Determine el valor de “m” si la suma de raíces de la ecuación es 3:

(m-1) x2 - 2mx +(m+2) = 0

Answer:

47/53 or 0.88 or 88%

Step-by-step explanation:

The probability that a student's score is less than 81 points on the reading ability test is 0.9772. We would expect approximately 489 students to earn a score less than 81 points if 500 students took the reading ability test. The probability of randomly selecting 35 students (all from the same class) that have a sample mean reading ability test score between 66 and 68 is approximately 0.2190.

To find the probability that a student's score is less than 81 points, we need to standardize the score using the z-score formula:

z = (x - μ) / σ

where x is the student's score, μ is the mean score, and σ is the standard deviation. Plugging in the values, we get:

z = (81 - 65) / 8 = 2.00

Using a standard normal distribution table or calculator, we can find the probability of a z-score less than 2.00 to be approximately 0.9772. Therefore, the probability that a student's score is less than 81 points is 0.9772.

Since the distribution is normal, we can use the normal distribution to estimate the number of students who would earn a score less than 81. We can standardize the score of 81 using the z-score formula as above and use the standardized score to find the area under the normal distribution curve. Specifically, the area under the curve to the left of the standardized score represents the proportion of students who scored less than 81. We can then multiply this proportion by the total number of students (500) to estimate the number of students who would score less than 81.

z = (81 - 65) / 8 = 2.00

P(z < 2.00) = 0.9772

Number of students with score < 81 = 0.9772 x 500 = 489

Therefore, we would expect approximately 489 students to earn a score less than 81 points.

The distribution of the sample mean reading ability test scores is also normal with mean μ = 65 and standard deviation σ / sqrt(n) = 8 / sqrt(35) ≈ 1.35, where n is the sample size (number of students in the sample). To find the probability that the sample mean score is between 66 and 68, we can standardize using the z-score formula:

z1 = (66 - 65) / (8 / sqrt(35)) ≈ 0.70

z2 = (68 - 65) / (8 / sqrt(35)) ≈ 2.08

Using a standard normal distribution table or calculator, we can find the probability that a z-score is between 0.70 and 2.08 to be approximately 0.2190. Therefore, the probability of randomly selecting 35 students (all from the same class) that have a sample mean reading ability test score between 66 and 68 is approximately 0.2190.

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Answer:

1.) RS ⊥ ST, RS ⊥ SQ, ∠STR ≅ ∠SQR | Given

2.) RS≅RS | Reflexive Property

3.) △RST ≅ △RSQ | AAS Triangle Congruence Property

Step-by-step explanation:

The required fill-in-the-blank below as:

1.) RS ⊥ ST, RS ⊥ SQ, ∠STR ≅ ∠SQR | Given

2.) RS≅RS | Reflexive Property

3.) △RST ≅ △RSQ | AAS Triangle Congruence Property

Two triangles are said to be congruent if their corresponding sides and angles are equal.

The given in question as:

RS ⊥ ST

RS ⊥ SQ

∠STR = ∠SQR

To prove:

△RST ≅ △RSQ

1.) RS ⊥ ST, RS ⊥ SQ, ∠STR ≅ ∠SQR | Given

2.) RS≅RS | Reflexive Property

According to AAS, two triangles are congruent if the two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle.

3.) △RST ≅ △RSQ | AAS Triangle Congruence Property

Hence, △RST ≅ △RSQ

Thus, the required fill-in-the-blank above is in the solution.

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The rate at which the level of the root beer in the cup is changing while the root beer is 2 centimeters deep is about -0.668 cm/sec.

We are able to use related rates to resolve the problem. let's anticipate that the cone is full, so its volume is:

V = (1/3)πr²h

wherein r is the radius of the top of the cone and h is the height.

We are given that the diameter of the top of the cone is 10 cm, so its radius is five cm. We are also given that the depth of the cone is 11 cm, so its height is 11 cm.

We want to find the charge at which the level of the basis beer in the cup is changing, that's dh/dt.

We're given that the basis beer leaves the cup on the rate of 7 cm^3/sec. this is the rate at which the quantity of the root beer is decreasing, so it is also the rate at which the extent of the cone is decreasing. therefore, we've got:

dV/dt = -7

The use of the formula for the volume of a cone, we will specific dV/dt in terms of dr/dt and dh/dt:

dV/dt = (1/3)πr² dh/dt + πrhdr/dt

We're interested in dh/dt when the depth of the root beer is 2 cm, this means that that h = 9 cm (eleven cm - 2 cm).

