A number cube is rolled
twice. What is the probability
of getting a 6 on the first roll,
then a number less than 5
on the second roll?
A) 1/9
B) 2/3
C) 5/36
D 5/12
E) 1/36

Answer:

-1/1

Step-by-step explanation:

it's negative 1 over one because the graph is constantly going down but still to the right side and the line is touching every corner of the boxes

The radius of Deimos to one significant digit in meters is approximately 9.4 m

.

Given the ratio of the Sun-from-Mars distance to Deimos-from-Mars distance is 365,000, the distance between Mars and Deimos can be found to bedeimos distance = Sun-Mars distance / 365,000

Next, we can find the diameter of Deimos by noting that 550 of its diameters is equal to the distance it takes to transit the shadow of Mars during a lunar eclipse.

Let's call the diameter of Deimos "d", so we can

diameter = 1/550 * deimos distance

Finally, the Sun appears about 8.4 times as large as Deimos in the Martian sky. If we call the radius of Deimos "r", then the radius of the Sun is 8.4r.

Using the information given, we can set up the following equation:

deimos distance / (3,000,000 + r) = 8.4r / (3,000,000)Simplifying and solving for r,

we get:r = 9.39 m (rounded to one significant digit)

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The largest area of the rectangle is 6502.5 square feet.

Given that,

Using fence parallel to one of the rectangle's sides, a cattle rancher wants to surround a rectangular area and divide it into four pens (see the figure below). To finish the task, 510 feet of fencing are available.

We have to find what could the four pens' combined total area be.

We know that,

The rectangular shape's length is l and its width is b.

Total fencing= 2l + 5b=510 feet

2l +5b =510 feet

We can write as,

l=1/2(510-5b)

Total area of the rectangle is length into breath

A(b) = l × b

A(b) = 1/2(510-5b)×b

A(b)= 1/2(510b -5b²)

For maximum area

A'(b)=0

1/2(510b -5(2b))=0

b=51

We get l as

l = 1/2(510-5b)

l = 1/2(510-5(51))

l = 127.5

Total area of the rectangle is 127.5 × 51

Total area of the rectangle is 6502.5 square feet.

Therefore, The largest area of the rectangle is 6502.5 square feet.

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Answer:

120-90

=30

the change in stock price is $30 per share

Answer:

21

Step-by-step explanation:

Set it up as 7/4 x 12/1.  Multiply the numerators and denominators.  That equals 84/4 which simplifies to 21.

Answer:

the answer is B

Step-by-step explanation:

Answer:

adults = 52

children = 108

Step-by-step explanation:

two equations can be derived from the question

x + y = 160 equation 1

2x + 5y = 476   equation 2

x = number of children

y = number of adults

multiply equation 1 by 2

2x + 2y = 320  equation 3

subtract equation 1 from 2

3y = 156

y =52

substitute for y in equation 1

x + 52 = 108

x = 160 - 52 = 108

The work done in pulling the rope to the top of the building is 57960 foot-pounds.

Mass of the rope = weight/g Gravity on Earth is 9.8 m/s² or 32.2 ft/s², mg = weight g , W = Fd where W is work, F is force, and d is displacement or distance. A force is needed to lift the rope from the ground to the top of the building. The mass of the rope can be determined as follows: m = (0.6 lb/ft) x 30 ft ⇒m = 18 lbs. The force needed to lift the rope from the ground to the top of the building can be determined using F = mg⇒ F = (18 lb) x (32.2 ft/s²)⇒F = 579.6 lb. The displacement is the vertical height that the rope is lifted over: d = 100 fts = 579.6 lb x 100 ft⇒W = FdW = (579.6 lb) x (100 ft)W = 57960 foot-pounds. Thus, the work done in pulling the rope to the top of the building is 57960 foot-pounds.

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ANOVA is appropriate because the independent variable is categorical and has three classes. The dependent variable is continuous, so ANOVA can be used to determine if there is a significant difference between the means of the three groups.

There are many different types of statistical tests that can be used to analyze data. When choosing a statistical test, it is important to consider the type of data that is being analyzed. In this case, the researcher is looking at an independent variable that is categorical and has three classes. The dependent variable is continuous. In this situation, the best test to use is an analysis of variance (ANOVA).

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Answer:

so what you would do is take length time width or 25*25 to find area

Step-by-step explanation:

The dimensions of the package of maximum volume that can be sent are approximately 7.8 inches in radius and 21.3 inches in height.

