What is the value of x in the triangle?
3 square root 2
x

The only force is free fall. Mass is not relevant and there is no air resistance

If a die is rolled 60 times, then it will land on number three 8 times.

When a die was rolled 60 times.

The die landed on one 11 times, two on 9 times, on four 12 times, on five 12 times, and on six 8 times.

Now, we know a die has six sides with numbers 1,2,3,4,5, and 6 marked on it.

Let x be the number of times the die landed on 3.

The total number of times the die rolled = the sum of the number of times each number landed when rolled.

number times 1 landed + number times 2 landed + number times 3 landed + number times 4 landed + number times 5 landed + number times 6 landed = 60

11 + 9 + x + 12 + 12 + 8 = 60

52 + x = 60

Subtracting 52 from each side of the equation,

52 + x - 52 = 60 - 52

x = 8

Hence, the number of times that three rolled is 8.

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The proportion of flour, water, sugar and butter required in the batter are 21, 9, 6 and 3 cups respectively

In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six. Similarly, the ratio of lemons to oranges is 6:8 and the ratio of oranges to the total amount of fruit is 8:14.

In this given question, we can find the value of each ingredient;

The cups of flour required is

[tex]7:3:2:1 = 7 + 3 + 2 + 1 = 13\\\frac{7}{13} * 39 = 21 cups[/tex]

The cups of water required is

[tex]\frac{3}{13}*39 = 9 cups[/tex]

The cups of sugar required is

[tex]\frac{2}{13}* 39 = 6 cups\\[/tex]

The cups of butter required is

[tex]\frac{1}{13}*39 = 3 cups[/tex]

The number of cups of flour, water, sugar and butter required are 21, 9, 6 and 3 cups respectively.

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Given data:

Total number of paperweights that needs to be packed in boxes = 1,150

Each box will hold paperweights = 12

Boxes will be needed to hold all the paperweights ,

Boxes = Total number of paperweights / Each box will hold paperweight

= 1,150 / 12

= 95.833

= 96

Thus, the boxes needed to hold all the souvenir paperweights is 96.

Answer

T' = (5, -1)

I' = (5, -3)

E' = (1, -1)

Explanation

Given the below triangle

T = ( -5, -1)

I = (-5, -3)

E = (-1, -1)

When reflected over y -axis, the x - cordinate is negated while the y - coordinate remains unchanged

Mathematically,

(x , y ) ------------------------ (-x , y)

T = ( -5, 1)

T' = [-(-5) , -1)]

T' = (5, -1)

I = (-5, -3)

I' = [-(-5) , -3)

I' = (5, -3)

E = (-1, -1)

E' = [-(-1), -1)]

E' = (1, -1)

Therefore, the reflected triangle over y - axis has the following points

T' = (5, -1)

I' = (5, -3)

E' = (1, -1)

The solution to the indicated operation will be 9 and 2/3.

We have to find the sum of 2 and 1/6 and 7 and 3/6.

We can write the mixed fractions as:-

2 and 1/6 = 13/6

7 and 3/6 = 45/6

Adding the improper fractions, we get,

(13+45)/6 = 58/6 = 29/3

We can this improper fraction write it as :-

9 and 2/3

Mixed fraction

It is a form of a fraction which is defined as the ones having a fraction and a whole number.

2 and (1/7), where 2 is a whole number and 1/7 is a fraction.

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The five number summary is:

Minimum = 3

First quartile(Q1) =3

Median =7

Third quartile(Q3) = 22

Maximum = 25

Given data, 6, 5, 3, 3, 25, 22, 3, 23, 7, 3, 20, 19, 23, 18, 5.

 we have  to arrange in ascending order ,

3, 3, 3, 3, 5, 5,6, 7, 18, 19, 20, 22, 23, 23, 25

Minimum value = 3

Maximum value = 25

since , number of data = 15

So , Median = middle term = 7

Median of first half = First quartile

here first half = { 3, 3, 3, 3, 5, 5, 6}

median of first half terms = 3 (middle term)

Q1 = 3

Third quartile = Median of second half terms

( 18, 19, 20, 22, 23, 23, 25)

median of second half  terms = 22

Q3 = 22

Hence, the five-number summary for the given data set :

min = 3, Q1 =3,  median =7 , Q3 = 22, max = 25 .

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the investment after 3 years will be worth $73.21

Amount invested = Principal

P = $55

n = number of time scompounded = annually

n = 1

rate = r = 10% = 0.1

FV = future value after 3 years

Using compound interest formula:

substituting the values in the formula:

Hence, the investment after 3 years will be worth $73.21

a) The cost of 1 cup coffee will be $2

b) The cost of 1 muffin will be $1.67

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The cost of a cup of coffee is $0.75 more than a donut.

Maya buys 12 donuts and 2 cups of coffee which costs $19.

Now,

Let the cost of coffee = x

And, The cost of donut = y

The cost of muffins = z

Since, The cost of a cup of coffee is $0.75 more than a donut.

So, we can formulate;

⇒ x = y + 0.75    .... (i)

And, Maya buys 12 donuts and 2 cups of coffee which costs $19.

So, We can formulate;

⇒ 12y + 2x = $19

Substitute the value of first equation in above equation we get;

⇒ 12y + 2x = $19

⇒ 12y + 2 (y + 0.75 ) = $19

⇒ 12y + 2y + 1.5 = $19

⇒ 14y + 1.5 = $19

⇒ 14y = $19 - 1.5

⇒ 14y = 17.5

⇒ y = 17.5 / 14

⇒ y = 1.25

Hence,

⇒ x = y + 0.75

⇒ x = 1.25 + 0.75

⇒ x = 2

Thus, The cost of 1 cup of coffee = $2

Since, Angelo buys 6 donuts and 2 muffins which costs $12.50 total.

So, we can formulate;

6z + 2y = $12.50

Substitute y = 1.25 in above equation, we get;

6z + 2 × 1.25 = $12.50

6z + 2.50 = 12.50

6z = 12.50 - 2.50

6z = 10.00

z = 10.00 / 6

z  = 1.67

Thus, The cost of 1 muffin will be $1.67.

Therefore,

a) The cost of 1 cup coffee will be $2

b) The cost of 1 muffin will be $1.67

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Let n be the integer. Then, we can write the following equation

which is equal to

We can solve this quadratic function by applying the quadratic formula:

where in our case a=1, b=1 and c= -90. By substituting these values into the last formula, we get

then, we have

Then, the first solution is

and the second solution is

Then, we have the following solutions:

- Negative integer: n= - 10

- Positive integer: n=9

Probability is calculated as follows:

In a standard deck of cards, there are 13 hearts and a total of 52 cards. Then, the probability of picking a heart is:

To find how many times she should expect to pick a heart, we have to multiply the number of times the event is repeated (60) by the probability of picking a heart, that is,

She should expect to pick a heart 15 times

A "Bisector" in Geometry is a line that divides a line into two different or equal parts. It is used on line segments and angles.

The Value of X  = angle BCF =90-45 =45.

Angle BCD = 90

angle FCD = 45

The Value of X  = angle BCF =90-45 =45.

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1) Examining the expressions, let's factorize them taking the LCM out of the parentheses

5a +10 The LCM 5,10 is 5

5(a +2)

16k +12 The LCM 16, 12 is 4

4(4k +3)

2) So the answers are 5(a +2) and 4(4k +3) notice that if we distribute those factors you'll get the initial form.

Answer:

wait do you need all the answers to it

Explanations;

Let the number of pots be "x"

Let the number of buckets be "y"

Since we have 192 items, hence;

x + y = 192 ............................... 1

If Pitts bought pots for 5 dollars each and joe bought buckets for 7dollars each and spent 140 dollars, this can be expressed as:

5x + 7y = 140 ............................ 2

Solve the equations simultaneously to get the value of x and y:

x + y = 192 ............................... 1 * 7

5x + 7y = 140 ............................ 2 * 1

_________________________________________________

7x + 7y = 1344

5x + 7y = 140

Subtract

7x - 5x = 1344 - 140

2x = 1204

x = 1204/2

x = 602

This shows that 602 pots were bought.

Substitute x = 602 into the equation 1 to get y:

602 + y = 192

y = 192 - 602

y = -410

Since the y value cannot be negative, we can say that 602 pots were bought but the solution to the system of equation is (602, -410)

Given:

Data is given as below

16 ; 17 ; 19 ; 20 ; 20 ; 21 ; 23 ; 24 ; 25 ; 25 ; 25 ; 26 ; 26 ; 26 ; 27 ; 27 ; 28 ; 29 ; 29 ; 32 ; 33 ; 33 ; 34 ; 35 ; 37 ; 39 ; 43

Find:

we have to find Mean, Median and Mode of the given data.

Explanation:

(a) Mean is 27.37

(b) Median is 26

(c) Mode is 25 ; 26

SOLUTION:

Step 1:

In this question, we are meant to find the x-intercept and y-intercept of the graph of :

First, we are meant to graph it

Second, we are meant to find:

a) x-intercept

b) y - intercept

Step 2:

The graph of :

is as follows:

Step 3:

Given the equation:

Next, given the equation:

Given:

Required:

To find the range of the function (uv)(x).

Explanation:

We know that

The horizontal asymptote of this function is at y=3.

So, the range of this function is from

Final Answer:

The range of (uv)(x) is

Given:-

water level rises 11 centimeters every 6 minutes.

To find:-

The y value at the point (18,y).

Considor the time as x axis and the water level as y axis. so we get an graph as,

Now to find the value at the point (18,y). we extend the graph,

So the value of y is 33.

This is our required answer.

The probabilities in this problem are given as follows:

a) False positive: 0.0321 = 3.21%.

b) Diagnosed as not having diabetes: 0.8872 = 88.72%.

c) Actually has diabetes, if diagnosed as not having: 0.0019 = 0.19%.

Conditional probability is the probability of one event happening, considering a previous event. The formula is given as follows:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which the parameters are described as follows:

For item a, we have that:

Hence the probability of a false positive is given as follows:

p = 0.9177 x 0.035 = 0.0321 = 3.21%.

For item b, the percentage of people who is not diagnosed as having diabetes is divided as:

Hence the probability is:

P(A) = 0.965 x 0.9177 + 0.02 x 0.0823 = 0.8872 = 88.72%.

For item c, we find the conditional probability, as follows:

[tex]P(A \cap B) = 0.02 \times 0.0823 = 0.001646[/tex]

Then:

P(B|A) = 0.001646/0.8872 = 0.0019 = 0.19%.

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Answer:

A line segment AE is part of a line that goes from A to E, so we can make a line m such that it contains line segment AE as follows

Line segment AE is the red part of the line that goes from A to E.

H0 : p0 = 0.12

H1 : p0 ≠ 0.12

Sample size, n = 600 ; α = 0.05

Zstatistic < Zcritical ; reject H0

P = 95/600 = 0.16

Zstatistic = (p - p0) ÷ sqrt((p0(1 - p0)) /n)

Zstatistic = (0.16 - 0-12)/ sqrt((0.12(0.88))/600)

Zstatistic = 3.01

Zcritical at 0.05, = - 1.96

Zstatistic > Zcritical

Answer:

C

Step-by-step explanation:

Answer:

are made of cells

Step-by-step explanation:

The equation of line is D. y = 3x - 9

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The m is a common symbol for slope.

The equation of a straight line is given by y=mx+c where m is the slope, c is the intercept, and x and y are variables.

Formula to be used :

[tex]m=\frac{y_{1}-y_{2} }{x_{1} -x_{2} }[/tex] where( y1,x1) and (y2 ,x2) are the coordinates of the points passing through the line.

Calculating Slope, [tex]m=\frac{3-(-3)}{4-2} =\frac{6}{2} =3[/tex]

Now, writing the equation of line is

[tex]y -y_{1} =m(x-x_{1} )\\y -3 =3(x-4)\\y-3 =3x - 12\\y =3x -12+3\\y =3x -9[/tex]

Thus, the slope-intercept form of the equation is y =3x -9.

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The equation of the polynomial is P(x) = -(x - 1)²(x + 5)(x - 4)

The given parameters are

The equation of the polynomial can be calculated as

P(x) = a * (x - zero)^ multiplicity

So, we have

P(x) = a * (x - 1)² * (x + 5) * (x - 4)

This gives

P(x) = a * (x - 1)²(x + 5)(x - 4)

From the question, we have

y-intercept = 20

This means that

P(0) = 20

So, we have

20 = a * (0 - 1)²(0 + 5)(0 - 4)

Evaluate products

20 = a * -20

Divide

a = -1

Substitute a = -1 in P(x) = a * (x - 1)²(x + 5)(x - 4)

P(x) = -(x - 1)²(x + 5)(x - 4)

Hence, the equation is P(x) = -(x - 1)²(x + 5)(x - 4)

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Solution.

Given that the fabric sample is in a shape of a circle

The answer is 221.558 ft^2

The equation of line passing through the point (-2 , 11) and (1, -4) will be;

⇒ y = - 5x + 1

What is Equation of line?

The equation of line in slope - intercept form is defined as;

⇒ y = mx + b

Where, m is slope

And, b is y - intercept.

Given that;

Two points on the line are (-2 , 11) and (1, -4).

Now, Equation of line is calculated as;

Slope of the line (m) = (- 4 - 11) / (1 - (-2))

                               = - 15/ 3

                               = - 5

The equation of line is;

⇒ y - y₁ = m (x - x₁)

Substitute all the values we get;

⇒ y - 11 = - 5 (x - (-2))

⇒ y - 11 = - 5 (x + 2)

⇒ y - 11 = -5x - 10

⇒ y = - 5x - 10 + 11

⇒ y = - 5x + 1

Thus, The equation of line passing through the point (-2 , 11) and (1, -4) will be;

⇒ y = - 5x + 1

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Given:

To state the domain of this using interval notation, means to find the values which x may assume for the function above.

We have:

Since there is a root, let's exclude any real number that leads to a negative number.

Here, let's solve for x by setting the radicand to be greater than or equal to zero.

x + 1 ≥ 0

x ≥ 0 -1

x ≥ -1

Therefore, the domain function using notation function will be:

(-1, ∞)

ANSWER:

(-1, ∞)

12°C above zero -----> means

0°C+12°C=12°C

answer is