A baseball dropped from the roof of a tall building takes 3. 1 seconds to hit the ground. How tall is the building? [neglect friction. ].

The required expression gives the rate of change will be d'(3) at which the depth is changing at 3 minutes.

Let d(t) represent the depth of the rain puddle at any time t,

⇒ d(t)  ....(i)

The depth is changing with respect to time, which is given in the question

Differentiate equation (i) with respect to t and we get

⇒ δd(t)/δt = d'(t) ....(ii)

This is the rate of change in depth unit time

As per the question, the depth is changing at 3 minutes

Substitute the value of t = 3 in equation (ii), and we get

⇒ d'(3)

Therefore, the required expression gives the rate of change will be d'(3).

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Answer:

16.4m

Step-by-step explanation:

Area of a triangle = 1/2bh

A=1/2(6.7)(4.9)

A= 16.4m

The two numbers are 2 and 4.

What is the greatest common factor?

The highest number that is a factor of all the numbers is known as the greatest common factor of two or more numbers.

Here, we have

Given

Least common multiple of 60 is code for "it's a really small number."

Less than or equal to 12 confirms that the number must be less than 12.

GCF of the two numbers is 2 tells me "it's the smallest number around."

Hence, the two numbers are 2 and 4.  Their multiples can arrive at 60, they are less than 12, and the GCF for both numbers is 2.

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Step-by-step explanation:

​Erik earns a 4% commission on each car he sells. A car listed at $39,499 sold for $36,800.

A. How much was Erik’s commission? Round your answer to the nearest cent.

4% = 0.04

36,800 * 0.04 = $1,472

Erik's Commission = $1,472

________________________________________

B. How much commission did Erik lose by not selling the car at the original listed price? Round your answers to the nearest cent.

would have made: 39,499 * 0.04 = $1,579.96

$1,579.96 - $1,472 = $107.96

Commission Lost = $107.96

The length of segment AC is given by the law of sines and trigonometric ratios as; 11.3 cm.

The law of sines states that in a triangle, the ratio of the sine of an interior angle of a triangle to the length of the side opposite the angle is constant.

The given parameters are;

The figure ABC is a triangle

The figure ADC is a straight line segment

The Segment BD is perpendicular to segment AC

The length of segment AB = 7 cm

Length of segment BC = 12 cm

The measure Angle BAD= 65°

By the Definition of segment BD being perpendicular to segment AC

BAC = 90 - 65 = 25

Using the law of sines, we have;

[tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]

A vertex of the triangle from the question is point B that gives;

AD = 7 × sin(65°) = 4√3

Similarly,

[tex]\dfrac{sin\angle 25}{12} = \dfrac{sin\angle B}{7}[/tex]

Therefore, AC = 7√2 ≈ 11.3

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Check the picture below.

so the chord we see in the picture in "green", has a length of XQ + QY, now, we can just use the pythagorean theorem to get the length of XQ, keeping in mind that the point of tangency at Q is always a right-angle, and thus that means that XQ = QY, so whatever the green chord is, is just really 2 * XQ.

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - a^2}=b \qquad \begin{cases} c=\stackrel{hypotenuse}{9}\\ a=\stackrel{adjacent}{7}\\ b=\stackrel{opposite}{XQ}\\ \end{cases} \implies \sqrt{9^2 - 7^2}=XQ \\\\\\ \sqrt{32}=XQ\implies 4\sqrt{2}=XQ\hspace{5em} \underset{\textit{\LARGE XY}}{\stackrel{(2)4\sqrt{2}}{{\Large \begin{array}{llll} 8\sqrt{2}\approx 11.31 \end{array}}}}[/tex]

Answer:

[tex]8\sqrt{x} 2 - 11.31\\[/tex]

It is deduced that b and s are not mutually exclusive events as A. No, because the probability of, b intersection s, equals the fraction 5 over 78

Two events are said to be mutually exclusive, if the two events cannot occur simultaneously, hence the intersection of such event defined as (BnS) will be 0.

We can obtain the probability of (BnS) as follows :

n(BnS) = number of students who are both in the band and in the sport team.

Let, this portion of students be represented as x :

(35-x) + (32-x) + x + 16 = 78

35 - x + 32 - x + x + 16 = 78

83 - x = 78

Collect like terms

83 - 78 = x

5 = x

Hence, n(BnS) = 5

Therefore, the probability of B and S will be :

n(BnS) / total number of students

P(BnS) = 5/78

Since, P(BnS) ≠ 0 ; then the events are not mutually exclusive

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"Statistical regression" should be regarded as a threat to internal validity if extremely low scores in a repeated measures design increase over time.

