A fair six-sided die is rolled. Find the probability of getting at least a 2.

The number of minutes to read is 6.25 pages and taking the test will be 5 minutes and 0.50 minutes, respectively.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

It takes you 0.8 of a minute to read each page of your health book. It takes you 5.5 minutes to take the test at the end.

The number of minutes to read 6.25 pages will be given as,

⇒ 6.25 x 0.8

⇒ 5 minutes

The number of minutes to take the test will be given as,

⇒ 5.5 - 5

⇒ 0.50 minute

⇒ 0.50 x 60

⇒ 30 seconds

The number of minutes to read is 6.25 pages and taking the test will be 5 minutes and 0.50 minutes, respectively.

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Answer:

0, it has no solution.

Step-by-step explanation:

The equation given is

We multiply the "3/5" with both F and G following the distributive property,

Now we take the term with "G" to one side and solve with the rules of algebra. We isolate G:

We dividing by a fraction, we can multiply by its reciprocal. It doesn't change anything.

So, further simplifying, we have:

Answer:

7.5 days

Step-by-step explanation:

7.5 days because it is 30 percent off then the the sale decreases 20 percent making it 10% off and if the price is 75 you'd have to divide it by 10 and you would get 7.5 days

Answer: 50% of young adults between the ages of 18 and 24 drink coffee

Step-by-step explanation:

50/100= 50% of young adults between the ages of 18 and 24 drink coffee

Answer: 50%

Step-by-step explanation:

The equations that has the solution x = all real numbers is 5(3x)+ 7x = 3x + 15 - x and 5(3x) + 7x = 3x + 10 - x,

Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.

A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.

Here given equations,

5(3x) + 6x = 3x + 15 + 2x

15x + 6x = 3x + 15 + 2x

15 x + 6x - 3x -2x = 15

16 x = 15

x = 15/16

5(3x).+ 7x = 3x + 15 - x

15 x + 7x = 3x + 15 - x

15 x + 7x - 3x + x = 15

22x - 3x + x = 15

20 x = 15

x = 15/20

x = 3/4

5(3x) + 7x = 3x + 10 - x

15x + 7x - 3x + x = 10

20x = 10

x = 10/20

x = 1/2

5(3x) + 7x = x + 15 - 3x

15x +7x - x + 3x = 15

24x = 15

x = 15/24

x = 5/8

Therefore the equations that has the solution x = all real numbers are :

5(3x).+ 7x = 3x + 15 - x and 5(3x) + 7x = 3x + 10 - x .

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Answer:

1:2

Step-by-step explanation:

"s" can be concluded from the premises

To use the rules of inference to show that "s" is a conclusion, we can use modus ponens,

This is a rule that allows us to infer a conclusion from a premise and its conditional statement.

Thus, "s" can be concluded from the premises "p → q", "q → r", "(q → r) → s", and "p".

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It takes 10 minutes for the number of bacteria in the population to double.

To determine the time it takes for the number of bacteria in a population to double, we need to find the value of t when the function f(t) equals twice the initial number of bacteria.

The given function is f(t) = 60,000 * 2^(t/10).

To find the time it takes for the number of bacteria to double, we set f(t) equal to twice the initial number of bacteria, which is 2 * 60,000 = 120,000:

120,000 = 60,000 * 2^(t/10).

Next, we can simplify the equation by dividing both sides by 60,000:

2 = 2^(t/10).

Since both sides of the equation have the same base (2), we can equate the exponents:

t/10 = 1.

To solve for t, we multiply both sides by 10:

t = 10.

Therefore, it takes 10 minutes for the number of bacteria in the population to double.

This result is obtained by setting the growth rate of the bacteria population in the given function. The exponent t/10 determines the rate of growth, and when t is equal to 10, the exponent becomes 1, resulting in a doubling of the initial number of bacteria.

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The solution for x in the equation given is x = -4.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

In the given equation above, we need to find the solution for x in the equation.

