

49+x^2=256

x^2=207

x=14.387=14

Answer:

14 units

Step-by-step explanation:

To find the length of the other leg of a right triangle, where one leg is 7 units long and the hypotenuse is 16 units long, use Pythagoras Theorem.

Pythagoras Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the legs.  

Let the legs of the right triangle be "a" and "b", and the hypotenuse be "c". Therefore:

[tex]\begin{aligned}a^2+b^2&=c^2\\a^2+7^2&=16^2\\a^2+49&=256\\a^2+49-49&=256-49\\a^2&=207\\\sqrt{a^2}&=\sqrt{207}\\a&=14.3874945...\\a&=14\;\sf(nearest\;whole\;number)\end{aligned}[/tex]

Therefore, the length of the other leg is 14 units (rounded to the nearest whole number).

The measure of each exterior angles of a regular hexagon is 60  degrees

The interior angle of the regular polygon is

d = 180(n - 2) / n

Where d is the measure of interior angle

n is the number of sides

The number of sides in a regular hexagon

d = 180(6 - 2) / 6

= 180×4 / 6

= 720 / 6

=120 degrees

The each interior angle of the regular hexagon is 120 degrees

The measure of exterior angle = 180 - The measure of interior angle

= 180 - 120

= 60 degrees

Hence, the measure of each exterior angles of a regular hexagon is 60  degrees

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Answer:

The answer is 3.

Step-by-step explanation:

The highest coefficient is 3 (5x^3), the second one is 2 (4x), and the other two without coefficient are considered 1.

Answer:

The answer is w= -1

Step-by-step explanation:

4w + 2 + 0.6w = -3.4w - 6

4.6w + 2 = -3.4w - 6

8w + 2 = -6

8w = -8

w = -1

Answer:

==========================

First, compare the negative numbers as they are smaller than positives since negatives are to the left from zero on the number line and positives are to the right.

Since - 15 is smaller than - 6, the least number is - 3:

Now compare the positives.

Therefore:

The complete order is:

Answer:

-3 < -6/5 < 1/6 < √7 < 45

Step-by-step explanation:

Now the values will be,

→ 1/6 = 0.17

→ -3 = -3

→ √7 = 2.65

→ -6/5 = -1.2

→ 45 = 45

Let's arrange in ascending order,

→ -3, -1.2, 0.17, 2.65, 45

→ -3, -6/5, 1/6, √7, 45

Hence, number -3 comes first.

Answer:

yes for helena: not sure for edwin

Step-by-step explanation:

for helena, it would be a 270 cc rotation and then scale

for edwin, again im not sure, but it could be a refection and then scale

0.5  is the p-value for this Z -test .

What is the Z test's p-value?

For a lower tail test, the test statistic z is determined to be zero that means

P(z<0)

Then p-value is

p-value = P(z<0) = 0.5 (From z score table )

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50 mg be the expected mass of the sample in the year 2002, to the nearest whole number

In 1990, a sample of a radioactive isotope had an initial mass of 110 mg and decayed exponentially over time.

A measurement in 1993 revealed that the sample's mass had decayed to 90

110 mg - 90 mg = 20 mg (amount decayed in the 3 total years)

20 mg ÷ 3 years = 6.6 mg decayed per year

6.6 × 9 years (years between 1993 and 2002) = 60 mg

110 mg - 60 mg = 50 mg, rounded to 50 mg

50 mg be the expected mass of the sample in the year 2002, to the nearest whole number

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The correct equation is f(x) = 4x³ + 6x² − x .  A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.

The value of the function is f(x). The slope of the line is m. b is either the function's value at x=0 or the position at which the line in the coordinate plane crosses the y-axis. x is the x-value. This form is called the slope-intercept form.

The slope of a linear function is calculated by rearranging the equation to its general form, f(x) = mx + c; where m is the slope.

in question f(-2) = - 6

so x= -2

In function f(x) = 4x³ + 6x² - x

F(-2) = 4(-2)³ + 6 (-2)² - (-2) = - 6

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The distance between the light house and the farthest island is 68 miles

The distance between the light house and the farthest island can be calculated by using the distance formula

The distance formula is d=√((x2 – x1)² + (y2 – y1)²).

d=√((61 – (-7))² + (9 – 9)²)

d = √(61 +7)²

d = 68

If each unit on the graph represents 1 mile

There are 68 units in the graph, so the light house is 68 miles away the farthest island

Therefore, The distance between the light house and the farthest island is 68 miles

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The solutions of the given quadratic equation are

[tex]x = 3 \ or \ x = -\frac{1}{4}[/tex]

What is quadratic equation?

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

A two degree equation is known as Quadratic equation.

