The volume of this rectangular pyramid.
9 ft
8 ft
7 ft

The solution to the Compound inequality 4x > -16 or 6x ≤ -48 is x > -4 or x ≤ -8, expressed either graphically or in interval notation.

The compound inequality 4x > -16 or 6x ≤ -48, we will solve each inequality separately and then combine the solutions.

1. Solving the inequality 4x > -16:

Dividing both sides of the inequality by 4 (since it is a positive number), we have:

x > -16/4

x > -4

2. Solving the inequality 6x ≤ -48:

Dividing both sides of the inequality by 6 (since it is a positive number), we have:

x ≤ -48/6

x ≤ -8

Now, let's combine the solutions:

The solution to the compound inequality 4x > -16 or 6x ≤ -48 is the combination of the individual solutions.

Since it is an "or" compound inequality, we consider the values that satisfy either of the two inequalities.

The solution is x > -4 or x ≤ -8.

Graphically, this represents two separate intervals on the number line. The interval for x > -4 is shaded to the right of -4, and the interval for x ≤ -8 is shaded to the left of -8.

In interval notation, the solution is (-∞, -8] ∪ (-4, +∞), where (-∞, -8] represents all values less than or equal to -8, and (-4, +∞) represents all values greater than -4.

the solution to the compound inequality 4x > -16 or 6x ≤ -48 is x > -4 or x ≤ -8, expressed either graphically or in interval notation.

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Answer:

A. The probability that both beads are red is 5/92.

B. The probability that one bead is black and the other is yellow is 6/23.

Step-by-step explanation: To find the probabilities, we need to calculate the total number of possible outcomes and the number of favorable outcomes for each scenario.

A. Both beads are red:

Total number of beads = 6 + 8 + 10 = 24

The first bead can be any of the 24 beads. After picking the first bead, there will be 5 red beads left out of the remaining 23 beads. Thus, the probability of picking a red bead is:

P(Red on first pick) = 6/24 = 1/4

For the second pick, there will be one less bead, and one less red bead. Therefore, the probability of picking another red bead is:

P(Red on second pick) = 5/23

To find the probability of both events occurring, we multiply the probabilities together:

P(Both red) = P(Red on first pick) * P(Red on second pick)

= (1/4) * (5/23)

= 5/92

Therefore, the probability that both beads are red is 5/92.

B. One bead is black and the other is yellow:

Total number of beads = 24 (same as before)

The first bead can be any of the 24 beads. After picking the first bead, there will be 8 black beads and 10 yellow beads remaining. Thus, the probability of picking a black bead is:

P(Black on first pick) = 8/24 = 1/3

For the second pick, there will be one less bead, and if the first bead was black, there will be 10 yellow beads left. If the first bead was yellow, there will be 8 black beads left. Therefore, the probability of picking a yellow bead after a black bead is:

P(Yellow on second pick after black) = 10/23

However, we also need to consider the case when the first bead is yellow and the second bead is black. In that case, the probability is:

P(Black on second pick after yellow) = 8/23

To find the probability of either event occurring (black then yellow or yellow then black), we add the probabilities together:

P(One black and one yellow) = P(Black on first pick) * P(Yellow on second pick after black) + P(Yellow on first pick) * P(Black on second pick after yellow)

= (1/3) * (10/23) + (1/3) * (8/23)

= 10/69 + 8/69

= 18/69

= 6/23

Therefore, the probability that one bead is black and the other is yellow is 6/23.

To summarize:

A. The probability that both beads are red is 5/92.

B. The probability that one bead is black and the other is yellow is 6/23.

Answer:

3x²-2x-8

Step-by-step explanation:

(3x+4)(x-2)=

3x²-6x+4x-8=

3x²-2x-8

The student takes 160 minutes to mow 4 lawns, which means he takes 40 minutes to mow one lawn. Therefore, the correct prediction is that it will take him 8 hours to mow 12 lawns. So, the correct answer is B).

Based on the given information, we know that the student takes 160 minutes to mow 4 lawns. Therefore, the time it takes him to mow one lawn is 40 minutes (160 divided by 4).

If the student has 12 lawns to mow, he will need to spend 12 times the time it takes him to mow one lawn.

So, the prediction is that it will take him 12 times 40 minutes, which equals 480 minutes, or 8 hours, to mow 12 lawns.

Therefore, the correct prediction is: It will take him 8 hours to mow 12 lawns. So, the correct answer is B).

