A line passes through the points (0,5) and (3,6). What is its equation in slope-intercept
form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answer:

(c) \(f_{X}(x)=\left \{ {{\frac{1}{35-25}=\frac{1}{10};\ 25<X<35} \atop {0;\ Otherwise}} \right.\)

(b) The probability that time taken by Ayesha to prepare breakfast exceeds 33 minutes is 0.20.

(c) The probability that cooking or preparation time is within 2 mins of the mean time is 0.40.

Step-by-step explanation:

The random variable X follows a Uniform (25, 35).

(a)

The probability density function of an Uniform distribution is:

\(f_{X}(x)=\left \{ {{\frac{1}{B-A};\ A<X<B} \atop {0;\ Otherwise}} \right.\)

Then the probability density function of the random variable X is:

\(f_{X}(x)=\left \{ {{\frac{1}{35-25}=\frac{1}{10};\ 25<X<35} \atop {0;\ Otherwise}} \right.\)

(b)

Compute the value of P (X > 33) as follows:

\(P(X>33)=\int\limits^{35}_{33} {\frac{1}{10}} \, dx \\\\=\frac{1}{10}\cdot\int\limits^{35}_{33} {1} \, dx \\\\=\frac{1}{10}\times [x]^{35}_{33}\\\\=\frac{35-33}{10}\\\\=\frac{2}{10}\\\\=0.20\)

Thus, the probability that time taken by Ayesha to prepare breakfast exceeds 33 minutes is 0.20.

(c)

Compute the mean of X as follows:

\(\mu=\frac{A+B}{2}=\frac{25+35}{2}=30\)

Compute the probability that cooking or preparation time is within 2 mins of the mean time as follows:

\(P(30-2<X<30+2)=P(28<X<32)\)

                                      \(=\int\limits^{32}_{28} {\frac{1}{10}} \, dx \\\\=\frac{1}{10}\cdot\int\limits^{32}_{28}{1} \, dx \\\\=\frac{1}{10}\times [x]^{32}_{28}\\\\=\frac{32-28}{10}\\\\=\frac{4}{10}\\\\=0.40\)

Thus, the probability that cooking or preparation time is within 2 mins of the mean time is 0.40.

1. The rate that Brand A is selling for is A) 10-unit rate.

2. The unit rate of Brand A is $0.10 per pound.

The unit rate refers to the variable cost per unit or the quotient of a division operation.

The unit rate shows a value's ratio in relation to another.

To compute the unit rate, we can use the division operation that makes the denominator the dividend, which is divided by the numerator (or divisor).

The quantity in Brand A = 20 pounds

The quantity in Brand B = 60 pounds

Cost of Brand A = $2

Cost of Brand B = $5

The unit rate for Brand A = $2/20 = $0.10, which can also be expressed as 10 units for $1 (20/$2).

Likewise, the unit rate for Brand B = $5/60 = $0.83, which we can describe as 12 units for $1 (60/$5).

Thus, we can conclude that the rate at which Brand A is selling is Option A.

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Answer Options:

A) 10-unit rate

B) 12-unit rate

C) 9-unit rate

D) 8-unit rate

Answer:

x=3

Step-by-step explanation:

Answer: x=3

Step-by-step explanation:

First, you need to subtract x and x by itself, and do the same with the 3x. Your equation should now look like 6 = 2x. Now, divide each side of the equation with 2, and now your equation should look like 3 = x!

-----------------------

So, to double check, replace the x's with 3. The equation should be 3 + 6 = 3(3). If you do the math, it equals 9 = 9!

Answer:

21 square feet

Step-by-step explanation:

In this answer, I have attached an image.

I have split the figure into two parts, A and B.

Area of A: \(6ft \times 2ft= 12\ square\ feet\)

Area of B: \((5ft-2ft)\times 3ft=3ft\times 3ft = 9\ square\ feet\)

Total Area: \(12\ square\ feet+9\ square\ feet=21\ square\ feet\)

Answer:

Step-by-step explanation:

You want the vertex and another point on the parabola f(x) = 2x² -12x +11.

The equation can be put into vertex form as follows:

  f(x) = 2(x² -6x) +11 . . . . . . . factor the leading coefficient from the variable terms

  f(x) = 2(x² -6x +9) +11 -2(9) . . . . add (6/2)² = 9 inside parentheses, subtract the same amount outside

  f(x) = 2(x -3)² -7 . . . . . . . . simplify to vertex form

Comparing this to the vertex form equation ...

  f(x) = a(x -h)² +k

we see that a=2, h=3, k=-7.

The vertex is (h, k) = (3, -7). This is one point on the parabola.