The given quadratic equation is

[tex]4x^2 - 11x - 3[/tex]

Now,

[tex]4x^2 - 11x - 3 = 0\\\\(2x)^2 - 2 \times 2x \times \frac{11}{4} + (\frac{11}{4})^2 - (\frac{11}{4})^2 -3 = 0\\\\(2x - \frac{11}{4})^2 = \frac{121}{16} + 3\\\\(2x - \frac{11}{4})^2 = \frac{121+48}{16}\\\\(2x - \frac{11}{4})^2 = \frac{169}{16}\\\\2x - \frac{11}{4} = \sqrt{\frac{169}{16}}\\\\2x - \frac{11}{4} = \pm\frac{13}{4}\\\\2x - \frac{11}{4} = \frac{13}{4} \ or \ 2x - \frac{11}{4} = -\frac{13}{4}\\\\2x = \frac{13}{4} + \frac{11}{4} \ or \ 2x = \frac{11}{4} - \frac{13}{4}\\\\[/tex]

[tex]2x = 6 \ or \ 2x = -\frac{1}{2}\\x = 3 \ or \ x = -\frac{1}{4}[/tex]

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The description of the motion of the ant which is a geometric series is as follows;

a) After covering 63/32 meters, the ant will have made 6 turns

b) The distance the ant will eventually travel is 2 meters

Geometric series is an infinite sum of terms in which the ratio between consecutive terms is a constant.

The distances traveled by the ant is a geometric progression of the form;

The sum of the distance is given by the sum of the geometric progression as follow;

[tex]S_n = \dfrac{a\cdot \left(1 - r^n \right)}{(1 - r)}[/tex]

Where;

aₙ = The distance traveled in the nth turn

Sₙ = The sum of the distances

a = The first term = 1 meter

r = The value of the common ratio = 0.5 meter ÷ 1 meter = 0.5

a) The number of turns the ant will have made after covering a distance of 63/32 meters is therefore;

[tex]S_n =\dfrac{63}{32} = \dfrac{1\times \left(1 - 0.5^n \right)}{(1 - 0.5)}[/tex]

31.5 = 32 × (1 - 0.5ⁿ)

32 × 0.5ⁿ = 32 - 31.5 = 0.5

0.5ⁿ = 0.5 ÷ 32

n = ln(0.5 ÷ 32) ÷ ln(0.5) = 6

b) The distance the ant travels eventually is given by the formula for the sum to infinity of a geometric progression as follows;

[tex]S_{\infty} = \dfrac{a}{1-r}[/tex]

Which gives;

[tex]S_{\infty} = \dfrac{1}{1-0.5} = 2[/tex]

The distance the ant eventually travels is 2 meters

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Answer:

9/4

Step-by-step explanation:

The proportion of American households who expect to buy a new car next year is[0.3191, 0.3609].

The Four answer choices:

[0.3152, 0.3648]

[0.3191, 0.3609]

[0.3394, 0.3406]

[0.3354, 0.3446]

According to the survey, 1,400 American households are expected to buy a new car next year. According to respondents, 34% plan on buying a new car next year.

The confidence interval for a population proportion is given by the following equation for large random samples

Sample proportion ± z × [tex]\frac{\sqrt{(sample proportion(1-sample proportion)}}{n}[/tex]

whereas z is a multiplier number that comes from the normal curve and determines the level of confidence.

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Let the speed of the small plane be 'R'.

Let the speed of the wind be 'S'.

Plane's time against wind = 2 hours and 10 minutes  = 13/6 hours.

Plane's time with wind = 1 hour and 50 minutes = 11/6 hours

Use formula;

Distance =  speed x time

Against the wind:

858 = (13/6) (R-S)  = (13/6) R - (13/6)S

With wind:

858 = (11/6)(R + S) = (11/6)R + (11/6)S  

Multiplies each by 6.

5148 = 13R - 13S

5148 = 11R + 11S

Use elimination method

56628 = 143R - 143S  (multiplies by 11)

66924 = 143R + 143S  (multiplies by 13)

Further solving;

123552 = 276R

R = 432 miles/ hr. (speed of small plane )

And,  S = 36 miles/ hr. (speed of wind)

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The rule in expressed in function notation and slope-intercept form of a line is f(x) = 3x -2

The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system

The equation of a line in slope-intercept form is y = mx + c.

Where m is the slope and c is the intercept

In order to obtain the equation of the line, we are going to pick any two convenient values of x and y from the table. Let's pick the first and last point. Thus:

point1: x₁ = 1, y₁  = 1

point2: x₂ = 4, y₂ = 10

Using the equation for 2 points:

y-y₁ / y₂-y₁ =  x-x₁ / x₂-x₁

y-1 / 10-1 = x-1 / 4-1

y-1 / 9 = x-1 /3

3(y-1) = 9(x-1)

y-1 = 3(x-1)

y-1 = 3x -3

y = 3x -3+1

y = 3x - 2

Thus, f(x) = 3x -2

Therefore, the rule in function notation, using the slope-intercept form of a line is f(x) = 3x -2

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5. Based on arc and central angle relationship, m∠BCD is: B. 108°.

6. The length of arc PQ is: H. 3.14 m

7. Length of CF is: A. 6 cm.

To find the length of an arc, the formula to use is:

Arc length = ∅/360 × 2πr

5. Measure of arc AB = 72°

Measure of arc BD = 180 - measure of arc AB

Measure of arc BD = 180 - 72

Measure of arc BD = 108°

Measure of angle BCD = measure of arc BD [central angle theorem]

Measure of angle BCD = 108°

The answer is: B. 108°

6. ∅ = 60°

r = 3 m

Arc length = 60/360 × 2 × π × 3

Arc length = 3.14 m

The answer is: H. 3.14 m

7. Since the distance between the two chords, AB and CD are equal, therefore, AB = CD.

AB = CD = 12 cm

CF = 1/2(CD)

CF = 1/2(12)

CF = 6 cm.

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We accept the null hypothesis, according to which the average amount of trash per bin is equal to 50.

acc to our question-

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Answer: 32130000

Step-by-step explanation:

Multiply all of your numbers

Answer: $372

Step-by-step explanation:

330 + (1.5% of 330) = 334.95

334.95 + (1.5% of 334.95) = 339.97425

339.97425 + (1.5% of 339.97425) = 345.073864

345.073864 + (1.5% of 345.073864) = 350.249972

350.249972 + (1.5% of 350.249972) = 355.503772

355.503772 + (1.5% of 355.503772) = 360.836392

360.836392 + (1.5% of 360.836392) = 366.248398

366.248398 + (1.5% of 366.248398) = 371.742124

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By using the concept of law of exponents,the required answers are: 5)  [tex]e^{-1} f^{-1}[/tex] and 8) [tex]b^{3}[/tex]

According to this law of exponents, exponents of numbers are added, subtracted, multiplied, and divided when numbers get multiply, divide, and number raised by another exponents.

Exponents are the power of numbers, which tells us how many time a number multiply by itself.

we have,

5)   [tex]\frac{ef^0}{e^2f}[/tex]

⇒  [tex]e^{1-2}f^{0-1}[/tex]

⇒  [tex]e^{-1} f^{-1}[/tex]

8)  [tex]a^{0}b^{6} b^{-3}[/tex]         ( [tex]a^{0}[/tex]=1 )

⇒  [tex]b^{6-3}[/tex]

⇒  [tex]b^{3}[/tex]

Hence, final answer are [tex]e^{-1} f^{-1}[/tex] and [tex]b^{3}[/tex]

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Step-by-step explanation:

[tex]\sf 12 \times \cfrac{12}{2} + 13[/tex]

First, let's divide 12 by 2:-

Multiply 12 × 6 :-

Add 72 + 13:-

Therefore, your answer is 85!!

____________________

Hope this helps!

Have a great day!!

Distance of Park bench from building is 275 m when  angle of depression  top of the building to a park bench on the ground.

What is the elevation and depression angle?

Angle of depression, θ = 54°

The height, h = 200

The distance of park bench from the building, d is given by

Tan θ = opposite / Adjacent

Tan 54  = d / 200

d = 200 * Tan 54

d =  200 *  1.3764

d = 275.28

D = 275 M

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large samples and small variance are combination of factors is most likely to produce a significant value  in standard deviation .

What is standard deviation?

t = x - μ/s/√n

t = √n( x- μ)/s

t will be significant when its value will be higher .

so, the answer is large samples and small variance .

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The total change in yards where the team started is 36 yards

The given parameters in the question are:

Yards per play = 4 yards

Number of plays = 9 consecutive plays

The total change in yards is the amount of yard per play multiplied by the number of plays

This is represented as

Total change = Yards per play * Number of plays

Substitute the known values in the above equation So, we have the following equation

Total change = 4 * 9

Evaluate

Total change = 36

Hence, the total change is 36 yards

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The expression, (–5.5 + 2p)(–2), after simplification is 11-4p.

According to the question,

We have the following expression:

(–5.5 + 2p)(–2)

Now, in order to simplify this expression, we will multiply -2 into the bracket:

(Note that when a number or a variable is multiplied into the bracket then it is multiplied into every number or term within the bracket.)

-5.5*-2+2p*(-2)

We know that when two negative integers are multiplied then the result is positive and when one negative and one positive integer is multiplied then the result is negative.

11-4p

Hence, the expression, (–5.5 + 2p)(–2), after simplification is 11-4p.

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The equivalent expressions are 7y + 2y+y and 10y & 8m-4m+4m and 8m.

Other expressions are not equivalent

Expressions 1

The expressions are given as

4(2a+7) and 8a +7

Open the brackets

8a+28 and 8a +7

The above expressions are not equal

Expressions 2

Here, we have

7y + 2y+y and 10y

Evaluate the like terms

10y and 10y

The above expressions are equal

Expressions 3

Here, we have

8m-4m+4m and 8m

Evaluate the like terms

8m and 8m

The above expressions are equal

Expressions 4

Here, we have

9e+2(e+5) and 11 +5

Open the brackets

9e+2e+10 and 11 +5

Evaluate the like terms

11e + 10 and 11 + 5

The above expressions are not equal

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