Find the slope of the line that passes through (8,3) and (1,7)

The mechanical advantage of the wheel and axle is 4

The mechanical advantage of the wheel and axle is determined by the ratio of the radii of the wheel and axle. This ratio is equal to the ratio of the circumference of the wheel to the circumference of the axle. Thus, if the radius of the wheel is twice the radius of the axle, the mechanical advantage of the wheel and axle is 2:1.Here we are given that  The radius of the wheel and axle is 4 times the radius of the axle. So considering x to be  the radius of the axle and 4x to be the radius of  the wheel .So, MA( mechanical advantage )= 4x/x= 4

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According to the question,

Given data.

Sugar cookies require 1.5 cups of butter for every 2 cups of sugar,

And

find that,

How many cups of butter are needed for 7 cups of sugar?

With the help of question,

1.5 cups of butter -----2 cups of sugar

  x cups of butter     = 7 cups of sugar

let us consider,

2 cup of sugar is 2x.

So, we can say that

2x= 1.5×7

  x=10.5/2

    =5.25 cups of butter

Then find the value of 5.25 cups of butter are needed for 7 cups of sugar.

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The rate at which the water level in the cylindrical tank rises is 0.25 m/min. This is because the volume of water in the conical tank is equal to the volume of water in the cylindrical tank when the water level in the conical tank is 3 m.

First, calculate the volume of the conical tank when the water level is 3 m. The formula for the volume of a cone is V = 1/3πr2h, where r is the radius and h is the height. In this case, r = 4 m and h = 3 m, so the volume of the conical tank is V = 1/3π(4 m)2(3 m) = 16π m3.

Next, calculate the volume of the cylindrical tank. In this case, r = 4 m and h = 5 m, so the volume of the cylindrical tank is V = π(4 m)2(5 m) = 80π m3.

Finally, calculate the rate at which the water level in the cylindrical tank must rise in order to keep the total volume of water constant. Since the volume of the conical tank is 16π m3 and the volume of the cylindrical tank is 80π m3, the total volume of water is 96π m3. Since the water level in the con

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After using algebraic expression the answer is 11.5x + 10.9y  = 145.3 when  x = 6 and y = 7 .

What do you mean by algebraic expression?

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms provide the basis of expressions.

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. Variables and constants can both be used in an algebraic expression.

Given expression:

11.5x + 10.9y

when x = 6 and y = 7

Substitute these values of x and y in above expression

11.5(6) + 10.9(7)

= 69 + 76.3

= 145.3

Therefore, 11.5x + 10.9y  = 145.3 when  x = 6 and y = 7

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Answer:

D.

Step-by-step explanation:

The sum of the length of any 2 sides is greater than the length of any 3rd side

10+8 = 18, so D is not possible

Before hitting the ground, the final velocity of the pine cone after falling for 2.5s will be 20.5 m/s.

        (a) → v = u + at

        (b) → S = ut + 1/2at²

        (c) → v² - u² = 2aS

Given is a pine cone falls for 2.05 s.

Assume the final velocity be [v] m/s. Using the first equation of motion -

v = u + at

Now -

[u] = 0

[a] = g

So, we can write -

v = gt

v = 10 x 2.05

v = 20.5 m/s

Therefore, the final velocity of the pine cone will be 20.5 m/s.

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The length of the CD is 15.354 cm

As we know that a perpendicular bisector divides a line segment into 2 equal halves and makes a right angle with the line.

Here, the CD is the perpendicular bisector of AB.

Now from the above definition, we can classify that

AD = BD = 9/2 cm

= 4.5 cm

Also,

ΔACD is a right-angled triangle

According to the Pythagoras theorem for any right-angled triangle

length² + base² = hypotenuse²

In the given triangle,

length = CD

Base = AD

hypotenuse = AC

Hence we get

CD² + 4.5² = 16²

or, CD² + 20.25 = 256

or, CD² = 235.75

or, CD = √235.75

or, CD = 15.354

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Complete Question

(image Attached)

Given, the pair of rational integers is 0.3 and 0.25 and the other two are 0.833 and 0.9 neither of the given rational numbers are not equivalent. To find whether any given pair is equivalent or not we use LCM.

LCM is the value that can divide both of the given numbers evenly. To find the LCM we employ the prime-factorization method.

Firstly start dividing the given integer with the smallest prime number first then repeat the division process until the quotient equals 1. To find the LCM multiply the highest powers of each prime factor.

Now, first pair is  3/10 and 25/100. LCM is 100.

3/10*10/10 = 30/100

and 25/100 = 25/100

Both 30/100 and 25/100 are not equivalent.

Next pair is 833/1000 and 9/10

LCM of 1000 and 10 is 1000

833/1000

and 9/10*100/100 = 900/1000

833/1000 and 900/1000 are not equivalent.

Therefore both the pair of rational numbers are not equivalent

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The probability that a randomly chosen return shows an adjusted gross income of $50,000 or more is 33.2%.

For mutually exclusive events, use the following addition rule:

        P(A or B) = P(A) +P(B)

The corresponding probabilities is :

   P( income > $50000) = P( >50)

= P(50 - 90) +P( 100 - 499) +P( ≥ 500)

= 0.215 + 0.100 +0.006

= 0.321

Therefore, the probability of a random selection returning is

P( income > 50000) = 0.321

Now ,

P( income ≥ 50000 and ≥ 100000 ) = P( > 100000)

= 0.100 + 0.006

= 0.106

The Probability Condition is:

   P(A/B) = P(A and B) / P(B)

Therefore,

P( ≥ $100000 / $ $50000)

=   P( ≥ $100000 and $ $50000)/ P( ≥ $50000)

= 0.106/ 0.321

≈ 0.3302

= 33.2%

Therefore, the conditional probability of earning at least $50000 and more is 33.2%

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If a 4m yardstick casts a 21m shadow, building is 12.19 tall with shadow of 64m.

Comparing one thing to another is what the word compare means in the dictionary. Mathematical number comparison is the process or method of comparing two numbers to determine whether one is less, bigger, or equal to the other. This week, comparison problems—which entail determining the similarities or differences between sets—were the focus. Finding out how many more there are in one set than the other is a form of comparative problem.

Given,

Yardstick:

= 4/21

Building:

Length:

= x/64

Comparing yardstick to building,

4/21 = x/64

21x = 64 × 4

21x = 256

x = 12.19

If a 4m yardstick casts a 21m shadow, building is 12.19 tall with shadow of 64m.

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$501.19 did the dealer pay for the skis.

What is percent?

A percentage in mathematics is a number or ratio that is expressed as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, though the percent sign, "%," is most frequently used. A percentage has no dimensions and no standard measurement.

Given:

A dealer sold a pair of skis for $371.25 after she marked them up 35%.

After mark for 35% it will be

371.25 x 35% = 371.25 x 0.35 = 129.94

So, dealer pay for the skis is,

$371.25 + $129.94 = $501.19

Hence, $501.19 did the dealer pay for the skis.

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Answer:

D

Step-by-step explanation:

9x + 5 (6/5x + 3) - 30

9x + 6x + 15 - 30

15x - 15

15(x-1)

The level of production explains 49% of the variation in total costs

What is a regression equation?

For evaluating the associations between a dependent variable and one or more independent variables, a regression equation is a set of statistical procedures.

Here, we have

Given,

A regression equation is set up, where the dependent variable is total costs and the independent variable is production. a correlation coefficient of 0.70.

The coefficient of determination is given as r²

which is 0.7²=0.49.

Hence, the level of production explains 49% of the variation in total costs.

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Complete Question.
A regression equation is set up, where the dependent variable is total costs and the independent variable is production. A correlation coefficient of 0.70 implies that:
A. The coefficient of determination is negative
B. The level of production explains 49% of the variation in total costs
C. There is a slightly inverse relationship between production and total costs
D. A correlation coefficient of 1.30 would produce a regression line with better fit to the data

Answer:You cannot, it is as simplified as it gets

Step-by-step explanation:

The proper decision is to reject the null hypothesis.

The concept, procedures, and method of testing a hypothesis against the null hypothesis. The testing hypothesis is said to have that level of significance if the null hypothesis is only rejected if its probability is less than a preset significance level.

Given: p-value = 0.02916

Level of significance = 9%

The P-value approach involves determining "likely" or "unlikely" by determining the probability — assuming the null hypothesis were true — of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed.

If the P-value is less than (or equal to), then the null hypothesis is rejected in favor of the alternative hypothesis. And, if the P-value is greater than, then the null hypothesis is not rejected.

Therefore, p-value is less than the level of significance.

Hence, we are rejecting the null hypothesis.

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Two lines are said to parallel when they have the same slope, from which we can find the equation for  both the lines.

The equation of two parallel lines on a graph can be determined by understanding the slope of the two lines. To find the equation of two parallel lines on a graph, first determine the slope of the two lines. This can be done by picking two points, (x1,y1) and (x2,y2), on the line and then calculating the slope using the formula: slope = (y2 - y1) / (x2 - x1). The two lines will have the same slope if they are parallel. After determining the slope, plug the slope and the coordinates of one of the points into the equation: y = mx + b, where m is the slope and b is the y-intercept. This equation will give the equation of the line in slope-intercept form. To find the equation of the second line, use the same slope and the coordinates of one of the points on the second line.

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Using the elimination method we got the value of x as 3 and the value of y as -4.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

-7x - 2y = -13

  x - 2y = 11  

(-)   (+)     (-)

-7x - x = = -13 - 11

-8x = -24

x = 3

Now,

x - 2y = 11

3 - 2y = 11

3 - 11 = 2y

2y = -8

y = -4

Thus,

The value of x is 3.

The value of y is -4.

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The expression x + 80 represents the number of coins Arthur has now, since he x pennies and an additional 6 dimes and 4 nickels.

