Brian invests £1900 into his bank account.
He receives 4.5% per year compound interest.
How much will Brian have after 7 years?

Answer:

(15/100*percentage fee* x O*Original price* + C*car price*)

1 expression: (15/100 x O) + C

2 expression: (15/100 + C) x (O + C)

3 expression: C + (O x 15/100)

The following statements are true:

Segment DEF is parallel to ABC

The line segment  AB is parallel to DE

Line FC is parallel to AD

the line that is skewed to DE is BC

One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.

The given diagram is a triangular prism. From the diagram, some of the sides are parallel to each other (that is facing each other directly)

Some of the lines are also parallel to each other. From the given diagram, the sides that are parallel to each other are;

DEF is parallel to ABC

CADF is parallel to CBEF

For the lines, the lines that are parallel to each other are:

AD is parallel to BE

AB is parallel to DE

FC is parallel to AD

Skew lines are straight lines that do not intersect and are not in the same plane. Hence the line that is skewed to DE is BC

The missing image is attached with the answer below.

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Using the Pythagorean theorem:

6^2 = 5^2 + x^2

Simplify:

36 = 25 +x^2

Subtract 25 from both sides:

11 = x^2

Square root of both sides:

x = sqrt(11) (exact) or 3.316625 as a decimal

Answer:

the answer is X=8

Step-by-step explanation:

2(8)+4=20

Answer:

x = 8

Step-by-step explanation:

Given

2x + 4 = 20 ( subtract 4 from both sides )

2x = 16 ( divide both sides by 2 )

x = 8

The correct answer is (D) The full length to which it can be extended.

The size classification of an extension ladder indicates the full length to which it can be extended.
An extension ladder's size classification indicates the total length the ladder can reach when its fly section is fully extended.

This helps users determine if the ladder will be long enough for their specific needs when working at height.

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In mathematics, a number is a quantity that represents a magnitude or size. Numbers can be used to measure, count, label, and represent values in a variety of contexts.

There are different types of numbers in mathematics, including:

Natural numbers: These are the counting numbers, starting from 1 and going up infinitely (1, 2, 3, 4, 5, ...).

Whole numbers: These are the natural numbers together with 0 (0, 1, 2, 3, 4, ...).

Integers: These are the whole numbers together with their negative counterparts (-3, -2, -1, 0, 1, 2, 3, ...).

Rational numbers: These are numbers that can be expressed as a ratio of two integers, such as 3/4, -2/5, or 7/1.

Irrational numbers: These are numbers that cannot be expressed as a ratio of two integers, such as π (pi) or √2 (the square root of 2).

Real numbers: These are all the rational and irrational numbers together.

Complex numbers: These are numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit (i.e., the square root of -1).

So, "number" is a general term in mathematics that refers to a wide range of quantities and types of values.

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4/6=2/3 (divide both numerator and denominator by 2 (gcd)).

Hope this helps.

2/3

Hope this helps!! Good luck! :)

Answer:

a reflection followed by a translation

Step-by-step explanation:

In the image line segment SE is the tangent. The secant line making an angle with tangent line SE is NS. So the angle is ∠GSE. So option B is the correct answer.

Tangent is a line which intersect with only a single point on the curve. The point where the line meets is the point of tangency. Tangent line is always perpendicular to the radius drawn to the point of tangency. Here the tangent line is SE, point of tangency is S.

Secant lines are the lines which passes through two points of a curve. A chord drawn to the circle is a secant line. Here there are two secant lines NS and NA. Here only NS makes an angle with the tangent line.

So the angle made by a tangent and secant line is ∠GSE.

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The image for the question is attached below.

The object is moving backward when the velocity function v(t) is negative. To determine when the object is moving backward, we need to consider the sign of the velocity function v(t).

Given that v(t) = 9 - 4t, we can set it less than zero to find when the object is moving backward. Solving the inequality 9 - 4t < 0, we get t > 9/4 or t > 2.25. Therefore, the object is moving backward for t > 2.25 seconds.

The acceleration function can be found by differentiating the velocity function with respect to time. The derivative of v(t) = 9 - 4t gives us the acceleration function a(t). Taking the derivative, we have a(t) = d(v(t))/dt = d(9 - 4t)/dt = -4. Therefore, the object's acceleration function is a(t) = -4 m/s². The negative sign indicates that the object is experiencing a constant deceleration of 4 m/s².

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Answer:

\(\huge\boxed{y=-x+9}\)

Step-by-step explanation:

The slope-intercept form of an equation of a line:

\(y=mx+b\)

m - slope

b - y-intercept

From the graph we have the y-intercept (0, 9) → b = 9.

Substitute it to the equation of a line:

\(y=mx+9\)

From the graph we have the x-intercept (9, 0) → x = 9, y = 0.

Substitute to the equation:

\(0=9m+9\)          subtract 9 from both sides

\(-9=9m\)         divide both sides by 9

\(-1=m\to m=-1\)

Finally:

\(y=-1x+9\)

Answer:

1) Yes

2) No

3) Yes

4) Yes

Step-by-step explanation:

Remember the rule: the sum of the two shortest sides must be bigger than the longest side. From there, the answers should be obvious. Just add up the smallest sides for each triplet of lengths and see if that is bigger than the largest side.

7 + 14 > 18, therefore this can be a triangle

3 + 8 < 17, therefore this can't be a triangle

3.2 + 9.0 > 11.5, therefore this can be a triangle

6 + 7 > 8, therefore this can be a triangle

The equation to predict how many hours, x, the second part of the trip will take is :x = (total distance - distance traveled in the first part) / average speed x = (125 - 75) / 50  x = 1

To predict how many hours, x, the second part of the trip will take, we can use the equation:

x = (total distance - distance traveled in the first part) / average speed

In this case, the total distance of the trip is 125 miles, and the distance traveled in the first part is the product of the average speed and the time taken for the first part, which is 50 miles/hour * 1.5 hours = 75 miles.

Substituting these values into the equation, we have:

x = (125 - 75) / 50

Simplifying the equation, we get:

x = 50 / 50

x = 1

Therefore, the equation to predict how many hours, x, the second part of the trip will take is:

x = (total distance - distance traveled in the first part) / average speed

x = (125 - 75) / 50

x = 1

This means that the second part of the trip will take 1 hour to complete after the bus stops to refuel.

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If the height of the triangle is three more than four times its base, then the base of the triangle is x units and height of the triangle is 4x+3 units

The base of the triangle = x units

The height of the triangle is three more than four times its base

Four times the base = 4 × x

= 4x

Three more than four times its base = 4x+3

The height of the triangle is three more than four times its base

The height = 4x+3 units

Hence, If the height of the triangle is three more than four times its base, then the base of the triangle is x units and height of the triangle is 4x+3 units

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You can use the fact that the middle area can be found by subtracting internal area from the total area.
The amount of wood(in area, assuming almost flat) needed by the carpenter to build the frame is given by

Option A: 5.5π + 106 sq. inches.

The middle area can be found by subtracting internal area from the total area.
For example, if you've got a big circle, and a small circle inside that big circle, and you want the remaining area in the big circle not occupied by smaller circle, then we have

Remaining area = Area of bigger circle - Area of smaller circle

The diagram is attached below.

The wooden region between those two semicircles in the top is of this below area

Area of bigger semicircle - Area of smaller semicircle.

Since bigger semicircle has 6 inch radius and smaller has 1 inch less(since width of the wood is 1 inch everywhere) which is 5 inch radius, thus,

As area of semicircle with radius r units is \(\dfrac{\pi r^2}{2} \: \rm unit^2\)

Thus,

Area of wood between two semicircles = \(\pi \times 6^2/2 - \pi \times 5^2/2 = \pi \times 11/2 = 5.5\pi \rm \: \: inch^2\)

Area of the wood in the bottom of the window = area of rectangle GLMH

Since |GL| = |HM| = 1 inch and |LM| = 12 inches, thus, as

Area of rectangle = length times width

thus,

Area of GLMH = \(1 \times 12 = 12 \rm \: inch^2\)

Remaining wood is as rectangle ABGE and CDFH

Since we have |AL| = 48 inches but |GL| = 1 inch, thus, |AG| = 47 inches(1 less than |AL|

Also, since |GE| = 1 inch wide, thus,

Area ABGE = \(1 \times 47 = 47 \: \rm inch^2\)

Similar to above case, we have

Since we have |DM| = 48 inches but |HM| = 1 inch, thus, |DH| = 47 inches(1 less than |DM|

Also, since |FH| = 1 inch wide, thus,

Area CDFH = \(1 \times 47 = 47 \: \rm inch^2\)

Thus, total wood used(in terms of area) = Area CDFG + Area ABCD + Area of bottom rectangle GLHM + Area of the internal of two semicircles on top ADCB(thick arc like shape)

or

Total area of wood = 47 + 47 + 12 + 5.5π = 5.5π + 106 sq. inches.

Thus,

The amount of wood(in area, assuming almost flat) needed by the carpenter to build the frame is given by

Option A: 5.5π + 106 sq. inches.

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Answer:

30000

Step-by-step explanation:

200x10x15=30000

The simplified form of the expression 2x^2 - 3x - 2 remains as 2x^2 - 3x - 2.

To simplify the expression 8x - 2x - x^2, we can combine like terms by adding or subtracting coefficients.

8x - 2x - x^2

First, let's combine the x terms:

(8x - 2x) - x^2

This simplifies to:

6x - x^2

Therefore, the simplified form of the expression 8x - 2x - x^2 is 6x - x^2.

Now, let's simplify the expression 2x^2 - 3x - 2:

The expression is already in simplified form, and no further simplification is possible.

Therefore, the simplified form of the expression 2x^2 - 3x - 2 remains as 2x^2 - 3x - 2.

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Particular solution to the given differential equation is dy/dt =\(e^t / (-2dt^2 + y dt)\), the constant d represents any arbitrary constant value,

To find a particular solution to the given differential equation:

dy/dt = \(e^t / (-2dt^2 + y dt)\)

We can use the method of undetermined coefficients. Let's assume the particular solution has the form:

y_p(t) = A ×\(e^{at)\)

where A and a are constants to be determined.

Now, we'll differentiate y_p(t) to find dy_p/dt and substitute it into the differential equation:

dy_p/dt = A * a * \(e^{at}\)

Substituting this into the differential equation, we get:

A * a *\(e^{at}\) = \(e^{t}\) / (-2dt² + A * \(e^{at}\) dt)

Now, let's solve for the values of A and a.

Comparing the terms on both sides, we can equate the coefficients:

A * a = 1 (equation 1)

-2d = A (equation 2)

From equation 2, we can solve for A:

A = -2d

Now, substitute this value of A into equation 1:

-2d * a = 1

Solving for a:

a = -1 / (2d)

Therefore, the particular solution to the given differential equation is:

y_p(t) = (-2d) * \(e^{-t/2d}\)

Note: The constant d represents any arbitrary constant value, and it is included in the particular solution.

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Answer:

Depends on the x value

Step-by-step explanation:

f(x) can only be a function if the x values are not repeating.

a 21.8 g sample of osmium would occupy a volume of approximately 0.9646 cm³.

To calculate the volume occupied by a sample of osmium, we can use the formula:

Volume = Mass / Density

Given:

Mass = 21.8 g

Density = 22.6 g/cm³

Substituting these values into the formula:

Volume = 21.8 g / 22.6 g/cm³

Simplifying:

Volume = 0.9646 cm³

what is volume?

Volume is a measure of the amount of space occupied by a three-dimensional object or substance. It quantifies the extent or capacity of an object or substance in terms of how much space it occupies.

In mathematical terms, volume is typically measured in cubic units (such as cubic meters, cubic centimeters, or cubic inches). It is calculated by multiplying together the three dimensions of the object (length, width, and height) or by using specific formulas depending on the shape of the object.

For example, the volume of a rectangular box can be calculated by multiplying its length, width, and height. The volume of a cylinder can be calculated using the formula πr²h, where r is the radius of the base and h is the height.

Volume is an essential measurement in various fields such as physics, engineering, chemistry, and everyday life. It helps determine capacities, quantities, displacements, and the amount of space occupied by objects or substances.

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The probability that a  randomly selected bolt will have a diameter greater than 19.705 mm is 0.9812.

Given that:

mean = 19.0

standard deviation = 0.3

P(18.295 < x < 19.705)

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

= P[(18.295 - 19.0)/0.3) < (x-mean)/standard deviation < (19.705-19.0)/0.3)]

= P(-2.35 < z < 2.35)

= P(z<2.35)-P(z<-2.35)

= 0.9906 - 0.0094

= 0.9812

Probability = 0.9812

Hence we get the required probability.

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The solutions or roots of a polynomial (f(x)) are the values of the function where it is equal to 0 (f(x)=0), when the graph of the function crosses the x-axis. They are also called the zeros of the function.

Answer: Zeros

Using the z-distribution, it is found that the 95% confidence interval for the mean lifetime of this type of drill, in holes drilled, is (10.4, 13.94).

We are given the standard deviation for the population, hence, the z-distribution is used. The parameters for the interval is:

Sample mean of  \(x = 12.7\)

Population standard deviation of  \(\sigma = 6.37\)

Sample size of .n = 50

The margin of error is:

\(M = z \frac{\sigma }{\sqrt{n} }\)

In which z is the critical value.

We have to find the critical value, which is z with a p-value of  \(\frac{1+\alpha }{2}\) , in which  \(\alpha\) is the confidence level.

In this problem, , thus, z with a p-value of , which means that it is z = 1.96.

Then:

\(M= 1.96\frac{6.37}{\sqrt{50} } = 1.77\)

The confidence interval is the sample mean plus/minutes the margin of error, hence:

x- M = 12.17 - 1.77 =10.4

x+M = 12.17 + 1.77 = 13.94

The 95% confidence interval for the mean lifetime of this type of drill, in holes drilled, is (10.4, 13.94).

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In the given model, the process {Yt} is a stationary process. The autocovariance function and autocorrelation function of {Yt} can be calculated.

(a) Stationarity of {Yt}:

To show that {Yt} is stationary, we need to demonstrate that its mean and autocovariance do not depend on time. Taking the expectation of Yt, we have E[Yt] = E[Xt + Zt] = E[Xt] + E[Zt] = 0 + 0 = 0, which shows that the mean of {Yt} is constant over time. For the autocovariance function, we calculate Cov(Yt, Yt+h) as Cov(Xt + Zt, Xt+h + Zh) = Cov(Xt, Xt+h) + Cov(Zt, Xt+h) + Cov(Xt, Zh) + Cov(Zt, Zh). Since {Xt} is an AR(1) process, the covariance terms involving Xt cancel out, leaving Cov(Zt, Zt+h). Since {Zt} is a white noise process, Cov(Zt, Zt+h) = 0 for h ≠ 0 and Cov(Zt, Zt) = Var(Zt) = σ². Hence, the autocovariance of {Yt} only depends on the lag h, indicating stationarity.

(b) Proving yʊ(h) = 0 for |h| > 1:

To prove that yʊ(h) = 0 for |h| > 1, we need to show that the cross-covariance between {Ut} and {Yt} is zero. By the given equation Ut = YtYt-1, we can rewrite it as Ut = (Xt + Zt)(Xt-1 + Zt-1). Expanding this expression, we get Ut = XtXt-1 + XtZt-1 + ZtXt-1 + ZtZt-1. The cross-term XtZt-1 involves Xt and Zt-1, which are not contemporaneously correlated due to the independence assumption. Therefore, E[XtZt-1] = E[Xt]E[Zt-1] = 0, and the cross-covariance yʊ(h) between {Ut} and {Yt} is zero for |h| > 1.

In conclusion, the process {Yt} is stationary, and its autocovariance function and autocorrelation function can be calculated. Additionally, it has been shown that yʊ(h) = 0 when |h| > 1 for the process {Ut}.

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The statement that accurately describes what Marisol should do next is that Marisol should go back and group the terms in Step1 as (6x³– 22x²) – (9x – 33) and it can be determined by using the factorization method.

Marisol grouped the terms and factored the GCF out of the groups of the polynomial \(\rm 6x^3- 22x^2- 9x + 33\).

To factor out the common GCF out of the group, the following steps should have been taken by Marisol.

Marisol grouped the terms and factored the GCF out of the groups of the,

To factor out the common GCF out of the group, the following steps should have been taken by Marisol following all the steps given below.

        \(\rm= 6x^3- 22x^2- 9x + 33\\\\= (6x^3-22x^2) - (9x-33)\)

        \(= (6x^3-22x^2) - (9x-33)\\\\= 2x^2(3x^2-11) -3(3x-11)\\\\= (2x^2-3) (3x-11)\)

Hence, The statement that accurately describes what Marisol should do next is that Marisol should go back and group the terms in Step1 as (6x³– 22x²) – (9x – 33).

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Answer:

13 hours

Step-by-step explanation:

65/5= 13

Answer:

13

65/10=x/2

ANSWER...

Answer:

M is congruent to P, N is congruent to Q, and O is congruent to R.

Step-by-step explanation:

Congruent angles are angles with exactly the same measure.

The possibility that something will occur, prior measures, and conventional objective measurements all influence the likelihood that something will occur.

What is probability and what types are there in total?

The study of probability is a field of mathematics that determines the probability of an event occurring, which is represented by a number between 1 and 0. When an event has a probability of 1, it can be said to be a certainty. For instance, if the coin lands flat, the likelihood that it will come up  "heads or  tails" is 1. There are no other possible outcomes. A probability of .5 indicates that there is an equal chance that an event will occur or not.

Probability can be quantitatively represented in the simplest form as follows: the total number of possible outcomes multiplied by the ratio of the number of occurrences of a targeted event divided by the sum of the occurrences and failures of occurrences:

P(a) = P(a)/[P(a) + P(b)]

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Answer:

the answer is 6.966×10^-3

Whenever possible, research should be designed so that the data can be anlyzed using option (a) statistics

-This includes both parametric tests (which assume that the data is normally distributed and meet certain assumptions) and non-parametric tests (which do not make these assumptions and are useful for non-normal data). SPSS is a software program commonly used for statistical analysis, but it is not necessary for conducting statistical analyses.

a. statistics

Research should be designed so that the data can be analyzed using statistics. Statistics provide a set of methods and tools for analyzing and interpreting data, which can help researchers draw meaningful conclusions from their findings. Statistical analysis can be used to identify patterns, trends, and relationships in data, as well as to test hypothesis and make predictions.

Depending on the research question, data type, and sample size, different types of statistical tests may be appropriate. Both parametric and non-parametric tests can be used to analyze data, depending on the assumptions made about the underlying distribution of the data and the level of measurement of the variables. SPSS is a statistical software program that can be used to perform statistical analysis, but it is not necessary for designing research studies or analyzing data.

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