Can the two triangles be proven congruent by SAS explain?.

Answer:

Step-by-step explanation:

The length of SR will be 15 units, using Pythagoras' theorem

What is Pythagoras' theorem?

The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Remember that BC2 = AB2 + AC2 in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.

Triangle SRT and triangle TRQ can be compared using the image. Since both triangles have equal sides and right angles (T), they are both triangles (RT)

Using Pythagoras theorem,  

RQ² = TQ² + TR²

20² = TR² + 16²

TR = 12

SR/RQ = TR/TQ

SR / 20 = 12 / 16

SR = 15 units

Hence the length of SR will be 15 units.

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Answer:

the third opinion: [tex]y = \frac{1}{4}x - 1[/tex] (or as you put it, y equals one fourth times x minus 1)

This is because it's written in slope-intercept form: y = mx + b . m is the slope, which is 1/4, and b is the y-intercept, -1

Total force exerted is 50N.

What is force?

Force is any interaction that, when unopposed, will change the motion of an object.

Main body:

F=Mg-Ma

then implied:

a=(F-Mg)/M

which seems unsound, it should have said:

a = (Mg - F)/M

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

Now, let's begin and use the previous gentleman's notation:

Mass of bucket=M

mass of cylinder=m

Tension force=F

So, regarding the bucket:

F + Ma = Mg

F = Mg - Ma

a = (Mg - F)/M

Also, regarding the cylinder: T = Iα

∴ (By the dot product of torque, radial vector crossed with force, r cross F, which is Frsinθ for θ = 90 degrees)

T = Iα = Fr = (1/2)(mr2)(a/r)

where α = a/r

And T = Fr because that's what torque is, just the radial distance times the force.

So

a = 2F/m

and we also have:

a = (Mg-F)/M

So 2F/m = (Mg-F)/M

2F = mg - mF/M

2F+(mF)/M = mg

F(2+m/M) = mg

F = mg/(2+m/M)

F = (127.4 )/(2+0.56)

F = 49.765 N

That is to say, the tension that the rope induces on the bucket is 50.5 Newtons in the upward direction (positive).

Hence force exerted is approx 50 N.

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The inverse of the functions are f⁻¹(x) = 2/[3(x + 4)], f⁻¹(x) = √[(x + 1)/2] and f⁻¹(x) = 1/x + 1

Function (a)

This function is given as

f(x)=2/(3x) - 4

The function needs to be represented as an equation

So, we have

y = 2/(3x) - 4

Swap the positions of x and y

x = 2/(3y) - 4

So, we have

2/(3y) = x + 4

Take the reciprocal of both sides

3y/2 = 1/(x + 4)

Multiply both sides by 2/3

y = 2/[3(x + 4)]

So, the inverse function is

f⁻¹(x) = 2/[3(x + 4)]

The inverse is a function with the domain x ≠ -4 and range of f(x) ≠ 0

See attachment 1 for the graphs

Function (b)

This function is given as

f(x) = 2x² - 1

The function needs to be represented as an equation

So, we have

y = 2x²- 1

Swap the positions of x and y

x = 2y² - 1

So, we have

2y²= x + 1

Divide both sides by 2

y²= 1/2(x + 1)

Take the square roots

y= √[(x + 1)/2]

So, the inverse function is

f⁻¹(x) = √[(x + 1)/2]

The inverse is a function with the domain x ≥ -1 and range of f(x) ≥ 0

See attachment 2 for the graphs

Function (c)

This function is given as

f(x) = 1/(x - 1)

The function needs to be represented as an equation

So, we have

y = 1/(x - 1)

Swap the positions of r and y

x = 1/(y - 1)

So, we have

y - 1 = 1/x

Add 1 to both sides

y = 1/x + 1

So, the inverse function is

f⁻¹(x) = 1/x + 1

The inverse is a function with the domain x ≠ 0 and range of f(x) ≠ 1

See attachment for the graphs

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By using operations on integers, it can be calculated that

Difference between the amount of memory allocated by char*arr[3] on the intel ia 32 versus the intel x86-64 is 12 bytes

What is operation on integers?

At first it is important to know about integers

Integers are those numbers without any fractional part. Integers can be positive or negative and zero is also an integer.

