The rectangular prism shown is formed by six intersecting planes.

Where do the planes ABFE and EFGH intersect

For p(x<62) and p(x>68), we can use the z-score formula to calculate the probability.

p(x<62), the z-score formula is (62-64)/18 = -0.11.

p(x>68), the z-score formula is (68-64)/18 = 0.22.

The rest answer are mentioned below with calculation.

It is (X-μ)/σ, where X is the value we are evaluating, μ is the mean of the population, and σ is the standard deviation of the population.

For the first two questions, p(x<62) and p(x>68), we can use the z-score formula to calculate the probability. The z-score formula is (X-μ)/σ, where X is the value we are evaluating, μ is the mean of the population, and σ is the standard deviation of the population.

For the first question, p(x<62), the z-score formula is (62-64)/18 = -0.11. This means that the probability of x being less than 62 is 0.3767 (from the z-score table).

For the second question, p(x>68), the z-score formula is

(68-64)/18 = 0.22.

This means that the probability of x being greater than 68 is 0.5987 (from the z-score table).

For the third question, the probability that a randomly selected pregnancy lasts less than 260 days can be calculated using the z-score formula.

The z-score formula is (260-266)/16 = -0.375. This means that the probability of a randomly selected pregnancy lasting less than 260 days is 0.3296 (from the z-score table).

For the fourth question, the probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less can be calculated using the Central Limit Theorem.

Since the sample size is 20, the standard deviation of the sample is

16/√(20) = 4.

The z-score formula is (260-266)/4 = -1.5.

This means that the probability of a random sample of 20 pregnancies having a mean gestation period of 260 days or less is 0.0668 (from the z-score table).

For the fifth question, the probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less can be calculated using the Central Limit Theorem.

Since the sample size is 50, the standard deviation of the sample is

16/√(50) = 1.83

The z-score formula is (260-266)/1.8 = -3.3.

This means that the probability of a random sample of 50 pregnancies having a mean gestation period of 260 days or less is 0.0062 (from the z-score table).

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Answer:

9/10 and it can't be simplified

Step-by-step explanation:

BRAINLIEST PLEASE  

Answer:

9/10

Step-by-step explanation:

1/2 = 5/10

2/5 = 4/10

5/10+4/10= 9/10

Answer:

x=2

Step-by-step explanation:

I don’t really have an explanation, it was all mental math

Answer:

Step-by-step explanation:

\(\sf 2(4-x)-3(x+3)=-11\)

Expand:-

Now, add 1 to both sides:-

Divide both sides by -5:-

Therefore, the value of x is 2!

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

Hope this helps!

Answer:

BDE I think I'm not completely sure though

Answer:

y = 55 , y = 100

Step-by-step explanation:

9

the sum of the 3 angles in a triangle is 180°

sum the angles and equate to 180

y + 75 + 50 = 180

y + 125 = 180 ( subtract 125 from both sides )

y = 55

10

the sum of the exterior angles of a triangle is 360°

sum the exterior angles and equate to 360

y + 120 + 140 = 360

y + 260 = 360 ( subtract 260 from both sides )

y = 100

No, the expression (x^3 - 1) / (x^2 - 1) does not simplify to x.

To simplify the expression, let's first factorize both the numerator and denominator.

The numerator can be factorized using the difference of cubes formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2). So, we have (x^3 - 1) = (x - 1)(x^2 + x + 1).

The denominator is a difference of squares: a^2 - b^2 = (a - b)(a + b). Therefore, (x^2 - 1) = (x - 1)(x + 1).

Now, we can simplify the expression by canceling out the common factors in the numerator and denominator:

[(x - 1)(x^2 + x + 1)] / [(x - 1)(x + 1)]

The (x - 1) terms cancel out, leaving us with:

x^2 + x + 1 / (x + 1)

So, the simplified form of the expression is (x^2 + x + 1) / (x + 1), which is not equal to x.

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Answer:

Step-by-step explanation:

There are four different color marbles.

Probability of blue:

Next, there are 3 marbles left in the bag since no replacement.

Probability of red after blue:

The probability of these two steps in order:

Complement of R is:

Based on the following graph, The hippocampus in the brain is the most likely site of the lesion.

The brain is a sophisticated organ that manages every bodily function as well as thought, memories, emotions, touch, motor function, vision, respiration, temperature, and hunger. Its central nervous system or CNS, is made up of the spinal cord that emerges from the brain.

The brain regulates many bodily functions, including the function of numerous organs as well as thinking, memory, language, arm and leg motions. By controlling heart and breathing rates, it also affects how people react to stressful situations (such as completing an exam, losing a job, having a baby, being ill, etc.).

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The probability distribution for x is:

x P(x)

0 0.214

1 0.571

2 0.214

Since there are 8 cameras in the box, the total number of ways to choose 2 cameras from the box is given by the combination formula:

C(8,2) = 8!/(2!×(8-2)!) = 28

So there are 28 possible ways to choose a sample of 2 cameras.

Now, let's calculate the probability of each possible value of x:

When x = 0, both cameras in the sample are non-defective. The number of ways to choose 2 non-defective cameras from the 4 non-defective cameras in the box is given by the combination formula:

C(4,2) = 4!/(2!×(4-2)!) = 6

So the probability of x = 0 is:

P(x=0) = (number of ways to choose 2 non-defective cameras)/(total number of ways to choose 2 cameras)

= 6/28

= 0.214

When x = 1, one camera in the sample is defective and the other is non-defective. The number of ways to choose 1 defective camera from the 4 defective cameras in the box and 1 non-defective camera from the 4 non-defective cameras in the box is given by the product of the corresponding combinations:

C(4,1) × C(4,1) = 4×4 = 16

So the probability of x = 1 is:

P(x=1) = (number of ways to choose 1 defective camera and 1 non-defective camera)/(total number of ways to choose 2 cameras)

= 16/28

= 0.571

When x = 2, both cameras in the sample are defective. The number of ways to choose 2 defective cameras from the 4 defective cameras in the box is given by the combination formula:

C(4,2) = 4!/(2!×(4-2)!) = 6

So the probability of x = 2 is:

P(x=2) = (number of ways to choose 2 defective cameras)/(total number of ways to choose 2 cameras)

= 6/28

= 0.214

Therefore, the probability distribution for x is:

x P(x)

0 0.214

1 0.571

2 0.214

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The function h(x) in its simplest form is \(h(x) = 4log_2(x)- 2\)

The functions are given as:

\(f(x) = log_2(x) + 2\)

\(g(x) = log_2(x^3) - 4\)

This is given as:

\(h(x) = f(x) + g(x)\)

So, we have:

\(h(x) = log_2(x) + 2 + log_2(x^3) - 4\)

Collect like terns

\(h(x) = log_2(x) + log_2(x^3)+ 2 - 4\)

\(h(x) = log_2(x) + log_2(x^3)- 2\)

Apply law of logarithm

\(h(x) = log_2(x \times x^3)- 2\)

\(h(x) = log_2(x^4)- 2\)

Apply law of logarithm

\(h(x) = 4log_2(x)- 2\)

Hence, function h(x) in its simplest form is \(h(x) = 4log_2(x)- 2\)

The equations are not given.

So, the question cannot be solved

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Answer:

24m

Explanation:

For a circle with a radius, r, the area:

The radius of the circle is 12m.

Therefore:

The diameter ​of the circle is 24m.

Hope attachment helps (✿^‿^)

Answer:

in 20 miles she would have taken her 100 minutes (or 1 hour and 40 mins)

Step-by-step explanation:

Divide 10 by 2 to see how many mins its takes to travel 1 mile which is 5 mins, then multiply 20 by 5 to get 100 minutes

2:10

1:5

2.5/1

your welcome

If only 2,836 students were admitted into the Ateneo among 27,813 students, who took the ACET this year, the Ateneo’s acceptance rate is b. 10.2%.

The rate is the ratio of one value, expression, measurement, or quantity compared to another.

The rate represents the quotient of the numerator and the denominator.

The rate is expressed as a percentage by multiplication with 100.

The number of students who took the ACET this year = 27,813

The number of students who were admitted into the Ateneo = 2,836

The percentage or rate admitted = 10.19667% (2,836 ÷ 27,813 × 100)

= 10.2%

Thus, we can conclude that the acceptance rate or percentage is Option B.

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The ability of the twins to divide the oddly shaped plot into two Identical plots along the grid lines depends on the presence of a line of symmetry.

To determine whether the set of twins can divide the oddly shaped plot of land into two identical plots along the grid lines, we need to consider the characteristics of the plot and the conditions required for the division.

For the division to be possible, the plot needs to have a line of symmetry that can be used to create two identical halves. A line of symmetry divides an object into two equal and mirrored parts.

If the plot of land has a line of symmetry, the twins can divide it by drawing a line along the symmetry axis. This line should cut the plot into two equal halves, ensuring that both plots are identical.

However, if the plot does not have a line of symmetry, it may not be possible to divide it into two identical plots along the grid lines. In this case, the twins would need to consider alternative methods of division or compromise on the goal of having two identical plots.

To determine if the plot has a line of symmetry, the twins can examine its shape and characteristics. They can look for any symmetrical patterns, such as equal sides or mirrored shapes, that indicate the presence of a line of symmetry.

If the plot does not have an obvious line of symmetry, the twins might need to explore other options, such as dividing the plot into two equal areas based on other criteria, such as the length or width of each half.

the ability of the twins to divide the oddly shaped plot into two identical plots along the grid lines depends on the presence of a line of symmetry. If such a line exists, they can divide the plot by drawing a line along the symmetry axis. However, if the plot lacks symmetry, they may need to consider alternative methods of division or adjust their expectations.

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Note the full question may be :

To determine whether the twins can divide the oddly shaped plot of land into two identical plots along the grid lines, we need more specific information about the shape and dimensions of the plot. the shape of the plot (rectangular, triangular, irregular), the lengths of its sides, any existing grid lines or divisions within the plot.

Answer:x

3

+

64

x

3

−

1

12

t

−

8

Step-by-step explanation:

Answer:

5 x (2+8) + (12-6/3) x2

5×10+(12-2)×2

50+10×2

50+20

70

The method you would use to prove the two triangles are congruent include the following: B. ASA.

In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides are proportional to the  lengths of corresponding altitudes when two (2) triangles are similar.

In Mathematics and Geometry, ASA is an abbreviation for Angle-Side- Angle and it states that when two (2) angles and their included side in two (2) triangles are congruent, then the triangles are said to be congruent.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

you did not provide enough information to answer the question

Answer:

1

Step-by-step explanation:

7x x9=7x10-7x

63x=70-7x

63x+7x=70

70x=70

x=1

Answer:

26, 90 and 64 :333

Step-by-step explanation:

3x-14 + x + 90 =180

4x - 14 +90 = 180

4x = 180 + 14 -90

4x = 104

x = 26

So the angles are:

26, 90 and 64 :333

The two-column method that can be used to prove the congruency of \(\overline{FA}\) and \(\overline{ED}\) is presented as follows;

Step         Statement      \({}\)                    Reason

1.  \({}\)          \(\overline{FG}\) ≅ \(\overline{EG}\)                                          

            \({}\) \(\overline{AB}\) ≅ \(\overline{CD}\)                             Given

\({}\)           ∠GBC ≅ ∠GCB    

2.          \(\overline{BC}\) ≅ \(\overline{BC}\)    \({}\)                          Reflexive property

3. \({}\)         \(\overline{FG}\) = \(\overline{EG}\)

\({}\)             \(\overline{AB}\) = \(\overline{CD}\)                               Definition of congruency

\({}\)             \(\overline{BC}\) = \(\overline{BC}\)

4.          \(\overline{BG}\) ≅ \(\overline{GC}\) \({}\)                              Legs of isosceles triangle

5.           \(\overline{BG}\) = \(\overline{GC}\)          \({}\)                     Definition of an isosceles triangle

6.          \(\overline{FC}\) = \(\overline{FG}\) + \(\overline{GC}\) \({}\)

            \(\overline{BE}\) = \(\overline{EG}\) + \(\overline{BG}\)                      

7.          \(\overline{FC}\) = \(\overline{BE}\)   \({}\)                             Substitution property

8.          \(\overline{AC}\) = \(\overline{BD}\)                        \({}\)        Substitution property

9.          ΔACF ≅ ΔDBE \({}\)                      SAS congruency rule

10.         \(\overline{FA}\) ≅ \(\overline{ED}\)   \({}\)                           CPCTC

Two segments are congruent if their lengths are the same.

The details of the reasons used in to prove the congruency of the segments \(\overline{FA}\) and \(\overline{ED}\) are as follows;

Reflexive property

The reflexive property of equality states that a number or value is congruent to itself.

Definition of congruency

Two geometric figures are congruent when their shape and sizes are the same

Isosceles Triangle

An isosceles triangle is one which has a pair of congruent sides.

Substitution property

The substitution property of equality states that if a variable a = b, then a can substitute b in any expression or equation.

SAS congruency rule

The SAS, Side-Angle-Side congruency postulate states that if two sides and an included angle of one triangle are congruent to two sides and an included angle of another triangle, then the two triangles are congruent.

CPCTC

CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent

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Answer:

12

Step-by-step explanation:

y= 51 x 4 = 204

x= 3 x 4 = 12

Answer:

Step-by-step explanation:

The value of X when Y is 204 is 12

Let the relationship between X and Y be a direct proportion

If Y and X is directly proportional then;

k is the constant of proportionality

If X = 3 and Y = 51

In order to get the value of X if Y is 204, Recall;

Hence the value of X when Y is 204 is 12

Answer: y = -7/5x -21/5

GIVEN POINTS

• ( x1;y1 ) = ( -8;7)

• (x2;y2 ) = (2;-7)

(i) Calculate the Slope -substitude given point into the slope formula below:

Therefore , the slope = -7/5

Our equation will follow the standard equation of a straight line :

(ii) Calculate the y - intercept

• Now, our equation looks like this ,: y = -7/5x +c

• Subtitute any of the given point and solve for point c , lets choose point (, 2;-7),

This means that the C value = -21/5

Answer

Sorry If this is not correct, but I believe you keep the X varriable the same and multiply the Y varriable by 4. This means it will move to the right on the grid.

New coordinates: G(3,4) T(1,4) B(3, 20)