Regression is a statistical technique used in the fields of finance, investing, as well as other disciplines that aims to establish the nature and strength of the relationship between a single dependent variable (often represented by Y) and a number of independent variables (called as independent variables).

Thus, statistical regression poses a danger to internal validity if extremely low scores in a multiple regression design rise over time (or exceptionally high scores fall over time).

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Answer: 14) 1.5, 15) 5/8, 16) 1/6

Step-by-step explanation:

For the first one, you want to find the least common denominator. The least common denominator is 10, so you multiply the numerator and denominator to get 9/10+6/10=15/10. 15/10 is 1.5 or 1 1/2

for the 2nd one you do the same thing. You can get 1/4 to have a denominator of 8 by converting it to 2/8. 7/8-2/8=5/8

finally, you can change 2/3 to 4/6 to get a common denominator. 5/6-4/6=1/6.

Answer:  For Number (14)    1  1/2

Step-by-step explanation:

Exact Form:

3/2

Decimal Form:

1.5

Mixed Number Form:

1  1/2

The stronger the evidence is against the null hypothesis, the higher the divergence from it.

What do you mean by null hypothesis ?

A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided observations. Using sample data, hypothesis testing is performed to judge a theory' veracity. It is sometimes referred to as just "the null," and its symbol is [tex]H_{0}[/tex]. To determine if a theory regarding markets, investing methods, or economies is correct or wrong, quantitative analysts employ the null hypothesis,

The null hypothesis states that the percentage of the population who works full time is 0.45.

As a result, 450 persons who are randomly selected from a population of 1000 work full-time.

A different hypothesis states that the ratio is higher than 0.45.

In the options provided, the proportion for the first option is 300/1000, or 0.3.

In the second choice, 500/1000 equals 0.5

Third alternative: 700/1000 = 0.7

Therefore, the stronger the evidence is against the null hypothesis, the higher the divergence from it.

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Total 8 angles are formed when parallel lines are cut by a transversal.There relationships are mentioned below.

When two lines don't intersect, they are said to be parallel. Parallel lines are two lines that run parallel to each other and meet at infinity.

A transversal is formed when a line intersects two lines at distinct points.

When a transversal intersects two or more parallel lines, various angle pairs are formed. As shown in the figure below, a and d are two parallel lines intersected by the transversal l at the points P and Q.

When a pair of parallel lines is transversally cut, 8 angles are formed, as shown in the figure.

The relationship between the angles are:

pair of angles was formed.                        Relationships between angles

Corresponding angle pairs.                  ∠1 = ∠6, ∠4 = ∠8, ∠2 = ∠5, ∠3 = ∠7

Alternate interior angles pairs.                     ∠4 = ∠5, ∠3 = ∠6

Alternate exterior angle pairs.                       ∠1 = ∠7, ∠2 = ∠8

Interior angle pairs that are on              ∠3 + ∠5 = 180°, ∠4 + ∠6 = 180°

same side of the transversal .

Vertically opposite angle pairs.         ∠7 = ∠6, ∠8 = ∠5, ∠1 = ∠3, ∠2 = ∠4,

Thus, total 8 angles are formed when parallel lines are cut by a transversal

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The actual price an employee would pay for 1200 is 1050.

Given:

In a particular shop employee are given a 12. 5% discount on any item they purchase.

Let x be the actual price.

= 1200*12.5%

= 1200*12.5/100

= 1200*125/1000

= 12*125/10

= 12*25/2

= 6*25

= 150

Actual price x = 1200 - 150

= 1050

Therefore The actual price an employee would pay for 1200 is 1050.