The operation on integers are

Addition

Suppose there are numbers and the sum of those numbers has to be calculated. For this addition is used

Subtraction

To find the difference between two integers, subtraction is used

Multiplication

Repeated addition is called multiplication. Multiplication is used to find the product of two or more integers

Division

Division is the process by which value of single unit can be calculated from the value of multiple unit.

The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.

There is a well known formula for division

Divisor x Quotient + Remainder = Dividend.

This problem can be solved using operation on integers

On Intel IA 32, the address is 32 bit or 32 [tex]\div[/tex] 8 = 4 bytes

On Intel x86 - 64, the address is 64 bit or 64 [tex]\div[/tex] 8 = 8 bytes

On an array of size 3,

On Intel IA 32, the address is  4 [tex]\times[/tex] 3 bytes = 12 bytes

On Intel x86 - 64, the address is  8 [tex]\times[/tex] 3 bytes = 24 bytes

Difference between the address = 24 - 12 = 12 bytes

Difference between the amount of memory allocated by char*arr[3] on the intel ia 32 versus the intel x86-64 is 12 bytes

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Complete Question

how many bytes difference will there be in the amount of memory allocated by the following code on the intel ia 32 versus the intel x86-64?

char*arr[3]

About 50 percent of its former width.

Now, According to the question:

Let's assume that our parameter of interest is given by θ and in order to construct a confidence interval we can use the following formula:

θ = ± ME(θ vector)

Where θ vector is an estimator for the parameter of interest and the margin of error is defined usually if the distribution for the parameter is normal as:

ME = [tex]z_\alpha[/tex]SE

Where [tex]z_\alpha /2[/tex]  is a quantile from the normal standard distribution that accumulates [tex]\alpha /2[/tex] of the area on each tail of the distribution. And SE represent the standard error for the parameter.

If our parameter of interest is the population proportion the standard of error is given by:

SE =[tex]\frac{p(1-p)}{n}[/tex]

And if our parameter of interest is the sample mean the standard error is given by:

SE = [tex]\frac{1}{\sqrt{n} }[/tex]

As we can see the standard error for both cases assuming that the other things remain the same are function of n the sample size and we can write this as:

SE = f(n)

And since the margin of error is a multiple of the standard error we have that

ME = f(n)

Now if we find the width for a confidence interval we got this:

Width = θ + ME (θ) - [θ - ME (θ)]

Width = 2ME(θ)

And we can express this as:

Width = 2f(n)

And we can define the function f(n) = [tex]\frac{1}{\sqrt{n} }[/tex]  since as we can see the margin of error and the standard error are function of the inverse square root of n. So then we have this:

[tex]Width_i[/tex] = [tex]2\frac{1}{\sqrt{n} }[/tex]

The subscript i is in order to say that is with the sample size n

If we increase the sample size from n to 4n now our width is:

[tex]Width_f[/tex] = [tex]2\frac{1}{\sqrt{4n} }[/tex] = [tex]2\frac{1}{\sqrt{n}\sqrt{4} }[/tex] = [tex]\frac{1}{\sqrt{n} }[/tex] = 1/2 [tex]Width_i[/tex]

The subscript f is in order to say that is the width for the sample size 4n.

So then as we can see the width for the sample size of 4n is the half of the with for the width obtained with the sample size of n. So then the best option for this case is:

about 50 percent of its former width.

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This is incomplete question:

Complete question is this :

In constructing a 95 percent confidence interval, if you increase n to 4n, the width of your confidence interval will (assuming other things remain the same) be:

about 25 percent of its former width.

about two times wider.

about 50 percent of its former width.

about four times wider.

It will cost $776.25 to paint the area of the rectangular wall

The area can be defined as the amount of space covered by a flat surface of a particular shape. It is measured in terms of the "number of" square units (square centimeters, square inches, square feet, etc.) The area of a rectangle is the number of unit squares that can fit into a rectangle. Some examples of rectangular shapes are the flat surfaces of laptop monitors, blackboards, painting canvas, etc.