We can use a value for x that is near the value of h to obtain another point on the parabola without much work. Using x = 4, we have ...

  f(4) = 2(4 -3)² -7 = 2(1) -7 = -5

Another point is (x, y) = (4, -5).

You can plot the vertex (3, -7) and the point (4, -5) to obtain your graph of the parabola using the parabola tool.

__

Additional comment

The points and the parabola are shown in the attached graph.

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Answer:

4%

Step-by-step explanation:

to solve this you need to subtract 156-150=6

then take 6 divided by 150 which is 0.04

then take 0.04x100=4

Answer:

4%

Step-by-step explanation:

156 divided by 150 = 1.04, which equals 4%

1. It is false that when non-Standard unit used is small few unit's are

needed .

2. Objects with different shapes can have the same volume. True

3. Length, width and height and multiplied to find volume of a rectangular prism. True

4. It is false that volume is measured in square unit.

5. It is true that Volume is a measure of the amount of space inside an object.

6. The formula for volume of a rectangular prism is V = l × w × h. True

7. It is true that Standard units give a consistent and accurate measure of a container.

8. It is false that Non-Standard units cannot be used to measure volume.

9. Volume is measured in cubic units. True

Volume can be defined as the amount of space inside and object. the object can be in different form such as cone, rectangular prism, cylinder and many other shapes. Even though shapes are different, It is possible for different shapes or objects to have the same volume when measure.

Measurement of volume can be through standard measurement and non standard measurements such as a cup of rice. However, for consistency and the sake of accuracy, it is advisable to always use standard measurements of volume where possible to avoid error that may occur in non standard measurement. The acceptable and recognized unit of volume is cubic meter (\(m^3\)).

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The values of x for which f(x) = 7 are x = 61 and x = 21.

To find the values of x for which f(x) = 7, we can set up the equation and solve for x.

The given function is f(x) = 0.5|x - 41| - 3.

Setting f(x) equal to 7, we have:

0.5|x - 41| - 3 = 7.

First, let's isolate the absolute value term:

0.5|x - 41| = 7 + 3.

0.5|x - 41| = 10.

To remove the absolute value, we can consider two cases:

Case: (x - 41) is positive or zero:

0.5(x - 41) = 10.

Multiplying both sides by 2 to get rid of the fraction:

x - 41 = 20.

Adding 41 to both sides:

x = 61.

So x = 61 is a solution for this case.

Case: (x - 41) is negative:

0.5(-x + 41) = 10.

Multiplying both sides by 2:

-x + 41 = 20.

Subtracting 41 from both sides:

-x = -21.

Multiplying both sides by -1 to solve for x:

x = 21.

So x = 21 is a solution for this case.

Therefore, the values of x for which f(x) = 7 are x = 61 and x = 21.

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Answer:

AD=25cm

Step-by-step explanation:

BC//AD

XY is also parallel to BC and AD as it bisects BA and CD.

BX=XA, CY=CD

so tge decreasing in length BC to XY is the same with XY to AD

29-27=2

27-2=25

That is why AD= 25cm

Answer:no idea

Step-by-step explanation:

Answer:

Cantaloupe = $6, peach=$5

Step-by-step explanation:

\(8x+3y=63\\2x+3y=27\\\)

Subtract the first one from the second one

\(8x-2x+3y-3y=63-27\\6x=36\\x=6\\\)

Plug in:

\(2(6)+3y=27\\12+3y=27\\3y=15\\y=5\)

Hope this helps plz hit the crown :D

Answer:

100°

Step-by-step explanation:

a + b = 140° because the sum of two interior angles in a triangle is equal to an exterior angle

Since this triangle is isosceles, which means QP = QR we can find the value of b as 40° because its supplementary to 140° that means the value of a = 140 - 40 = 100°

Answer:

a = 100°

Step-by-step explanation:

This is an isosceles triangle, so angle b = angle c:

140° is an angle outside the triangle. We need the angle in the triangle:

180 - 140 = 40°

angle b = 40°

Total sum of angles in a triangle: 180°

180° = a + b + c

Find a:

= a + 40° + 40°

a = 180° - 80°

a = 100°

Result

-224 + 2x + 2x^2

Answer:

You can find the area of a sector of a circle if you know the angle between the two radii. A circle has a total of 360 degrees all the way around the center, so if that central angle determining a sector has an angle measure of 60 degrees, then the sector takes up 60/360 or 1/6, of the degrees all the way around.

Step-by-step explanation:

That's the answer

The measure of each angle in the given circle is 120°.

A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.

Th given circle is divided into 3 equal parts.

We know that, central angle of circle measures 360°.

Now, each angle measures =360/3

= 120°

Therefore, the measure of each angle in the given circle is 120°.

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Answer: 13 + 2x = 63 and the cost of one ticket is $25 (x=25)

Step-by-step explanation:

Build the equation from what it tells you.

The entire trip costs $63

The concert ticket that is included costs $13

Two passes cost the same amount, use x for what you don't know, 2x.

So,  13 + 2x = 63.

Find x = cost one pass.

13 + 2x = 63

-13.          -13

      2x= 50

    2x/2= 50/2

     x= 25

Answer:

The solutions to the equation 9 + 6/x = x + 10 are x = -3 and x = 2.

Step-by-step explanation:

To solve the equation 9 + 6/x = x + 10 for x, we can follow these steps:

Subtract 9 from both sides of the equation to isolate the 6/x term:

6/x = x + 1

Multiply both sides of the equation by x to eliminate the fraction:

6 = x^2 + x

Rearrange the equation into standard quadratic form:

x^2 + x - 6 = 0

Factor the quadratic:

(x + 3)(x - 2) = 0

Use the zero product property to find the solutions:

x + 3 = 0 or x - 2 = 0

x = -3 or x = 2

Therefore, the solutions to the equation 9 + 6/x = x + 10 are x = -3 and x = 2.

Travis' famous letter, addressed to "The People of Texas and All Americans in the World," in which he passionately appealed for reinforcements and vowed to "never surrender or retreat," has become a symbol of the fortitude and sacrifice displayed by the Texan defenders at the Alamo.

The commander of the Texan forces at the Alamo during the famous battle in 1836 was Colonel William B. Travis. Travis, a lawyer and soldier, was chosen as the leader of the Texan garrison at the Alamo, a former mission turned fortress in San Antonio, Texas. He assumed command of the Texan forces in early 1836 and played a crucial role in the defense of the Alamo against the Mexican army led by General Santa Anna.

Travis and his men, along with notable figures such as James Bowie and Davy Crockett, bravely defended the Alamo against overwhelming odds for thirteen days. Despite their courage and determination, the Texan defenders were ultimately overrun by the Mexican forces on March 6, 1836, and suffered heavy casualties, including the deaths of Travis, Bowie, and Crockett.

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Answer:

5x-60=x - solution,..........

Answer:

Answer:

5x +60/x -15x +15/x-20

60/x+15/x-15x+5x-20

75/x-10x-20

is your answer

combined liked terms by adding and subtracting.

The angle measures for this problem are given as follows:

The sum of the measures of the internal angles of a triangle is of 180º.

The triangle in this problem is ABC, hence the measure of a is obtained as follows:

a + 68 + 50 = 180

a = 180 - (68 + 50)

a = 62º.

c and d are corresponding angles to angle a, as they are on the same position relative to parallel lines, hence their measures are given as follows:

Angle b is a corresponding interior angle with angle a, hence they are supplementary and it's measure is given as follows:

a + b = 180

62 + b = 180

b = 118º.

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Answer:

w < 1.5

Step-by-step explanation:

We solve these almost identical to solving equations. By going backwards in the process.

14 - 12.5 = 1.5

w < 1.5

Hope this helps!

Answer:

eight hours long to operate

By interpretating the graph of a quadratic equation, the initial height of the ball is equal to 5 feet above ground.

In this problem we must determine the initial height of the ball according to a graph, whose form resembles quadratic equations. Graphically speaking, the initial height is the y-coordinate of the y-intercept. First, the coordinates of the y-intercept of the equation are:

(t, h) = (0 s, 5 ft)

Second, the final height of the ball is equal to:

h = 5 ft

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Answer:

2x

Step-by-step explanation:

You're dividing 14 multiplied by a number by 7 multiplied by a number. So you'd get 2 multiplied by a number.

Answer:

72 minutes

Step-by-step explanation:

in minutes,

1/90 + 1/x = 1/40

x = 72

Answer:

6

Step-by-step explanation:

Area of sq:

A = bh

A = (2)(2)

A = 4

Area of triangle:

A = 1/2bh

A = 1/2(2)(2)

A = 2

Combined:

4 + 2 = 6

Answer:

3x + y^3 z

3×x+y×y×y×z

there is common 1

1(3×x+y×y×y×z)

factor =1,&(3x+y³z)

Answer:

compound interest

Step-by-step explanation:

compound interest yields higher profit than simple interest

Answer:

the simple interest function will be greater in the beginning, but the

compound interest equation will overtake the simple after a while.

it appears that the 4% compound equation will overtake the simple at about 10 years

Step-by-step explanation:

\(1 + .05t = 1(1.04)^t\)

Answer:

{x,y}={8,5}

Step-by-step explanation:

12x + 12y = 156  4x + 6y = 62