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Answer:

x = 7

Step-by-step explanation:

3(2x - 10) + 4(x-7)= 12

6x - 30 + 4x - 28 = 12

combine x terms on left side:

10x - 30 - 28 = 12

combine numbers on left side:

10x - 58 = 12

add 58 to both sides:

10x - 58 + 58 = 12 + 58

10x = 70

divide both sides by 10:

10x/10 = 70/10

x = 7

The y -intercept of the exponential function is; 2

The y -value of the solution in Quadrant I is; 5

The number of points of intersection is; 1

The y -intercept of the linear function is; 7

We are given the functions as;

Exponential function: y = 4ˣ + 1

Linear Function: y = -2x + 7

1) The y-intercept of the exponential function will be the point at which x = 0. Thus;

y = 4⁰ + 1

y = 1 + 1

y = 2

2) From the attached graph, we see that the coordinates of intersection in Quadrant 1 is; (1, 5)

Thus, the y-value is 5

3) The number of points of intersection of the linear and exponential function is; 1 point

4) The y-intercept of the linear function is the value of y when x = 0. Thus;

y = -2(0) + 7

y = 7

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(a)The precise expression is

P (X > 1) = 1 − P(X ≤ 1) = 1 − Σ (365/x) x (1/512)^x x (511/512)^365-x

(b) The normal or the Poisson approximate for p(x>1) is

P(X > 1) = 1 − P(X ≤ 1) = 1 – Σe^-365/512. (365/512)^x/x!=0.1603

Probability is the branch of mathematics regarding numerical descriptions of how probable an occasion is to occur, or how possible it is that a proposition is genuine. The probability of an event is a number between zero and 1, wherein, kind of talking, zero suggests the impossibility of the occasion and 1 indicates fact.  

The better the possibility of an occasion, the more likely it is that the event will occur. An easy example is the tossing of an honest (impartial) coin. since the coin is fair, the two results ("heads" and "tails") are both similarly likely; the possibility of "heads" equals the probability of "tails"; and given that no different effects are viable, the chance of either "heads" or "tails" is half off (which could also be written as 0.5 or 50%).

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The 90% confidence interval is [36.19, 39.21]. The population mean of users that are connected at the same time is greater than 35.

What are null hypotheses and alternative hypotheses?

In null hypotheses, there is no relationship between the two phenomenons under the assumption or it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.

The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.

In order to ensure efficient usage of a server, it is necessary to estimate the mean number of concurrent users.

According to records, the average number of concurrent users at 100 randomly selected times is 37.7, with a standard deviation of 9.2.

With this approximation, you can construct the 90% confidence interval the approximate z will be

u± z0.90* σ/[tex]\sqrt{n}[/tex]

z 0.90= 1.64

Then we have

37.7± 1.64*9.2/[tex]\sqrt{100}[/tex]

[36.19, 39.21]

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If 15 postage stamps cost $8.25 then 12 stamps will cost $6.6 if all the stamps cost the same amount.

To calculate the cost of 12 stamps we first calculate the cost of one postage stamp by division.

Since 15 stamps cost $8.25 we can calculate the cost of one stamp by dividing the cost of 15 stamps by 15

cost of one stamp = $8.25 ÷ 15

cost of one stamp = $0.55

Since the cost of one stamp is calculated to be $0.55, we can calculate the cost of 12 stamps by multiplication as follows;

cost of 12 stamps = cost of one stamp × 12

cost of 12 stamps = 0.55 × 12

cost of 12 stamps = $6.6

Although a part of your question is incorrect, you might be referring to this question:

Kwai bought 15 postage stamps for $8.25. All stamps cost the same amount. How much will 12 stamps cost?

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Answer:

x=21.1

Step-by-step explanation:

m1 + m2 = 180

(4x-11)+(6x-20)=180

10x-31=180

x=21.1

The combined area is 0.9545.

Given:

The area under the normal curve to the left of z=-2 plus the area

under the normal curve to the right of z = 2.

Area under the normal curve to the left of z = -2 is:

= 0.0228

Area under the normal curve to the right of z = 2

= 0.9772

Combined area is = 0.9545

Therefore The combined area is 0.9545.

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The coin is not fair with certainty p<0.1 but not p<0.1.

What is the sample mean?

The mean value of a sample of data calculated from a large population of data is referred to as the Sample Mean. If the sample size is large and the statistical researchers randomly select fragments from the population, it is an effective tool for determining the population mean.

We have,

sample size, n = 80

the sample mean p = 0.56

90% confidence interval  [0. 61, 0. 52],

99% confidence interval of [0. 63, 0. 49].

for a fair coin mean should be of 0.5

population mean = 0.5 for a fair coin

from both the confidence interval, it is clear that 0.5 is within the 99% interval, whereas 0.5 is outside the 90% confidence interval.

[i.e 0.5 ∈ [0. 61, 0. 52], 0.5 ∉ [0. 61, 0. 52] ]

Hence, the coin is fair as per a 99% confidence level and unfair as per 90% confidence level.