The formula of area of a rectangle is given as;

A = L * W

Imputing the values and calculate the area of the rectangular wall;

A = 12.5 * 18

A = 225ft²

But in the question, the cost of painting the wall is $3.45 per square feet.

1ft² = 3.45

225 = x

x = 3.45 * 225

x = 776.25

The cost of painting the wall is $776.25

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Answer: If any two angles and the side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by ASA rule.

The Angle Side Angle Postulate (ASA) says triangles are congruent if any two angles and their included side are equal in the triangles. An included side is the side between two angles.

Step-by-step explanation:

The simplified expression is - (4z⁴ + 4z³ - 14z² - 47z - 70) / z + 2

Simplification of an algebraic expression can be defined as the process of writing an expression in the most efficient and compact form without affecting the value of the original expression.

The process entails collecting like terms, which implies adding or subtracting terms in an expression.

In the given expression;

7 - 2z - 4 [z³ - (z³ + 4z² + 11z + 14) / (z + 2) ]

This is simplified to ;

7 - 2z - 4 [z³ - (z³ + 4z² + 11z + 14) / (z + 2) ] = - (4z⁴ + 4z³ - 14z² - 47z - 70) / z + 2

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On using the critical value (13.89 – 0.3485, 13.89 + 0.3485) when, the mean is13.89 the confidence level is 95%.

Given, a juice drink filling machine, when in perfect adjustment, fills the bottles with 14 ounces of drink on an average. a random sample of 41 bottles is selected, and the contents are measured.

as the standard deviation = 0.3485 ounces

mean = 13.89 ounces.

we have to find the confidence level,

The critical value we will use is (13.89 – 0.3485, 13.89 + 0.3485) when, the mean is 13.89.

The confidence interval for a population with a known standard deviation is based on the fact that the sample means follow an approximately normal distribution. Suppose

So, on using the critical value (13.89 – 0.3485, 13.89 + 0.3485) when, the mean is13.89 the confidence level is 95%.

Hence, on using the critical value (13.89 – 0.3485, 13.89 + 0.3485) when, the mean is13.89 the confidence level is 95%.

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The p-value statistic to test the claim that the average weight of all babies is greater than 7.5 lbs. is 7.293.

a) Data set : 9.2, 6.5, 4.3, 5.5, 7.2, 9.5, 11.2, 8.5, 5.2, 4.7, 11.0, 7.4, 8.2, 6.9, 4.1

mean of the data set = sum / frequency

mean = 7.293.

Standard deviation

=  √(871.96-797.98)/14

= 2.3001

Hence the point of estimate = 7.293

b) Using p-value> q(.80)

p> 1.282

And the sample average is just mean(x)

p>7.2933

So our margin of error is

e <- 1.282*(2.3001/sqrt(15))

e<0.7614

The lower and upper bounds are:

= mean(x) - e = 6.5319

= mean(x) + me = 8.0547

Hence the lower and upper bounds for the p-value will be 6.5319 and 8.0547 .

A statistical calculation known as a p-value is employed to assess the applicability of a hypothesis to the data. A p-value establishes the likelihood that the outcomes that were observed would occur if the null hypothesis were true. The found difference becomes statistically more significant as the p-value decreases.

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A tip of 18% was given to the restaurant after the meal and tax to the nearest percentage.

Cost of the food = $25.30

Tax on the food cost = 8%

Tax amount

= 8% of 25.30

= 0.08  × 25.30

= 2.204

Total cost of food before tip = 25.30 + 2.204 = $27.504

Tip given = 32.24 - 27.504 = 5.036

Tip percentage

= 5.036 / 27.504 × 100%

= 18.31%

≈ 18%

Hence a tip of 18% was given to the restaurant after the meal and tax to the nearest percentage.

Percentage increases and decreases are calculated by computing the difference between two numbers or by comparing that difference to the starting value.

One can calculate how significantly the initial value has changed mathematically by dividing the result by the starting value and using the absolute value of the difference between the two values.

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According to the volume of the box, the height of the box is (2x + 3)

Volume:

Volume is defied as the space occupied within the boundaries of an object in three-dimensional space.

Given,

In order to package products for her business class, Jessica needs to determine the size of a box in which they would fit. To meet shipping specifications, the volume of the box should be 6x² - 15x-36. The box is in the shape of a rectangular prism. The width of the box must be 3, and the length of the box must be x - 4.