Given equation:

\(\rightarrow\boxed{\sf \frac{5}{3} x+4=\frac{2}{3} x}\)

\(\sf \dfrac{5}{3} x + 4 = \dfrac{2}{3}x \ (multiply \ through \ by \ 3 \ to \ clear \ the \ fractions)\)

\(\sf 5x + 12 = 2x \ (subtract \ 2x \ from \ both \ sides)\)

\(\sf 3x + 12 = 0 \ (subtract \ 12 \ from \ both \ sides)\)

\(\sf 3x = - 12 \ (divide \ both \ sides \ by \ 3)\)

Hence, the solution for x in the equation given is x = -4

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Answer:

A) reflection over the x-axis

Step-by-step explanation:

answer: A survey

explanation: The manager of the restaurant is conducting a survey to determine which sandwich is more preferred by customers. He is taking a random sample of customers that have tried both sandwiches and asking them which sandwich they like best. The survey method is a statistical way of collecting data and it is a non-experimental design, because the manager is not controlling the variables that may affect the outcome. The outcome of this survey is based on the customers' preference of the sandwiches, and it is a way to gather data on their opinion

Answer:

27

Step-by-step explanation:

The volume of a solid formed by revolving the region bounded above by the line is (932π/15)

To use the disk method, we need to integrate over the axis of revolution, which is the y-axis in this case. We can break the solid into vertical disks of thickness dy.

The radius of each disk is given by the distance between the y-axis and the curve \(x = y^2 - 1\). So the radius is:

\(r = y^2 - 1\)

The height of each disk is the difference between the y-coordinate of the top curve y = 3 and the y-coordinate of the bottom curve y = 1. So the height is:

h = 3 - 1 = 2

The volume of each disk is then:

\(dV = \pi r^2h dy\)

Substituting r and h, we have:

\(dV = \pi (y^2 - 1)^2 (2) dy\)

To find the total volume, we integrate over the range of y from 1 to 3:

\(V = \int_{1}^{3} \pi(y^2 - 1)^2 (2) dy\)

This integral can be simplified by expanding the squared term:

\(V = \int_{1}^{3} \pi (y^4 - 2y^2 + 1) (2) dyV = 2\pi \int_{1}^{3}(y^4 - 2y^2 + 1) dyV = 2\pi [(1/5)y^5 - (2/3)y^3 + y]^3_1\)

V = \(2\pi [(1/5)(3^5 - 1^5) - (2/3)(3^3 - 1^3) + (3 - 1)]\)

V = 2π [(1/5)(242) - (2/3)(26) + 2]

V = 2π [(242/5) - (52/3) + 2]

V = 2π [(726/15) - (260/15) + 30/15]

V = 2π [(466/15)]

V = (932π/15)

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Note: The full question is

Use the disk method or the shell method to find the volumes of the solids generated by revolving the region bounded by the graphs of the equations about the given lines. y = 1, y = 3, x = y^2 - 1.

Answer:

is it like this

64653=65000

Answer:

là 64652/64654

Answer:

$140

Step-by-step explanation:

If a package of gift cards has a total value of $1050, the total price for 2 gift cards will be 2×$1050 = $2100

If there are 15 in an average set of 2 gift cards, the average cost of the two gift cards will be expressed as;

Total price of 2gift cards/amount of card per group.

Average cost of of 2 gift cards = $2100/15

= $140

Hence the average cost of 2gift cards if there are 15 in a group is $134

Answer:

a. Amplitude: 19.65446

b. Vertical Shift: 58.00713

c. Period: 2/0.22797 = 27.56146

d. 19.65446 * sin(0.22797x + 1.79552) + 58.00713

e. Model's Temperature at 10 A.M.: f(-7) = 61.91

   This value is 9.91 degrees higher than the actual value.

Step-by-step explanation:

With 1 am being timed as t = 1, we fitted the temperature data collected at different points during the day in Portland, Oregon using sine regression. After receiving the sine function, we respond to the many questions connected to the sine function's properties.

A smooth, repeating oscillation characterizes a sinusoidal function. Sine is an oscillation that is smooth and repeated, thus the name "sinusoidal." A pendulum swinging, a spring bouncing, or a guitar string vibrating are a few examples of commonplace objects that may be described by sinusoidal functions.

Given, The hourly temperature at Portland, Oregon, on a particular day is recorded.

Using sine regression on the given data with t = 1 being the hour 1 am etc, we get the following sine regression formula using the TI-83 Graphing Calculator where T is the temperature:

T = a sin(bt + c) + d

Where a = 19.65, b = 0.28, c = -2.93, d = 58.01

From the sine regression function above:

a. The amplitude of the sinusoidal function is a = 19.65.

b. The vertical shift is d = 58.01.

c. The period is 2*pi /b = 2*pi/ 0.28 = 22.44

d. At 5 PM, the time value is t = 17. Hence the temperature distribution with 5 PM being t = 0 will be

t = asin[b(t - 17) + c] +d.

e. From the table, at 10 AM, the actual value of the temperature is 52 degrees.

Using the model in part a., at 10 AM, with t = 10, the temperature will be

T = a sin(10b + c) + d

T = 55.46 degrees

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Complete question:

Answer:

Step-by-step explanation:

Find all real solutions of the equation. ( 2 b + 4 ) 2 − 12 = 0

( 2 b + 4 ) 2 − 12 = 0

4b + 8 - 12 = 0

4b - 4 = 0

4b = 4

b = 1

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

check

(2*1+4)*2-12=0

12 - 12 = 0

0 = 0

the answer is good

Answer:

all real values of x where x < -1

The correct statement is all real values of x where x < -1.

Option A is the correct answer.

We have,

To determine the values for which the graph of the function

f(x) = (x - 3)(x + 1) is positive and decreasing, we need to analyze the behavior of the function.

Let's consider the factors individually:

(x - 3): This factor is positive for x > 3 and negative for x < 3.

(x + 1): This factor is positive for x > -1 and negative for x < -1.

To determine the overall sign of the function, we need to consider the signs of both factors together.

When both factors are positive or both factors are negative, the function is positive.

When the factors have opposite signs, the function is negative.

From the above analysis, we can conclude the following:

When x > 3, both factors are positive, so the function is positive.

When -1 < x < 3, the factor (x - 3) is negative, while the factor (x + 1) is positive. Therefore, the function is negative.

When x < -1, both factors are negative, so the function is positive again.

Since we are looking for values where the function is positive and decreasing, we can eliminate the options that include positive and increasing regions (such as x > 3).

Thus,

The correct statement is all real values of x where x < -1.

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If a translation of T (2, -7) is applied to the triangle ABC as shown in the figure attached hereby for reference, and B (1, 5) gets repositioned to B', then the current coordinates of B' are (3, -2).

As per the question statement, a translation of T (2, -7) is applied to the triangle ABC as shown in the figure attached hereby for reference, and B (1, 5) gets repositioned to B'.

We are required to calculate the coordinates of B'.

To solve this question, we need to know what Translation (a, b) to (x, y) and (-a, -b) to (x, y) means. Translation (a, b) to (x, y) means the abscissa "x" is to be shifted to the right by "a" units while the ordinate "y" is to be shifted to the right by "b" units, i.e., after translation, the new coordinates become [(a + x), (b + x)]. On the other hand, Translation (-a, -b) to (x, y) means the abscissa "x" is to be shifted to the left by "a" units while the ordinate "y" is to be shifted to the left by "b" units, i.e., after translation, the new coordinates become [(a - x), (b - x)].

Here, as per the above mentioned concept, a translation of T (2, -7) if applied to the point B (1, 5), the new point B' will be at \([(1+2), (5+(-7)]=[3, (-2)]\).

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Answer: D (3,-12)

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

Slope = Δy/Δx

Slope = 10-10/4-1

Slope = 0/3

Slope = 0

It is a Horizontal Line

-Chetan K

Hello and Good Morning/Afternoon!

Let's take this problem step by step:

Let's consider some facts:

 ⇒ angles are opposite each other

    ⇒ by the Vertical Angle Theorem

        ⇒ angles opposite each other are equal in measure

So:

 \(\hookrightarrow 4x + 12 = 64\)

Let's solve

  \(4x + 12 = 64\\4x = 52\\x = 13\)

x's value is 13

Answer: 13

Hope that helps!

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Answer:

53.72

Step-by-step explanation:

apply area of triangle and rectangle and add them

Given:

A farmer in China discovers a mammal hide that contains 57% of its original

amount of C-14.

The given formula is

where k =0.0001.

Required:

We need to find the age of the mammal hide.

Explanation:

The number of mammals hiding is 57% of the original.

We get

Take a natural log on both sides of the equation.

Final answer:

The age of the mammal hide is 5621 years.

Answer:

.

Step-by-step explanation:

Answer:

There are 3 two topping sundaes possible.

Step-by-step explanation:

The order in which the toppings are chosen is not important. For example, chocolate and caramel topping is the same as a caramel and chocolate topping. So we use the combinations formula to solve this question.

Combinations Formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

How many 2 topping sundaes are possible?

2 toppings from a set of 3(chocolate, caramel and strawberry). So

\(C_{3,2} = \frac{3!}{2!(3-2)!} = 3\)

There are 3 two topping sundaes possible.

Answer:

\(A(t)=16(0.99948)^t\)

Step-by-step explanation:

The exponential function is modeled using the equation:

\(A(t)=A_o(1\pm r)^t\)

Where the plus sign indicates growth and the negative sign indicates exponential decay.

For an exponential function has a starting value of 16 and a decay rate of 0.52%.

\(A_0=16\\r=0.052\%=0.00052\)

This gives:

\(A(t)=16(1- 0.00052)^t\\A(t)=16(0.99948)^t\)

The function that models this situation is:

\(A(t)=16(0.99948)^t\)

Answer:

f(x) = 6ˣ⁻⁷-3

Step-by-step explanation:

The basic transformations of an exponential function from the parent function can be given by the equation:

f(x) = b^x [parent exponential function]

f(x) = ab^((x/c)-h) + k [transformation of parent exponential function]

Where b is the parent growth or decay, a is the vertical stretch or compression, c is the horizontal stretch or compression, h is the horizontal translation, and k is the vertical translation.

Given a translation down 3 units, and another translation right 7 units, we are only using h, and k.

Given that our original function is g(x) = 6ˣ. We know our parental growth or b is 6. So just substitute our quantities and solve:

f(x) = g(x-7) - 3 → (1)6^((x/1)-7) - 3 → 6^(x-7) - 3 → 6ˣ⁻⁷-3.

Answer:

f(x) = 6ˣ⁻⁷-3

Step-by-step explanation: I took the test

The  x and y-intercept of the equation [8x - 9y = 15] are ( 15/8, 0 ) and ( 0, -5/3 ) respectively.

Given the equation;

8x - 9y = 15

First, we find the x-intercepts by simply substituting 0 for y and solve for x.

8x - 9y = 15

8x - 9(0) = 15

8x = 15

Divide both sides by 8

8x/8 = 15/8

x = 15/8

Next, we find the y-intercept by substituting 0 for x and solve for y.

8x - 9y = 15

8(0) - 9y = 15

- 9y = 15

Divide both sides by -9

- 9y/(-9) = 15/(-9)

y = -15/9

y = -5/3

We list the intercepts;

x-intercept: ( 15/8, 0 )

y-intercept: ( 0, -5/3 )

Therefore, the  x and y-intercept of the equation [8x - 9y = 15] are ( 15/8, 0 ) and ( 0, -5/3 ) respectively.

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Answer:

Step-by-step explanation:

x<-1, x>9