Therefore, the coin is not fair with certainty p<0.1 but not p<0.1.

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I, III, and IV  quadrants.

What do the four graph quadrants represent?

The x and y and y-coordinates are both positive in quadrant I. X and Y coordinates in quadrant II are opposite one other. X and Y coordinates are both positive in quadrant III. In quadrant IV, the x-coordinate and y-coordinate are both positive.

Why are the first and third quadrants used?

Typically, we assume that after a projection is made on the horizontal plane, it spins clockwise. We employ first angle and third angle projection for this purpose. Because only within these two quadrants will we receive both viewpoints following the horizontal plane's clockwise rotation.

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Solutions for the inequality y is less than or equal to two-thirds times x minus 4 will exist in the I, III, and IV quadrants.

What do the four graph quadrants represent?

In quadrant I, the x and y coordinates are both positive. In quadrant II, the X and Y coordinates are orthogonal. In quadrant III, both the X and Y coordinates are positive. The x- and y-coordinates are both positive in quadrant IV.

What is the inequality's y-intercept?

Inequality y image result

Any straight-line's equation, known as a linear equation, can be written as y = mx + b,

Where m is the slope of the line and b is the y-intercept.

This line's y-intercept is the value of y at the point where the line intersects the y-axis.

We usually assume that after a horizontal plane projection, it spins clockwise. For this, we use first and third-angle projections. Because only within these two quadrants will we receive both viewpoints after the horizontal plane rotates clockwise.

Solutions for the inequality y is less than or equal to two-thirds times x minus 4 will exist in the I, III, and IV quadrants.

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The expression will become cos²(7x) = [tex]\frac{1}{2}[/tex](1 + cos14x).

Power reduction formulas like double angle and half angle formula are used to simplify the calculations requires to solve a given expression.

Power reduction formulas allow us to reduce the power on one of the trigonometric functions when the power is an even integer.

The trigonometric power reduction identities allow us to rewrite expressions involving trigonometric terms with trigonometric terms of smaller powers.

The power reduction formula is

cos²θ = [tex]\frac{1}{2}[/tex](1 + cos2θ)

sin²θ =[tex]\frac{1}{2}[/tex](1 - cos2θ)

For the given equation we will use cosine formula.

Therefore

cos²(7x) = [tex]\frac{1}{2}[/tex](1 + cos2(7x))

cos²(7x) = [tex]\frac{1}{2}[/tex](1 + cos14x).

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Angle opposite to the equal side of the triangle is always equal here we apply on the vice versa.Thus the length of BC is 17 units.

Given:

Angle B and Angle C are congruent.

The length of the side AC is labeled as x plus 9.

The length of the sides AB is labeled as 2x minus 8.

The length of the side BC is labeled as x.

We know that,

The angle opposite to the equal side of the triangle is always equal.

Therefore,

<B = <C

so

AB = AC

2x - 8 = x + 9

2x - x = 9 + 8

x = 17.

Therefore the length of BC is 17 units.

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Full question:

What is the length of BC? Enter your answer in the box. units triangle ABC with horizontal side BC. Vertex A lies above side BC.Angle B and Angle c are marked congruent.The length of side AC is labeled as x plus 9.The length of side AB is labeled as 2x minus 8.The length of side BC is labeled as x.

Coach Salinas has to find the kicker with the best goal-scoring percentage. The correct answers are identify the kicker with the greatest degree of precision and find the player that scores the most field goals per game.

The process of obtaining data for statistical analysis, inference, and conclusion-making is known as data collection.

Several crucial aspects of statistics include:

The great majority of data in statistics is numerical.

Statistical data can be used to make predictions about the future.

They are also used to make decisions.

For instance, soccer player statistics data, such as the ratio of goals to games, the number of completed dribbles per game, the maximum number of take-ons, the number of tackles, or the number of interceptions per game, can be used to decide which player to buy for a football.

To find the kicker with the highest goal success rate, Coach Salinas in the scenario supplied wants to examine the kicking statistics of their team's kickers.

For this, Coach Salinas ought to do the following actions:

the most accurate kicker to find

Identify the kicker who scores the most field goals per game.

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Yes, AAS Theorem is a valid theorem for congruency when used along with two more theorems to prove congruency of triangles.