We shall convert the pennies, dimes and nickels into same unit before adding to get the expression for the number of coins Arthur will have in total.

A penny = 1 cent, so

x pennies = x cents

A dime = 10 cents so;

6 dimes = 6 × 10cents

6 dimes = 60 cents

A nickel = 5 cents so;

4 nickels = 4 × 5 cents

4 nickels = 20 cents

Arthur's coins in total = (x + 60 + 40) cents

Arthur's coins in total = (x + 80) cents.

Therefore, the expression expression x + 80 represents the number of coins Arthur will have in total, wether in pennies, dimes or nickels.

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By using testing of hypothesis, it can concluded that

Population mean is 25.

What is testing of hypothesis?

Suppose there is a data at hand and there is a hypothesis to be tested. Testing of hypothesis determines whether the given hypothesis can be supported with the data at hand.

Here,

Sample size = 23

Population mean = 25

Sample mean = 28.739

Sample standard deviation = 10.015

Here,

The null hypothesis [tex]H_0 : \mu = 25[/tex]

The alternative hypothesis [tex]H_a : \mu \neq25[/tex]

Here, the population standard deviation is unknown. So two tailed test is used.

Here, level of significance = 0.05

Critical value for two tailed test is 2.07

The test statistic t = [tex]\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

                               [tex]=\frac{28.7391 - 25}{\frac{10.0146}{\sqrt{23}}}[/tex]

                               = 1.79

1.79 lies between -2.07 and 2.07

So we fail to reject the null hypothesis

So it can be claimed that population mean is 25.

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Answer:

The measure of angle XBC can be calculated by subtracting the measures of angles ABX and ABC from the measure of the whole angle, which is 180 degrees. So, if m∠ABX = 2y+10, and m∠ABC = 10y-4, then the measure of angle XBC is 180 - (2y+10) - (10y-4) = 180 - 12y - 6 = 168 - 12y.

Answer:

3h 20 min.

Step-by-step explanation:

Triangle B C D is shown. Angle BDC is 67 degrees and Angle CDB is 60 degrees. What is m∠ABC is

d. m∠ABC = 127°

Any three points in Euclidean geometry that are not collinear result in a singular triangle and singular plane (i.e. a two-dimensional Euclidean space). In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle.In the Euclidean plane, all triangles are contained within a single plane; however, in higher-dimensional Euclidean spaces, this is no longer the case.We can use the exterior angle theorem to solve this problem.

The sum of the two opposite inner angles determines the triangle's outer angle.

Therefore, m∠ABC = mBDC + mCDB

m∠ABC = 67° + 60°

m∠ABC = 127°

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Answer:

"Yes"

Step-by-step explanation:

1, 4, 9, 16 and 25 36, 49, 64, 81, 100, 121 and 144 are the first five square numbers.

The monthly payment for Ashton's $200,000 15-year mortgage with an APR of 5.5% and a 10% down payment is $1,547.16. The monthly interest is $765.16.

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Answer:

19

Step-by-step explanation:

first solve for the missing value in the first expression:

x + 6 = 22

   -6     -6

x = 16

Now solve the second expression with the found missing value

x + 3 = _

16 + 3 = 19

If a collection of nickels and dimes are 15 and valued at $1 the system of equation is

The number of dimes and nickels are 5 and 10 respectively

The equation to represent the information is written bearing in mind that

10 dimes  = 1 dollar = 20 nickels

let the dimes be d and the nickels be n

d + n = 15

0.1d + 0.05n = 1

solving simultaneously gives

d = 5

n = 10

There are 10 5 dimes and 10 nickels

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Answer:

17,7

Step-by-step explanation:

just use cauculator

Answer:

see explanation

Step-by-step explanation:

(x + 2)(5x + 1) = 5x(x + 1) ← expand factors on left side using FOIL

5x² + 11x + 2 = 5x² + 5x ( subtract 5x² from both sides )

11x + 2 = 5x ( subtract 5x from both sides )

6x + 2 = 0 ( subtract 2 from both sides )

6x = - 2 ( divide both sides by 6 )

x = [tex]\frac{-2}{6}[/tex] = - [tex]\frac{1}{3}[/tex]

Answer: you already stated that you know it is x = -1/3

Step-by-step explanation: first, open the parenthesis by multiplying (x+2) and (5x+1), which equals 5x^2 + 11x + 2, the current expression is 5x^2 + 11x + 2 = 5x(x+1).

now, do the same thing to the other side, distribute the 5x to (x+1), which equals 5x^2 + 5x.

Now the expression is 5x^2 + 11x + 2 = 5x^2 + 5x. subtract 5x^2 from both sides, and subtract 5x from both sides, which leaves you with 6x + 2 = 0,

subtract 2 from both sides, now, 6x = -2, lastly, divide both sides by 6 to isolate x, and you get x = -2/6, or, if you write it in it's smallest form, -1/3. hope I helped

Answer:

-8/5

Step-by-step explanation:

hope it helps!