Let's assume that the package has a height 'h' and a radius 'r'. The perimeter of the cross-section of a cylinder is the circumference of the circle plus the height multiplied by two, which can be written as:

Perimeter = 2πr + 2h

Given that the maximum combined length and circumference is 114 inches, we can write:

2πr + 2h + 2r = 114

Simplifying this equation, we get:

πr + h = 57 - r ----(1)

The volume of the cylinder is given by:

\(V = πr^2h\)

Now, we can use equation (1) to eliminate 'h' from the volume equation:

\(V = πr^2(57 - r - πr)\)

Expanding and simplifying this equation, we get:

\(V = πr^3 - π^2r^3/3 + 57πr^2 - 57π^2r\)

To find the dimensions of the package that maximize the volume, we need to find the value of 'r' that maximizes the volume. We can do this by taking the derivative of the volume equation with respect to 'r' and setting it equal to zero:

\(dV/dr = 3πr^2 - π^2r^2 + 114πr - 57π^2 = 0\)

Solving for 'r', we get:

r ≈ 7.8 inches

Substituting this value of 'r' back into equation (1), we can find the value of 'h':

h ≈ 21.3 inches

Therefore, the dimensions of the package of maximum volume that can be sent are approximately 7.8 inches in radius and 21.3 inches in height.

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The given angles are vertical and have a measure of 75°. The value of the angle (4x-25)° is also 75°, and the value of x is 25.

The given angles are vertical angles, which means they are opposite angles formed by the intersection of two lines.

Vertical angles are always congruent, which means they have the same measure. Hence, we can set the two given angles equal to each other and solve for the value of x. 75° = (4x-25)°

Adding 25 to both sides, we get: 100° = 4x

Dividing both sides by 4, we get: x = 25 Hence, The value of the angle (4x-25)° is: (4x-25)° =

\((4 \times 25-25)°\)

= 75°

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Bad things do happen to good people, is the story's central theme or premise.

H.H. Munro, a British novelist who wrote under the pen name Saki, examines the issues of pride, moral instruction, and inappropriate conduct for kids during the Edwardian era in his book "The Storyteller." In his short stories, Saki cherished satirizing upper society. Pride comes before a fall is the idea that the bachelor's story in "The Storyteller" best illustrates.

Thus, among the available possibilities, the third is the one that is correct. The "aunt," who struggles to give her nieces and nephews a tale that will amuse them while also imparting a valuable lesson, would be the story's protagonist. The aunt's tale has as its main message that doing kind often pays off.

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The length of arc BC is 8/3 feet.

To find the length of arc BC, we first need to find the measure of angle BOC, where O is the center of the circle. Since angle BAC is 1/3 of one radian, and the central angle BOC intercepts the same arc BC, we know that angle BOC is three times angle BAC, or one radian.

Since the radius of the circle is 8 feet, the circumference is 2πr, or 16π feet. Since angle BOC is one radian, it subtends an arc on the circumference that is 1/2 of the total circumference, or 8π feet.

Therefore, the length of arc BC is 1/3 of arc BOC, or 8π/3 feet.

To find the length of arc BC, we will follow these steps:

1. Identify the given information: The radius of the circle is 8 feet, and the angle BAC is 1/3 of a radian.

2. Determine the central angle in radians: Since angle BAC is 1/3 of a radian, the central angle (θ) of the circle that corresponds to arc BC is also 1/3 of a radian.

3. Calculate the length of arc BC using the formula: Arc length (L) = radius (r) × central angle (θ).

In this case, r = 8 feet and θ = 1/3 radian.

L = 8 × (1/3)
L = 8/3

4. Simplify the expression: L = 8/3 feet.

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The required new price of the shirts and pair of paints is given as y = [s - 10]/2 and y = [2p]/2 respectively,

Given that,
At a store, a shirt was marked down in price by $10.00. A pair of pants doubled in price. Following these changes, the price of every item in the store was cut in half.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
let y be the total cost for each different item
cost of the shirt = s - 10 and pair of pants = 2p
According to the question,
y = s - 10 / 2  and y = 2p / 2

Thus, the required new price of the shirts and pair of paints is given as y = [s - 10]/2 and y = [2p]/2 respectively,

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The equation of the graphed function is given as follows:

f(x) = x³ + 2x² - 5x - 6.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

From the graph, the zeros of the function are:

Hence the function is:

f(x) = a(x + 3)(x + 1)(x - 2).

In which a is the leading coefficient.

Expanding the product, we have that:

f(x) = a(x² + 4x + 3)(x - 2)

f(x) = a(x³ + 2x² - 5x - 6).

When x = 0, y = -6, hence the leading coefficient a is obtained as follows:

-6a = -6

a = 1.

Hence the function is:

f(x) = x³ + 2x² - 5x - 6.

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Answer:

Yes

Step-by-step explanation:

If you do 17/2.49 is 6.8

6.8 * 6 is 40.8

With 19 students 40.8/19 is  2.1, which rounded down would just be 2

So yes

Answer: No

Step-by-step explanation:

At $2.49, $17 can buy 6 packs of cookies. There are six packs of 6 cookies so 36 cookies.

36/19= 1.89

So no, She cannot provide her 19 students with 2 cookies each.

Answer:

pi/8 + k(pi/2)

Step-by-step explanation:

2x=t

sint - cost = 0

sint/cost - cost/cost = 0

tant = 1

t= pi/4 + k(pi) = 2x

x = pi/8 + k(pi/2)

[0;2pi]

x= pi/8

x= pi/8 + pi/2 = 5pi/8

x= 9pi/8

x= pi/8 + 3pi/2 = 13pi/8

Answer:

(-6,-4)

Step-by-step explanation:

The mean weight can be calculated by summing up the recorded weights of the 16 small bags of candies and dividing the sum by 16. The mean weight represents the average weight of the sampled bags.

To determine the mean weight of the small bags of candies from the sample, we need specific information about the recorded weights. However, assuming that the population distribution of bag weights is normal, we can calculate the mean weight by taking the average of the recorded weights in the sample. Without the specific data, it is not possible to generate an exact answer to the mean weight.

In this scenario, the mean weight can be calculated by summing up the recorded weights of the 16 small bags of candies and dividing the sum by 16. The mean weight represents the average weight of the sampled bags. However, since we don't have the recorded weights or any additional information about the sample, we cannot generate a specific answer for the mean weight. The calculation of the mean weight requires the actual weights of the bags from the sample.

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Answer:y=10

Step-by-step explanation:u see the right side numbers increase by 7

The steps that are used to solve the above equation by substitution include the following:

1.) X = 11 + 2y

2.) -7 ( 2y + 11) -2y = -13

3.) -14y -77- 2y = -13

4.) -16y - 77 = -13

5.) -16y = 64

6.) y= -4

7.) X = 2(-4) + 11 --> X = 3

8.) (3, -4)

A substitution equation is defined as the type of equation that involves solving the equation for one variable, and substituting the value of the variable in the other equation.

The given equation is as follows;

-7x -2y = -13

X - 2y = 11.

To solve for X the following is done;

X = 2y + 11

Substitute X = 2y + 11 into equation 1

-7 ( 2y + 11) -2y = -13

Multiple out to open the brackets;

= -14y -77- 2y = -13

= -16y - 77 = -13

= -16y = 64

= y= -4

Then substitute y = -4 into equation two as follows;

X = 2(-4) + 11

X = 3

Therefore, y = -4, while X = 3 that is ( 3,-4)

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He can buy 5 candy at most with this inequality 2c-3<9 as the inequality will result in c<6 as the definition of inequality says, "In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another".

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another. The equation-like form of the expression 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. This shows that the left part, 5x 4, is bigger than the right part, 2x + 3. The greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), and not equal to symbol () are the five inequality symbols. Take the same amount away from both sides. Add the same positive number to both sides. Subtract the same positive number from both sides. Reverse the sign and multiply both sides by the same negative number.

Here,

2c-3<9

add 3 both side,

2c-3+3<9+3

2c<12

divide both side by 2,

c<6

According to the definition of inequality, "In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another," he can only purchase a maximum of 5 candies with the inequality 2c-3<9.

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First let's find how many kilometers the jeep traveled, by subtracting the odometer readings:

Now, to find the miles per gallon, we just need to divide the kilometers by the amount of gallons of gasoline:

So Harry got 17.8 miles per gallon with the Jeep.

Answer:

−103

Step-by-step explanation:

Answer:

Step-by-step explanation:

Convert the given equation into slope-intercept form:

The slope is -2, the y-intercept is 2/3

Correct choice is A

⇒ 3(y - 2) + 6(x + 1) - 2 = 0

⇒ 3y - 6 + 6x + 6 - 2 = 0

⇒ 3y = -6x + 2

⇒ y = (-6x + 2)/3

⇒ y = -2x + ⅔

Slope = -2

Y - intercept = +⅔

Option (a) is the correct answer .

Answer:

h = 20 cm

Step-by-step explanation:

Base Area = 18 cm * 5 cm = 90 cm²

Volume = 600 cm³

Arranging the formula for h:

h = \(\frac{3(Volume)}{base Area}\)

h = \(\frac{3(600)}{90}\)

h = \(\frac{1800}{90}\)

h = 20 cm

Answer:

A

Step-by-step explanation:

The triangles are the same. Congruent is when all three sides are equal to each other on both triangles

Answer: 13x

Step-by-step explanation: Multiply x to 11 and 2

11x+2x=13x