AAS Theorem states if two angles of a triangle and the non included side in the angles are congruent to the corresponding two angles and the non included side in the two angles of the second triangle. Then the triangles are similar.

The AAS Theorem is valid for congruency of triangles if it follows the above given conditions along with the fact that two more theorems such as SSS or AAA.

As congruency in triangles is the condition in which both the given triangles are proven to be of the same shape and size.

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The number of coins that has to be collected to have a total score of 1,110 is 6.

The relationship between two variables are directly proportional, if the two variable move in the same direction. If one of the variables increases, the other variable increases. If one of the variables decreases, the other variable decreases.

The equation that is used to represent direct proportion is:

y = kx

Where:

370 = 2k

k = 370 / 2

k = 185

110 = 185x

x = 1110 / 185

x= 6

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The approximate ratio is 52 to 18 micrograms/ml.

Step 1:

This is a general question in which we need to analyze only the graph.

Regression of the calibration curve of GNE-A in mouse plasma is given.

Step 2:

In the given data, the ratio of area of GNE-A to GNE-B is taken in y axis and GNE - A concentration is taken in x axis. From the graph, it is clear that the concentration of GNE-A corresponding to the GNE-A to GNE-B ratio 52 is 18.

The approximate ratio of areas for gne-a to gne-b when the gne-a concentration is 18 micrograms/ml is 52 : 18.

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The required area is 12 cm².

A rectangle is a type of parallelogram having equal diagonals.

All the interior angles of a rectangle are equal to the right angle.

The diagonals of a rectangle do not bisect each other.

The given shape is there on a centimeter square grid.

The side of each square is 1 cm.

Then, it is clear from the figure that it consists of a rectangle of dimensions 4 × 2 and one triangle having height h = 2 cm and base b = 4cm.

Now, the area of the given shape is the sum of the area of the rectangle and the triangle.

It can be written as,

Area of the shape  = Area of rectangle + Area of triangle

                               = length × breadth + 1/2 × base × height

                               = 4 × 2 + 1/2 × 4 × 2

                               = 12

Hence, the area of the given shape is 12 cm².

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The required area of the given figure is 12 squared units.

Given that,
A figure has been shown we have to determine the area of the figure,

Surface area is defined as the measure of a region or surface is called as surface area.

Here,
The area of the given figure is given as,
Area = area of the rectangle + area of the larger triangle - area of the small triangle.
Area = 2 × 4 + 1/2 [6 × 2] - 1/2 [2×2]
Area = 8 + 3×2  - 2
Area = 8 + 6 - 2
Area = 14 - 2
Area = 12 squared units.

Thus, the required area of the given figure is 12 squared units.

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The pool area measures the following dimensions:

Length = 58 feet.

Width = 30.5 feet.

Equations are used to express the data since the 119-foot fence should only contain three sections of the pool (two wide and one long).

First, a calculation that determines the total number of feet in the fence

X + 2Y = 119 (where X is the length and Y is the width)

X = 2Y-3 (because the length is 3 feet less than twice the width)

We proceed to solve for Y using these equations to replace the second equation in the first equation:

X + 2Y = 119

2Y -3 + 2Y = 119

4Y - 3= 119

4Y= 122

Y = 122/4, and Y = 30.5 feet.

We apply the second equation to determine the value of X because we already know that the width equates to 30.5 feet: X = 2Y-3 X = 2 (30.5)-3 X = 61 - 3 X = 58

It can be seen from this that the length is 58 feet.

As a result, the pool area measures Length = 58 feet and Width = 30.5 feet.

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The lower limit that she traveled in three second is 33.45 feet and the upper limit that she traveled in three second is 43.45 feet

The speed of a runner increased steadily during the first three seconds of a race

Therefore the time = 3 seconds

Her speed at half-second intervals is given in the table

We know,

Speed = Distance / Time

Similarly

Distance = Speed × Time

Δt = 0.5 seconds

Then the lower limit of total distance traveled = 0.5(0 + 6.7 + 9.2 + 14.1 + 17.5 + 19.4)

Add the terms and multiply it

= 0.5 × 66.9

= 33.45 feet

The upper limit of total distance traveled = 0.5( 6.7 + 9.2 + 14.1 + 17.5 + 19.4 + 20)

= 0.5 × 86.9

= 43.45 feet

Hence, the lower limit that she traveled in three second is 33.45 feet and the upper limit that she traveled in three second is 43.45 feet

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