We also can find dr/dt by using using the fact that the diameter of the top of the cone is lowering on the identical price as the level of the basis beer within the cup. consequently, we've got:

dr/dt = -dh/dt

Substituting dr/dt and dh/dt into the equation for dV/dt, we get:

-7 = (1/3)π(5²)dh/dt + π(5)(-dh/dt)

Simplifying, we get:

-7 = (25/3)πdh/dt - 5πdh/dt

-7 = (10/3)πdh/dt

dh/dt = -21/(10π) ≈ -0.668 cm/sec

Therefore, the rate at which the level of the root beer in the cup is changing while the root beer is 2 centimeters deep is about -0.668 cm/sec.

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The rate of increase in the volume V is 30π cubic inches per second when the surface area S becomes 100π square inches.

What is volume?

Volume refers to the amount of three-dimensional space occupied by an object or a substance.

To find the rate of increase in the volume V of a sphere when the surface area S becomes 100π square inches, we need to use the formulas relating the surface area and volume of a sphere to its radius.

The surface area S of a sphere is given by the formula:

\(S = 4\pi r^2,\)

where r is the radius of the sphere.

The volume V of a sphere is given by the formula:

\(V = (4/3)\pi r^3.\)

To find the rate of increase in volume with respect to time, we need to differentiate the volume formula with respect to time.

Given that the radius r is increasing at a uniform rate of 0.3 inches per second, we can write:

dr/dt = 0.3 inches per second.

Now, let's differentiate the volume formula with respect to time:

\(dV/dt = d/dt [(4/3)\pi r^3].\)

Using the power rule of differentiation, we get:

\(dV/dt = (4/3)\pi * 3r^2 * (dr/dt).\)

Simplifying further, we have:

\(dV/dt = 4\pi r^2 * (dr/dt).\)

Since we want to find the rate of increase in cubic inches per second, we need to express the volume in cubic inches.

Substituting the value of the surface area S = 100π square inches into the surface area formula:

\(100\pi = 4\pi r^2.\)

Dividing both sides by 4π, we get:

\(r^2 = 25.\)

Taking the square root of both sides, we find:

r = 5.

Now, we can substitute the value of r into the rate of increase formula:

\(dV/dt = 4\pi(5^2) * (0.3).\)

Simplifying the expression:

dV/dt = 4π(25) * 0.3.

dV/dt = 30π cubic inches per second.

Therefore, the rate of increase in the volume V is 30π cubic inches per second when the surface area S becomes 100π square inches.

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Answer:

100

Step-by-step explanation:

mode : the most common number that appears

Answer:

100

Step-by-step explanation:

The mode is the number that is repeated the most. In this case, 100 is the only number that is repeated, and therefore it is the mode.

Answer:

About .9332

Step-by-step

This tells us that the probability that a z value is less than or equal to 1.5 is about .9332. Thus, the shaded region is about 93.32% of the entire curve. Let's try another example.

Step-by-step explanation:

7, HT= \(\sqrt{8^2 + 15^2}\) =17 cm

8, S = 1/2.AC.BC.sinC≈28,01 cm^2

9, S =1/2.SR.RT.sin R≈ 3615,7 m^2

Prove:

the area of the ABC triangles is S

sin A = BH/AB

S = 1/2 BH.AC=1/2 sinA.AB.AC=1/2*c*b*sinA

Answer:

1

Step-by-step explanation:

d=-4 , f = 3

so, [8-(-4)]/4 × 3

= (8+4)/12

= 12/12

=1

Hope it helps

Answer:

1 is the answer

Step-by-step explanation:

8-(-4) / 4(3) = 1

Answer: -2

Step-by-step explanation:

Answer:the 3rd 1

Step-by-step explanation:

Answer:

\( x = 4 \sqrt{3} \)

Step-by-step explanation:

By Pythagoras Theorem:

\( {x}^{2} = {( \sqrt{8 \times 4}) }^{2} + {(4)}^{2} \\ \\ {x}^{2} = {( \sqrt{32}) }^{2} + {(4)}^{2} \\ \\ {x}^{2} = 32 + 16 \\ \\ {x}^{2} = 48 \\ \\ x = \sqrt{48} \\ \\ x = \sqrt{ {4}^{2} \times 3} \\ \\ x = 4 \sqrt{3} \)

Answer:

Z=54 And Z+45=99

Step-by-step explanation:

The acceleration of the object moving at a constant speed in a circular path of radius r at a rate of 1 revolution per second is given by option C, 2π^2r^2.