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Answer:

x^2 - 7

Step-by-step explanation:

To simplify the expression (x + √7)(x - √7), we can use the distributive property of multiplication:

(x + √7)(x - √7) = x(x) + x(-√7) + √7(x) + √7(-√7)

Now, let's simplify each term:

x(x) = x^2

x(-√7) = -x√7

√7(x) = √7x

√7(-√7) = -7

Combining all the terms:

x^2 - x√7 + √7x - 7

We can rearrange the terms:

x^2 + (√7x - x√7) - 7

Notice that (√7x - x√7) simplifies to 0 since the two terms cancel each other out. Therefore, we have:

x^2 - 7

Thus, the simplified form of (x + √7)(x - √7) is x^2 - 7.

Hope this helps!

The probability of events A and B occurring is given as follows:

P(A and B) = 1/3.

The parameters that are needed to calculate a probability are given as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For each event, the probability is given as follows:

As the events are independent, the probability of both events happening is given as follows:

P(A and B) = 2/3 x 1/2

P(A and B) = 1/3.

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Answer:

x = 11

Step-by-step explanation:

The two angles measuring (7x + 14)° and (9x - 8)° are corresponding angles, which are always congruent to each other and thus equal to each other.  

Step 1:  Thus, we can find the value of x by setting the two angles equal to each other:

7x + 14 = 9x - 8

7x + 22 = 9x

22 = 2x

11 = x

Optional Step 2:  We can check that we've found the correct answer by plugging in 11 for x in both (7x + 14) and (9x - 8) and checking that we get the same number:

7(11) + 14 = 9(11) - 8

77 + 14 = 99 - 8

91 = 91

hello

the answer to the question is:

[tex] \sin(s) = \frac{tu}{x} \\ \sin(24) = \frac{22.5}{x} \\ x = 25[/tex]

The common ratio and the first term of the exponential sequence are 2.25 and 1.29 respectively.

The third and fifth terms of an exponential sequence of a positive terms are 12 and 5.3333 respectively.

The common ratio (r) of an exponential sequence is found by dividing any term by the previous term.

Therefore, r = 12/5.333 = 2.25

The first term can be found using the formula aₙ = arⁿ⁻¹.

Since we know the third term (a₃ = 12) and the common ratio (r = 2.25), the first terma₁ can be calculated as follows:

a₁ = a₃/r³ = 12/2.253 = 1.29

Hence, the common ratio and the first term of the exponential sequence are 2.25 and 1.29 respectively.

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When a number subtracted from 13 gives -15​ then the number is -2.

We have to find the number which is subtracted from 13 gives -15​.

Let x be the unknown number.

By the given information, let us form a equation:

x-13=-15

We have to solve for x:

Add 13 on both sides of the equation:

x=-15+13

x=-2

Hence, -2 is the unknown number.

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Answer:

The product of 8 * 453 * 125 is 453000.

Step-by-step explanation:

We can rearrange the factors to make the multiplication easier.

For example, we can group the 8 and the 125 together to get 8 * 125 = 1000. We can then multiply this by 453 to get 453000.

Another way to rearrange the factors is to group the 453 and the 125 together to get 453 * 125 = 56625. We can then multiply this by 8 to get 453000.

No matter how we rearrange the factors, the product will always be 453000.

Answer:

2144.67 m³

Step-by-step explanation:

Volume of sphere = (4/3) X π X r ³

= (4/3) π (8)³

= (2048/3) π

= 2144.67 m³ to nearest hundredth

Answer:

Irrational

Step-by-step explanation:

[tex]\sqrt{56} = 7.48331477355[/tex]

so the decimal is not a repeating pattern so it is irrational

Probability, data, trends, likelihoods, and statistics are used in various aspects of veterinary medicine. Here are some examples:

Diagnosis: Veterinarians use probability and statistical analysis to diagnose diseases in animals. For example, they may use Bayesian analysis to estimate the probability of a particular disease based on the animal's symptoms, medical history, and test results.

Treatment: Veterinarians use data and trends to develop treatment plans for animals. They may use statistical analysis to evaluate the effectiveness of different treatments and to identify which treatments are most likely to be successful.

Epidemiology: Veterinarians use statistics and likelihoods to study the occurrence and spread of diseases in animal populations. They may use surveillance data to identify outbreaks of diseases and to track their spread over time.

Research: Veterinarians perform research on animal health and disease using statistical analysis to interpret their findings. They may use experimental design and statistical methods to test the efficacy of new drugs or treatments, or to identify risk factors for certain diseases.

Public health: Veterinarians work to protect public health by monitoring animal diseases that can be transmitted to humans. They may use statistical analysis to identify trends in disease incidence or to evaluate the effectiveness of public health interventions.

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Answer:

[tex]f(x)=(x-4)^2+28[/tex]

Step-by-step explanation:

Here are the steps to convert the quadratic function [tex]f(x)=x^2-8x+44[/tex] into vertex form:

Step 1: Group the [tex]x[/tex] terms together:
[tex]f(x)=(x^2-8x)+44[/tex]

Step 2: Complete the square within the parentheses by adding and subtracting the square of half the coefficient of the [tex]x[/tex] term:
[tex]f(x)=(x^2-8x+16)-16+44[/tex]

Step 3: Rearrange the expression:
[tex]f(x)=(x^2-8x+16)-16+44[/tex]

Step 4: Factor the perfect square trinomial [tex](x^2-8x+16)[/tex]:
[tex]f(x)=(x-4)^2-16+44[/tex]

Step 5: Simplify and combine constants:
[tex]f(x)=(x-4)^2+28[/tex]

Therefore, the quadratic function [tex]f(x)=x^2-8x+44[/tex] in vertex form is [tex]f(x)=(x-4)^2+28.[/tex] The vertex of the parabola is located at the point [tex](4,28)[/tex].

The corresponding rectangular coordinates for point Q is (-3√3, 3)

To convert polar coordinates  (r, θ) to rectangular coordinates  (x, y). Use the following relations:

x = rcosθ

y = rsinθ

We have:

(r, θ) = (6, 5π/6)

x = 6 cos (5π/6)

x = 6 * -√3/2

x =  -3√3

y = 6 sin (5π/6)

y = 6 * 1/2

y = 3

Therefore, the corresponding rectangular coordinates for point Q is (-3√3, 3)

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Answer:

g'(1,-5)

Step-by-step explanation:

Rule

(x,y) → (y -x)

(-5,-1) → (-1,5)

Helping in the name of Jesus.

Answer:

For new coordinates of each point, we can use the following formula:

(x, y) [tex]\longrightarrow[/tex] (y, -x)

To rotate a point 90 degrees clockwise about the origin, we swap the x and y coordinates and negate the x coordinate.

Therefore, the rotated points are:

G(-5,-1) [tex]\longrightarrow[/tex] G'(-1, 5)

H(-3,-2) [tex]\longrightarrow[/tex] H'(-2, 3)

J(-3,-5) [tex]\longrightarrow[/tex] J'(-5, 3)

K(-5,-4) [tex]\longrightarrow[/tex] K'(-4, 5)

Therefore, The vertex of G is (-1,5)

Given that 'd' = (n-1)/2.

This means there is a vertex 'u' at most (n-1)/2 distance away from 'v'.

A tree with 'n' vertices has the longest path of 'n-1' edges (path graph property).

Let 'd' be the maximum distance from 'v' to any other vertex.

The longest path must pass through 'v', else we could extend it by adding 'v' and a neighbor, contradicting maximality.

Thus, 'd' is at least half the length of the longest path, i.e., d >= (n-1)/2. If 'd' > (n-1)/2, then the longest path exceeds 'n-1', a contradiction.

So, 'd' = (n-1)/2.

This means there is a vertex 'u' at most (n-1)/2 distance away from 'v'.

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The point on the y-axis is on the line that passes through point r and is parallel to line PQ is; (0, 2/3)

To find the point on the y-axis that lies on the line passing through point r and is parallel to line pq, we need to first find the slope of line pq.

Substituting the given points, we get:

slope = (-1 - (-3))/(3 - (-3)) = 2/6 = 1/3

Since the line passing through point r is parallel to line pq, it will have the same slope as line pq.

The line passing through point r with slope 1/3.

Using a point-slope form of the equation of a line;

y - (-2) = 1/3(x - 1)

y = 1/3x + 2/3

So, the line passing through point r with slope 1/3 is;

y = 1/3x + 2/3.

y = 1/3(0) + 2/3 = 2/3

therefore, the answer is (0,2/3 )

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The expression in ascending order is  [tex]e^{log4} < log_326 < log_233 < log_22^6[/tex].

We have,

Using a log and exponent calculator we get,

log 4 = 0.60

So,

[tex]e^{log 4}[/tex] = [tex]e^{0.60}[/tex] = 1.82

[tex]log_233[/tex] = 5.044

[tex]log_22^6[/tex] = 6

[tex]log_326[/tex] = 2.97

Now,

Arranging from least to greatest:

[tex]e^{log4} < log_326 < log_233 < log_22^6[/tex]

Thus,

The expression in ascending order is  [tex]e^{log4} < log_326 < log_233 < log_22^6[/tex].

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Star: 0.1667, 16.67%; Circle: 0.1875, 18.75%; Triangle: 0.0625, 6.25%; Cylinder: 0.1875, 18.75%; Heart: 0.5, 50%.

We have,

Fraction form: star 1/6

Decimal: 0.1667

Percentage %: 16.67%

Fraction form: circle 3/16

Decimal: 0.1875

Percentage %: 18.75%

Fraction form: triangle 1/16

Decimal: 0.0625

Percentage %: 6.25%

Fraction form: cylinder 3/16

Decimal: 0.1875

Percentage %: 18.75%

Fraction form: heart 8/16

Decimal: 0.5

Percentage %: 50%

Thus,

Star: 0.1667, 16.67%; Circle: 0.1875, 18.75%; Triangle: 0.0625, 6.25%; Cylinder: 0.1875, 18.75%; Heart: 0.5, 50%.

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Answer:

30 or 12/13

Step-by-step explanation:

Please mark me brainliest, verify, and say thank you.

The time when the movie finishes is 19:37 using the 24-hour clock.

Sebastian started watching the movie at 17:30. The movie has a duration of 1 hour 54 minutes, which is equal to 1 + 54/60 = 1.9 hours.

Adding this duration to the start time gives:

17:30 + 1.9 hours = 19:24

This would be the time when the movie finishes if Sebastian didn't pause it. However, he paused it for 13 minutes, so we need to add this pause time to the finish time.

To do this, we can convert the pause time to hours and add it to the finish time:

13 minutes = 13/60 hours

19:24 + 13/60 hours = 19:37

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The complete values are:

1. Scale factor = 1/2

DE = 17.69

AC = 6.5 unit

AB = 8.845 unit

2.  Scale factor = 2/3

UT = 11.34 unit

YZ =  12 unit

XY =  17 unit

1. In ΔACB and ΔDFE

Using Pythagoras

DE = √13² + 12²

DE = √169 + 144

DE = √313

DE = 17.69

AC = 6.5 unit

AB = 8.845 unit

and, Scale factor = 6/12 = 1/2

2. In ΔTUV and ΔXYZ

Scale factor = 8/12 = 2/3

Using Pythagoras

UT= √64 + 64

UT = 11.34 unit

So, YZ = 8  x 3/2 = 12

and, XY = 11.34 x 3/2 = 17

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(1) To find the values of x that satisfy the equation a/x + p = b^x + c, you would need specific values for a, b, c, p, and q. Without these values, we cannot determine the exact solutions.

(2) To find the values of x that satisfy the inequality b^x + c - a/x + p <= q, we would need the specific values of a, b, c, p, and q. Without these values, we cannot determine the exact solutions.

(3) To determine the values of x for which f(x) <= g(x), we need the specific values of a, b, c, p, and q, as well as the shapes of the graphs. Without this information, we cannot provide a specific answer.

(4) The x-intercept of a function f(x) is the point where the graph intersects the x-axis. To find the x-intercept of f(x) = a/x + p + q, we need the specific value of a. Similarly, the y-intercept is the point where the graph intersects the y-axis, and we need additional information to determine its coordinates.

(5) The equation of an asymptote depends on the behavior of the function and the given equations. Without specific details about the graphs and their behavior, we cannot determine the equations of the asymptotes.

Hello !

Answer:

[tex]\boxed{\sf x=2\ or\ x=-3}[/tex]

Step-by-step explanation:

[tex]\sf 5x^2+5x-30[/tex]

This equation is a quadratic equation in the form ax²+bx+c=0

The solution of this equation is given by the quadratic formula :

[tex]\sf x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

There are 3 cases depending on the values of the discriminant :

Let's calculate the discriminant :

[tex]\sf b^2-4ac=5^2-4\times5\times(-30)=625 > 0[/tex]

There are 2 real roots.

Now let's use the quadratic formula to find the two roots.

[tex]\sf x=\frac{-5\pm\sqrt{5^2-4\times5\times(-30)}}{2\times5}\\x=\frac{-5\pm\sqrt{625}}{10} \\x_1=\frac{-5+\sqrt{625}}{10}=2\\x_2=\frac{-5-\sqrt{625}}{10}=-3\\\boxed{\sf x=2\ or\ x=-3}[/tex]

Have a nice day ;)

The number of index cards that Paquita has now is 6.

Given that,

Paquita has 63 index cards.

She uses 57 of them for a project.

We have to find the number of cards left with her.

It is clear that, we have to subtract the total number of cards with the number of cards she used for the project.

Total number of index cards that Paquita has= 63

Number of cards she used for the project = 57

Number of cards left with her = 63 - 57

                                                  = 6

Hence the number of cards that Paquita has now is 6.

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