Now, we have to find the expression or the height of the box.

From the given details, we know that,

Volume of the box = 6x² - 15x-36

Width of the box = 3

length of the box = x - 4

Let us consider the height of the box is h.

By using the volume of the box formula, we have calculated the height of the box as,

=> 6x² - 15x-36 = (3) × (x-4) × h

Here we need the value of h,

The given expression is rewritten as,

=> (6x² + 15x-36) / 3(x - 4) = h

When we factorize the numerator, then we get,

=> 3(2x + 3)(x - 4)/3(x-4) = h

Therefore, the expression for h is 2x + 3.

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The equation of given line in slope-intercept form is 5x – 4y + 20 = 0 if the line makes intercepts –4 and 5 on the x- and y-axes respectively.

The diagram of the straight condition y = mx + c is a line with m as incline, m and c as the y-block. This type of the direct condition is known as the incline block structure, and the upsides of m and c are genuine numbers. The incline, m, addresses the steepness of a line. The incline of the line is additionally named as inclination, in some cases. The y-catch, b, of a line, addresses the y-direction of the place where the chart of the line converges the y-hub.

We have x-intercept as -4 and y-intercept as 5

Equation of the line in intercept form is:

(x/a) + (y/b) = 1

Substituting the values of a and b, we get the equation as:

=>(x/-4) + (y/5) = 1

=>(-5x + 4y)/20 = 1

-=>5x + 4y = 20

=>5x – 4y + 20 = 0

Hence, line equation is 5x – 4y + 20 = 0

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(Complete question) is:

What is the equation of the given line in slope-intercept form if x-intercept is -4 and y intercept is 5?

Answer:

24

Step-by-step explanation:

120 minus 80% = 120 times 20% (fractions division method)

120 times 20% = 120 times 0.2 (simplify)

120*0.2 = 24, so the answer is 24

As per the concept of inverse function, For a function f: X → Y to have an inverse, it must have the property that for every y in Y, there is exactly one x in X such that f(x) = y.

Inverse function:

Inverse function refers a function that serves to “undo” another function.

Given,

Here we need to find the a function to have an inverse, it must be what type of function.

Based on the explanation of the inverse function, if the function is a inverse function, then it means that for all x values must have the relation in y similarly, for a the y values must have the x values.

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Translation of x with 5 units to the left is ( x + 5 ) and 7 units up is ( x + 7 ) .

As given in the question,

The translation represents the movement of the original shape in the coordinate plane.

Translation of x for the given conditions :

5 unit to the left :

Here function shift 5 units to the left by adding 5 in the function.

x → ( x + 5 )

7 units up

Function shift 7 units up by adding 7 in the function.

x → ( x + 7 )

Therefore, translation of the function by 5 units left is x+5 and 7 units up is x + 7.

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For all possible samples of 100 stores taken from the population of 1,000 stores, 95% of the confidence intervals developed will contain the true population means is true or false depending on the points shown below.

A. Referring to the problem statement, if the population had consisted of 10,000 stores, the confidence interval estimate of the mean would have been wider in the range is false since increasing sample size will decrease the width of the confidence interval

B. Referring to the problem statement, of all possible samples of 100 stores drawn from the population of 1,000 stores, 95% of the sample means will fall between 5.623 and 6.377 lawnmowers is false since the interval is for the population mean and not the sample mean.

C. Referring to the problem statement, of all possible samples of 100 stores taken from the population of 1,000 stores, 95% of the confidence intervals developed will contain the true population mean within the interval is true.

D. Referring to the problem statement, 95% of the stores have sold between 5.623 and 6.377 lawnmowers is false.

E. Referring to the problem statement, we do not know for sure whether the true population means between 5.623 and 6.377 lawnmowers sold is true since this is a confidence interval that has only 95% confidence to contain the true population means.

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The net present value formula helps us to determine the net present value of boat repair model B14 model by Cleveland Cove enterprises.

so, the net present value is 384,285.714.

Net present value: The net present value is applied to a series of cash flows occurring at different times. The present value of a cash flow always depends on the interval of time between now and the cash flow.