The object experiences centripetal acceleration towards the center of the circle. Although its speed remains constant, the direction of its velocity continuously changes, resulting in acceleration. The magnitude of centripetal acceleration can be calculated using the formula a = (v^2) / r, where v is the linear velocity and r is the radius of the circular path. In this case, the linear velocity is the circumference of the circle (2πr) divided by the time (1 second), squared, and divided by the radius (r), resulting in 2π^2r^2.

The acceleration of an object moving in a circular path is directed toward the center of the circle and is known as centripetal acceleration. In this scenario, the object moves at a constant speed of 1 revolution per second, which means it completes a full circular path in 1 second. The linear velocity can be calculated by dividing the circumference of the circle (2πr) by the time taken to complete one revolution (1 second). Since the speed is constant, there is no tangential acceleration. However, the object experiences centripetal acceleration due to the continuously changing direction of its velocity. The magnitude of the centripetal acceleration is given by the formula a = (v^2) / r, where v is the linear velocity and r is the radius. Plugging in the values, we get a = ((2πr) / 1)^2 / r = 4π^2r^2 / r = 4π^2r, which corresponds to option D, 4π^2r.

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Corresponding parts of congruent triangles are congruent.

What do you mean by congruency?

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. Formally speaking, two sets of points are said to be congruent if—and only if—they can be changed into one another by an isometry, which is a combination of rigid movements like translation, rotation, and reflection. This indicates that one item may be exactly aligned with the other object by moving and reflecting it, but not by resizing it. So if we can cut out and then perfectly match up two separate plane figures on a sheet of paper, they are congruent. The paper may be turned over.

Corresponding parts of congruent triangles are congruent.

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Probability that the arrow will stop on the same letter twice = 1/3 (c).

What is probability?

The area of arithmetic called likelihood deals with numerical representations of the chance that a happening can occur or that an announcement is true.

Main body:

Given : Maria will spin the arrow on the spinner 2 times.

To find : What is the probability that the arrow will stop on the same letter twice.

Solution : We have given a spinner that spin twice and stop on the same letter.

Formula for probability = no. of favourable outcome/ total outcomes

Here, total part of spinner = 3 and it spin two times

So, total possible outcome = 6.  Arrow stay on same letter twice( favorable outcome) =2.

Plugging the values in formula :

Probability =  2/6

Probability =  1/3

Therefore,  probability that the arrow will stop on the same letter twice =  (c).

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The contract between Expert Pavers, Inc., and Fabricated Building Corporation for repaving Fabricated's parking lot includes various elements that are essential to the agreement and its enforceability.

A contract is a legally binding agreement between two or more parties that outlines the rights and obligations of each party. In the case of Expert Pavers, Inc., and Fabricated Building Corporation, the contract for repaving the parking lot encompasses several elements. First, there must be an offer from one party, which in this case is Expert Pavers, Inc., to perform the repaving services. Fabricated Building Corporation must then accept the offer and agree to pay for the services provided. This acceptance can be expressed orally, in writing, or even implied by the conduct of Fabricated Building Corporation. Furthermore, for a contract to be valid, there must be consideration, meaning that each party must provide something of value to the other. In this situation, Expert Pavers, Inc., provides the repaving services, and Fabricated Building Corporation provides payment. Additionally, the contract should clearly define the scope of work, timeline, and any other specific terms or conditions agreed upon by both parties. It is crucial for contracts to be clear, unambiguous, and mutually agreed upon to ensure enforceability and protect the rights of both parties involved.

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Answer:

8...the value of d variable =45 degree

corresponding angles are equal(reason)

9.

Answer:

if one angle is 35 degree... the other angle which one is opposite must be 35 degree

Step-by-step explanation:

now we can collect two angle and try to complete 180 degree. 45+35+ other angle equal to 180 degree and the other angle is 100 degree and we have Z rules so x=100 C°

An exponential function is y = 0.5ˣ.

What is an exponential function?

Calculating the exponential growth or decay of a given collection of data is done using an exponential function, which is a mathematical function. Exponential functions, for instance, can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, and disease spread.

Here, we have

Given: (-2,4) & (1,0.5)

We have to find an exponential function.

An exponential function is in the general form

y = a(b)ˣ

We know the points  (-2,4) & (1,0.5)  so the following is true:

4 = a(b)⁻².....(1)

0.5 = ab.....(2)

From equation(1), we get

4 = a/b²

4b² = a

Now we put the value of a in equation(2) and we get

0.5 = b(4b²)

0.5/4 = b³

b = 0.5

If b = 0.5 then the value of a is:

0.5 = a(0.5)

a = 1

Giving us the equation:

y = 1(0.5)ˣ

y = 0.5ˣ

Hence, an exponential function is y = 0.5ˣ.

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A manufacturer of compact fluorescent light bulbs advertises have a standard deviation of 1,000 hours so the values are:

A normal distribution with,

μ = 9000

σ = 1000

a) The standardized score is the value x decreased by the mean and then divided by the standard deviation.

x = 105000 - 9000 / 1000 ≈ 1.50

Determine the corresponding probability using the normal probability table in appendix,

P(X>10500) = P(Z>1.50) = 1 - P(Z<1.50)

= 1 - 0.9332 = 0.0668.

b) n = 15

The sampling distribution of the mean weight is approximately normal, because the population distribution is approximately normal.

The sampling distribution of the sample mean has mean μ and standard deviation σ/√n

μ = 1000/√15 = 258.19

c) The sampling distribution of the sample mean has mean μ and standard deviation σ/√n

The z-value is the sample mean decreased by the population mean, divided by the standard deviation:

z = x-u/σ/√n = 10500-9000/1000√15 = 5.81

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The 35th term in the arithmetic sequence is -9.

To find the thirty-fifth term in an arithmetic sequence, we need to use the formula for finding the nth term. This formula is given as:

nth term = a + (n-1)d

Where "a" is the first term in the sequence, "n" is the term number we want to find, and "d" is the common difference between the terms in the sequence.

In this problem, we are given the twenty-third term and the fifty-third term in the sequence, so we can use this information to find the common difference. We can write two equations using the formula above:

23rd term = a + (23-1)d
53rd term = a + (53-1)d

We are given the values for these two terms, so we can substitute them into the equations:

-5 = a + 22d
35 = a + 52d

Now we can solve for "a" and "d" by using these two equations. First, we can subtract the first equation from the second equation:

40 = 30d

Dividing both sides by 30, we get:

d = 4/3

Now we can substitute this value of "d" into either of the two equations above to solve for "a". Let's use the first equation:

-5 = a + 22(4/3)

-5 = a + 88/3

Subtracting 88/3 from both sides, we get:

a = -163/3

Finally, we can use the formula for finding the 35th term in the sequence:

35th term = -163/3 + (35-1)(4/3)

35th term = -163/3 + 34(4/3)

35th term = -163/3 + 136/3

35th term = -27/3

35th term = -9

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Answer:

Step-by-step explanation:

26

There are 27,405 ways to choose 4 students out of 32 for the academic challenge team.

The number of ways to choose 4 students out of 32 can be calculated using the combination formula, which is denoted as "32 choose 4" or written as C(32, 4).

To calculate the number of ways to choose 4 students out of 32, we can use the combination formula:

C(n, r) = n! / (r! * (n - r)!)

where n is the total number of students (32 in this case) and r is the number of students to be chosen (4 in this case).

Applying this formula, we have:

C(32, 4) = 32! / (4! * (32 - 4)!)

Simplifying this expression:

C(32, 4) = 32! / (4! * 28!)

Now, calculating the factorial expressions:

32! = 32 * 31 * 30 * ... * 3 * 2 * 1

4! = 4 * 3 * 2 * 1

28! = 28 * 27 * 26 * ... * 3 * 2 * 1

The common terms between 32! and 28! cancel out, leaving:

C(32, 4) = (32 * 31 * 30 * 29) / (4 * 3 * 2 * 1)

Evaluating this expression, we find:

C(32, 4) = 27,405

Therefore, there are 27,405 ways to choose 4 students out of 32 for the academic challenge team.

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Answer:

11/8 is a fraction for 137 but it is in the simplest form as a fraction...

Step-by-step explanation:

%?

The computation of the equation shows that the extra data that will be used to have the same amount will be 5 gigabytes.

Let the amount of extra data used be represented by x.

Plan 1 = 35 + (5 × x) = 35 + 5x

Plan 2 = 50 + (2 × x) = 50 + 2x

35 + 5x = 50 + 2x

Collect like terms

5x - 2x = 50 - 35

3x = 15

x = 15/3 = 5

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Answer:

False.

Step-by-step explanation:

In translation, rotation and reflections there is no size change but in dilation the size of the pre-image changes.

So, it is false.

The value of expression  (√3+1)(1-2√3)​ is -5-√3

An expression is combination of variables, numbers and operators.

The given expression is (√3+1)(1-2√3)​

Square root three plus one times of one minus two root three.

(√3+1)(1-2√3)​

Now distribute each terms

√3-2√3√3+1-2√3

√3-2(3)+1-2√3

Add the like terms

√3-6+1-2√3

√3-5-2√3

-5-√3

Hence, the value of expression  (√3+1)(1-2√3)​ is -5-√3

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Answer:

okay?... and...?

Step-by-step explanation: