Using the word HIPPOPOTAMUS, match the items in the left column to the items in the right column
1 the ratio of P's to O's

2. the ratio of O's to other letters

3. the ratio of letters to P's

4. the ratio of vowels to consonants

5. the ratio of total letters to consonants

The right column has 3:2,12:7,1:5,5:7,4:1

The equation of the line in the slope-intercept form is: y = -2.00 x + 10.

The slope and provided point are both in the equation for the straight line.

The generic point (x, y) must satisfy the equation if we have a non-vertical land in a that passes through any point(x1, y1) has gradient m.

y-y₁ = m(x-x₁)

It is the necessary equation for a line in the form of a point-slope.

That gift card to the Coffee Café has been provided. = $10

Medium coffee = $2.00

customers

The quantity of coffees a consumer can purchase can be represented using a linear equation.

Slope formula

m = (8 - 10)/(1 - 0)

m = -2

Now consider the line's point-slope shape.

y-y₁ = m(x-x₁)

( y - 10) = -2.00 ( x - 0)

y = -2.00 x + 10

The slope: m = - 2.00

The equation of the line: y = -2.00 x + 10

The y-intercept is 10

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Answer: -3.11 x 10^ 1

Step-by-step explanation: - 3

3.11 X 10 = -31.1, in decimal form -3.11 x 10^ 1

I

The slope of the line through each pair of points (16,1), (17,7) is 6.

A line's slope serves as a gauge for its steepness. Between any two locations on the line, it is the ratio of the vertical change to the horizontal change.

The slope of a line can be positive, negative, zero, or undefined.

In algebraic equations, the letter "m" frequently stands in for slope. In slope-intercept form, a line's equation is written as y = mx + b, where m denotes the line's slope and b its y-intercept.

To find the slope of the line that passes through two points (x1, y1) and (x2, y2), you can use the following formula

m = (y2 - y1) ÷ (x2 - x1)

where m is the slope of the line and (x1, y1) and (x2, y2) are the coordinates of the two points.

In this case, the slope of the line through the points (16,1) and (17,7) is:

m = (7 - 1) ÷ (17 - 16) = 6 ÷ 1 = 6

So the slope of the line is 6.

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If motorboat 1 hour longer to travel 84 miles against the current than travel the same distance with the current.The speed of the current is 1 mph.the speed of the motorboat in still water is 13 mph.

What is linear equation?

A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane.

Let's denote the speed of the motorboat in still water by "s" (in mph).

When the motorboat is traveling with the current, its effective speed is the sum of its speed in still water and the speed of the current, so it covers the 84 miles in a time of:

t1 = 84 / (s + 1)

When the motorboat is traveling against the current, its effective speed is the difference between its speed in still water and the speed of the current, so it covers the same 84 miles in a time of:

t2 = 84 / (s - 1)

According to the problem statement, it took the motorboat 1 hour longer to travel against the current than with the current. Therefore, we can set up the following equation:

t2 - t1 = 1

Substituting the expressions for t1 and t2 from above, we get:

84 / (s - 1) - 84 / (s + 1) = 1

Multiplying both sides by (s - 1)(s + 1), we get:

84(s + 1) - 84(s - 1) = (s - 1)(s + 1)

Simplifying and solving for s, we get:

168 = s^2 - 1

s^2 = 169

s = 13 mph

Therefore, the speed of the motorboat in still water is 13 mph.

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If Cole brought 21 cans and his sister brought 7 cans less, then the total number of cans brought by them is 35 cans.

The number of cans which Cole brought = 21 cans of food.

His sister brought in 7 fewer cans than he did, which means she brought in:

⇒ 21 - 7 = 14 cans of food,

Let the total number of food-cans be = "f",

So, the equation to find the number of cans is written as :

⇒ x = 21 + 14,

On adding the number of cans,

We get,

⇒x =  21 + 14 = 35,

Therefore, together they brought in 35 cans of food.

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Answer:

0.7788 = 77.88% probability that more than three customers arrive in 10 minutes

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

\(f(x) = \mu e^{-\mu x}\)

In which \(\mu = \frac{1}{m}\) is the decay parameter.

The probability that x is lower or equal to a is given by:

\(P(X \leq x) = \int\limits^a_0 {f(x)} \, dx\)

Which has the following solution:

\(P(X \leq x) = 1 - e^{-\mu x}\)

The probability of finding a value higher than x is:

\(P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}\)

In this question, we have that:

The time between arrivals of customers at an automatic teller machine is an exponential random variable with a mean of 4 minutes, and we have three customers, which means that \(m = 3*4 = 12, \mu = \frac{1}{12} = 0.0833\)

(a) What is the probability that more than three customers arrive in 10 minutes

This is P(X > 3). So

\(P(X > 3) = e^{-0.0833*3} = 0.7788\)

0.7788 = 77.88% probability that more than three customers arrive in 10 minutes

Answer:

A)

\(\left \{ {{80} \atop {20}} \} * \left \{ {{60} \atop {20}} \} * \left \{ {{40} \atop {20}} \} * \left \{ {{20} \atop {20}} \}\)

B)

\(\left \{ {{20+4-1} \atop {4-1}} \} = \left \{ {{23} \atop {3}} \}\)

C)

= \(\left \{ {{17+4+1} \atop {4-1}} \} = \left \{ {{20} \atop {3}} \}\)

D)

= \(\left \{ {{20} \atop {3}} \} - \left \{ {{17} \atop {3}} \}\)

Step-by-step explanation:

A) How many ways can you put all Jellybeans in a row

Total number of Jellybeans = 80

The first jellybeans = 20 yellow , second is 20 orange jellybeans , third is 20 red jellybeans , fourth is 20 green jellybeans

Therefore the number of ways the Jellybeans can be put in a row is :

\(\left \{ {{80} \atop {20}} \} * \left \{ {{60} \atop {20}} \} * \left \{ {{40} \atop {20}} \} * \left \{ {{20} \atop {20}} \}\)

B) How many ways are there to select a handful of 20 jellybeans

lets assume:

yellow jellybeans = a , orange jellybeans = b , red jellybeans = c , green jellybeans = d

a + b + c + d = 20

This is the number Non-negative integer solutions

= \(\left \{ {{20+4-1} \atop {4-1}} \} = \left \{ {{23} \atop {3}} \}\)

C) This is also the number of Non-negative integer solutions but in this case the value of C ≥ 3

hence the number of ways to select a handful of 20 jellybeans that contains at least 3 red

= \(\left \{ {{17+4+1} \atop {4-1}} \} = \left \{ {{20} \atop {3}} \}\)

D) In this case the value of C ≥ 3 and B ≤ 2

Hence the number of ways to select a handful of 20 jellybeans that contains at least 3 red and at most 2 orange

= \(\left \{ {{20} \atop {3}} \} - \left \{ {{17} \atop {3}} \}\)

The correct option is B. The students knew whether or not music was playing while they were taking the exam

Given,

The class was split into two groups.

The first group took the midterm exam while background music was playing, and the second group took the exam without any background music.

In a blind experiment, any information that might affect the subjects is kept secret until the experiment is over. The pupils in this instance are aware of their group membership.

In order to answer this question, an experiment is carried out to see how music affects learning. One group of students studies while background music is playing, while the other group does not.

However, because of the background music playing here, the pupils are aware of which group they belong to. The experiment's outcomes are impacted by this.

Therefore the correct option is B. The students knew whether or not music was playing while they were taking the exam.

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Answer:

C. (2, -3)

Step-by-step explanation:

Easiest and fastest way to get the solution set is to graph the systems of equations and analyze where the graphs intersect.

Answer:

n=91

Step-by-step explanation:

(n×7)+2=100

n+9=100

-9 from both sides

n=91

Remember that

The Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than the measure of the third side

You only need to see that the two smaller sides are greater than the largest side

In this problem

we have

28,50,22

so

28+22 > 50

50 > 50 -----> is not true

therefore

Answer:

4/15

Step-by-step explanation:

2/5 drive

1/3 bus

and rest walk

fraction of those who walk is 1-(2/5+1/3)

2/5+1/3=(6+5)/15=11/15

15/15-11/15=4/15

Answer:

SAS

Step-by-step explanation:

Side:  AB ≅ BC

Angle:  ∠ABD ≅ ∠CBD

Side:  ΔABD and ΔCBD share BD, which is a side length

Answer:

  3024π square inches

Step-by-step explanation:

The surface area is the sum of ...

The relevant area formulas are ...

  A = πrs . . . . . lateral area of cone with radius r and slant height s

  A = 2πrh . . . . lateral area of cylinder with radius r and height h

  A = πr² . . . . . area of a circle of radius r

The radius is half the diameter, so is (36 in)/2 = 18 in. When we add up these areas, we can factor out a common factor to simplify the expression a bit.

  A = πrs +2πrh +πr²

  A = πr(s +2h +r) = π(18 in)(30 in +2(60 in) +18 in) = π(18)(168) in²

  A = 3024π in² . . . . surface area

Check the picture below.

so, to get the area of the object, we'll use the lateral area of a cone with a height of 30 and a radius of 18, and the lateral area of a cylinder with height of 60 and radius of 18, and sum those two up.

\(\stackrel{\textit{lateral area of a cone}}{\pi r\sqrt{r^2+h^2}}\implies \pi 18\sqrt{18^2+30^2}\implies 108\pi \sqrt{34} \\\\\\ \stackrel{\textit{lateral area of a cylinder}}{2\pi rh\implies 2\pi (18)(60)}\implies 2160\pi\)

\(\stackrel{\textit{area of the bottom circle of the cylinder}}{\pi r^2\implies \pi 18^2\implies 324\pi } \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{total area of the shape}}{108\pi \sqrt{34}+2160\pi +324\pi ~~\approx~~9782.1115~~\implies ~~\stackrel{\textit{rounded up}}{\boxed{9782~~in^2}}}\)12

Answer:

41x+16

Step-by-step explanation:

4x+2+3x-9+c=48x+9. You can move all the things you know to the other side.

c= 48x-4x-3x-2+18

c=41x+16

Answer:

The correct answer is 5.

Step-by-step explanation:

Step-by-step explanation:

Based on the information given, we have a diagram with two sides labeled as 13.3 mm and 5.5 mm, and another side labeled as X mm.

To find the length of X, we can use the fact that the sum of the lengths of the sides of a triangle is equal to the perimeter.

Perimeter = 13.3 mm + 5.5 mm + X mm

The perimeter is the total distance around the triangle. Since we have three sides, the perimeter is the sum of the lengths of those sides.

To find X, we can subtract the sum of the known sides from the perimeter:

X mm = Perimeter - (13.3 mm + 5.5 mm)

Since the value of X is not given, we cannot calculate it without the perimeter value. If you provide the perimeter value, I can help you find the length of X.

This shows that the measure of the central angle, in radians is within pi/2 to pi radians

The standard conversion of degrees to radians is given as:
180 degrees = πrad

Given the following degrees

theta = 125 degrees

Convert to radian

theta = 125/180π

Simplify

theta = 25/36π ras

This shows that the measure of the central angle, in radians is within pi/2 to pi radians

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Answer:

19

Step-by-step explanation:

4(4)+3

16+3=19

Answer:

19

Step-by-step explanation:

4x+3

4(4)+3

16+3

19

hope it helps

9514 1404 393

Answer:

  40°

Step-by-step explanation:

Since DP is an angle bisector, the angles it creates are congruent:

  ∠1 = ∠2 = 20°

The requested angle is the sum of the measures of angles 1 and 2:

  ∠FDE = ∠1 + ∠2 = 20° +20°

  ∠FDE = 40°

The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.

Let's assume the width of the rectangle is "b" cm.

According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.

The formula for the perimeter of a rectangle is given by:

Perimeter = 2 * (length + width)

Substituting the given perimeter value, we have:

7 1/3 cm = 2 * (2b + b)

To simplify the calculation, let's convert 7 1/3 to an improper fraction:

7 1/3 = (3*7 + 1)/3 = 22/3

Rewriting the equation:

22/3 = 2 * (3b)

Simplifying further:

22/3 = 6b

To solve for "b," we can divide both sides by 6:

b = (22/3) / 6 = 22/18 = 11/9 cm

Therefore, the width of the rectangle is 11/9 cm.

To find the length, we can substitute the width back into the equation:

Length = 2b = 2 * (11/9) = 22/9 cm

So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.

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Answer: (1/6)^2

Step-by-step explanation:

Answer:

The third answer is correct

Step-by-step explanation:

Use the properties of degrees:

1)

\( {( \frac{1}{108} })^{3} = \frac{ {1}^{3} }{ {108}^{3} } = \frac{1}{6561} \)

\( \frac{1}{6561} ≠ \frac{1}{36} \)

.

2)

\( ({ \frac{1}{9} })^{3} = \frac{ {1}^{3} }{ {9}^{3} } = \frac{1}{729} \)

\( \frac{1}{729} ≠ \frac{1}{36} \)

.

3)

\( ({ \frac{1}{6} })^{2} = \frac{ {1}^{2} }{ {6}^{2} } = \frac{1}{36} \)

\( \frac{1}{36} = \frac{1}{36} \)

Answer:

You read where the line start on the x axis first witch on you homework is positive 3 and then read the y axis witch for you is -4 so the answer should be (3,-4)

The following elements were included in the response: labeling x-axis as age, labeling y-axis as texting speed, plotting points according to age and texting speed, and identifying a relationship between texting speed and age.

In the response, the following elements were included:

1. Labeling the x-axis as the input variable, age: This is important to indicate the independent variable being plotted.

2. Labeling the y-axis as the output variable, texting speed: This is crucial to indicate the dependent variable being represented.

3  Plotting the points according to age and texting speed: This involves placing the ordered pairs (age, texting speed) on the coordinate plane, with age values on the x-axis and texting speed values on the y-axis.

4. Identifying a relationship between the change in texting speed as age increases: By analyzing the plotted points and examining the pattern or trend, one can determine if there is a relationship between age and texting speed. For example, if the texting speed generally increases as age increases or if there is a linear or nonlinear relationship between the two variables.

Including all of these elements allows for a comprehensive analysis of the relationship between age and texting speed, providing a visual representation and enabling the identification of any patterns or trends.

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Answer:

11 1/8

Step-by-step explanation:

Answer:

it's 11/8

Step-by-step equation:

you have eleven out of eight pizza slices

Answer:

it is AB+bc to the nearest 100

Step-by-step explanation:

it is divided by 2

Answer:

∠CDF = 48°

Step-by-step explanation:

∠CDE = ∠EDF + ∠CDF

Given that,

∠CDE = 114°

∠EDF = 66°

So, to find the value of ∠CDF, you have to subtract the value of ∠EDF from ∠CDE.

∠CDF = ∠CDE - ∠EDF

∠CDF = 114 - 66

∠CDF = 48°

Answer:

n = 12

Step-by-step explanation:

Given expression:

\(\dfrac{a^n}{a^3} = a^9\)

multiply both sides by a³

\(\dfrac{a^n}{a^3} \times a^3 = a^9 \times a^3\)

simplify following

\(a^n = a^9 \times a^3\)

apply indices law

\(a^n = a^{9+3}\)

simplify

\(a^n = a^{12}\)

compare powers

\(n = 12\)

Answer:

n = 12

Step-by-step explanation:

Given function:

\(\dfrac{a^n}{a^3}=a^9\)

\(\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:\)

\(\implies a^{n-3}=a^9\)

\(\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):\)

\(\implies n-3=9\)

Add 3 to both sides:

\(\implies n-3+3=9+3\)

\(\implies n=12\)

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