NPV = Rt /(1+i)^t

where , Rt --> net cash flow at time t

i --> discount rate

t --> time of cash flow

We have given that , A company has narrowed their choices down to two: the B14 Model and the F54 Model.

F54 Model :

Residual value , = 18,000

Annual net cash inflow = 30,000

investment = 230,000

time , t = 10

rate of return,r = 12%

B14 Model :

Residual value , = 10,000

Annual net cash inflow = 80,000

investment = 330,000

time , t = 10

rate of return,r = 8%

we have to calculate the net present value for model B14.

so, Net present Value = present value of annually cash - investment

present value of annually cash

= 80000/1.12 = 71,428.571

Net present value =71,428.571 ×10 - 330000

= 714,285.71 - 330,000 = 384,285.714

hence, net present value for model B14 is 384,285.714

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Complete question:

Cleveland Cove Enterprises is evaluating the purchase of an elaborate hydraulic lift system for all of its locations to use for the boats brought in for repair. The company has narrowed their choices down to two: the B14 Model and the F54 Model. Financial data about the two choices follows. B14 Model investment 330,000 useful life (yr) 10 , estimated annual cash inflow 80,000

F54 Model Investment 230 comma 000 Useful life (years) 10 10 Estimated annual net cash inflows for useful life 33 comma 000 Residual value 18 comma 000 Depreciation method Straightminusline Straightminusline Required rate of return 12% 8% What is the net present value of the B14 Model?

The orders numbers from least to greatest are 2.509, 2.925, and 2.95 respectively.

What is ascending order?

When numbers are arranged in ascending order, they are done so from least to greatest.

Ordering Decimal from Least to Greatest.

Compare each decimal's whole number component first. The smallest number is the one with the smallest entire number.

Compare the decimal parts in the same way as we compare the whole numbers if the whole number parts are the same.

Given, 2. 95,  2. 509, 2. 925

Arranging numbers from least to greatest, we get

2.509, 2.925, 2.95

Hence, the order numbers from least to greatest are 2.509, 2.925, and 2.95 respectively.

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The sentences is completed as follows

To model 2x + 4, you need:

To model 3x + (−1) you’ll need:

An algebra tile model is a graphic representation made out of various arrangements of algebra tiles. A model's function is to depict a polynomial expression or equation.

Algebra tiles it self are shapes of different colors that represents numbers or parts of numbers.

In the question, algebra tiles are used to represent the equations used in the problem. The tiles in the problem will be of 3 types

2x + 4

In this case, the equation will require the twice the x-tiles then 4 positive unit tiles

3x + (−1)

In this case, the problem is represented using 3 x-tiles and 1 negative unit tile.

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Answer:2,4,positive,negative

Step-by-step explanation:

Rate at which volume of the snowball decreasing when the radius is 12 cm is 180.864 cm^3/min

Given:

a spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.1 cm/min. at what rate is the volume of the snowball decreasing when the radius is 12 cm.

Let r be the radius of the spherical snowball

Radius is decreasing at rate of 0.1 cm/min.=> dr/dt = -0.1

(negative sign indicates decreasing)

Volume v = 4/3πr^3

dv/dt = 4/3 π 3r^2*dr/dt

= 12π/3*r^2*(-0.1)

= 4π*12^2*(-0.1)

= 4π*144*-1/10

= 4π*(-14.4)

= -57.6π

= 180.864 cm^3/min

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Answer:

base is 4 units

Step-by-step explanation:

the formula for a triangle is (b x h)/2= a

So we can fill in what we know

(b x 12)/2=24

Our goal is to solve for b or the base

12b/2=24

X2.       x2

12b=48

/12.   /12

b=4

Hopes this helps please mark brainliest

No, there is no price discrimination in the given question

Price discrimination is a marketing strategy where a firm levies its customers variously for a similar commodity based on the standards they have set. It is offering customers various products at various price points based on their purchasing power and demographics.

Since the retailer does not charge different prices for various products, there is no price discrimination in the given question. It cannot be argued that a local boutique owner is engaging in price discrimination if they offer a discount to a customer who is unaware of it without asking them first. Additionally, it is no priced discrimination if the shop owner does not give more than a 15% discount or any incentives for purchasing in bulk.

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Excess capacity (e.g., factories can make more than the optimal industry production quantity) within the industry is not a deterrent to entry into an industry

Barriers to entry is an economics and business term describing factors that can prevent or impede newcomers into a market or industry sector, and so limit competition. Barriers to entry may be caused naturally, by government intervention, or through pressure from existing firms

Common barriers to entry include special tax benefits to existing firms, patent protections, strong brand identity, customer loyalty, and high customer switching costs.

According to the question,

Prevalence of learning curves in the industry , Production that requires expensive machinery that can be resold and High economies of scale in the industry are all deterrent or barriers to entry

But Excess capacity (e.g., factories can make more than the optimal industry production quantity) within the industry is not a deterrent to entry into an industry because when there is excess capacity in the industry , existing firms can cut the prices making it harder for new entrant to make a profit.

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YES, the absolute value of an integral is always less than the integral of the absolute value for Lebesgue integrals.

An integral is like a sum, but fancier. So look at a sum 1+(-5)+2+(-3)=-5. Take the absolute value, |1+(-5)+2+(-3)|=5. But, if you take the absolute value of the individual terms and then add them, you get |1|+|-5|+|2|+|-3|=1+5+2+3=11. 11>5

The reason is that when you add them all up and then take the absolute value, the positive and negative terms of the sum get to cancel each other out and make the absolute value of the sum greater overall. When you take the absolute value of individual terms, you force them all to "point in the same direction" (positive) so they are working together and the sum gets higher.

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The discriminant of the given quadratic equation is 17.

The discriminant is defined as the part of the quadratic formula underneath the square root symbol: b²-4ac. Thus, the discriminant usually tells us whether there are two solutions, one solution, or no solutions in a quadratic equation.

Now, the given quadratic equation is √2x² — 5x + √2 = 0.

This equation is of the general quadratic form of ax² + bx + c = 0.

Where,

a = √2

b = —5

c = √2

Now, discriminant is gotten as;

D = (b² - 4ac)

D= {(-5)² - (4 × √2 × √2)}

D = 25 - (4 × √4)

D = 25 - (4 × 2)

D = 25 - 8

D = 17

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The probability that a randomly chosen subject completes at least three puzzles in the 5 minute period while listening to soothing music is 0.4.

Probability is the branch of discrete mathematics. It is used for calculating how likely an event is to occur or happen. The probability of a random variable can be given by,

                                ⇒    f ( x ) p ( x )    =   P ( X = x )

As per the question,

        P ( X = 1 )   =   0.2

        P ( X = 2 )   =   ?

        P ( X = 3 )   =   0.3

        P ( X = 4 )   =   0.1

⇒   P ( X ≥ 3 )   =   P ( X = 3 ) + P ( X = 4 )

                         =   0.3 + 0.1

      P ( X ≥ 3 )   =   0.4  

Therefore, 0.4 is the probability that a randomly chosen subject completes at least three puzzles in the 5-minute period while listening to soothing music.

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The complete question is

The correct answer is 7XS when RR' = 14, then RZ = 7 when the parallelogram PQRS is reflected across the line of reflection.

Given that,

If RR' = 14, then RZ = 7 when the parallelogram PQRS is reflected across the line of reflection.

SX = 5 if Y = 5.

In Euclidean geometry, a parallelogram is a straightforward (non-self-intersecting) quadrilateral with two sets of parallel sides.

A parallelogram has equal-length opposing angles and facing or opposing sides.

The Euclidean parallel postulate or one of its equivalent formulations must be used in order to demonstrate the congruence of opposite sides and angles because both requirements flow naturally from this postulate.

A quadrilateral with only one pair of parallel sides, on the other hand, is referred to in British or American English as a trapezoid or trapezium.

We get,

The parallelepiped is a three-dimensional representation of a parallelogram.

So, 7 XS is the right response to the question.

Therefore, The correct answer is 7XS when RR' = 14, then RZ = 7 when the parallelogram PQRS is reflected across the line of reflection.

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Answer:

1. 7

2. XS

Step-by-step explanation: