Scores on a certain standardized test have a mean of 500, and a standard deviation of 100. How common is a score between 600 and 700? calculate the probability.

The equation of the line passing through the point (1, -2) and cutting off equal intercepts from the axes will be x + y +1 = 0.

The equation of the line in the intercept form is expressed as

x/a + y/b = 1

where a is x intercept, b is y intercept and x and y are independent and dependent variables respectively.

Now, according to the question both the intercepts are equal that is

a = b

So, the equation will become

x/a + y/a = 1

x + y = a

Now, since the line passes through (1, -2), so

1 + (-2) = a

=> a = -1

So, the equation of line will be

x + y = -1 or x + y +1 = 0.

Learn more about Intercept form at:

brainly.com/question/25722412

#SPJ4

Complete Question:

What is the equation of the straight line which passes through the point (1, -2) and cuts off equal intercepts from the axes?

The length of one side of square garden that Sam built in Area 4x² + 28x + 49 is (2x+7) feet.

Area is the region enclosed by the shape of an object. The space covered by a figure or any two-dimensional geometric shape in the plane is called the area of the shape. Area is measured in square units (m², cm², inch², etc.)

Example: The area of a rectangular floor is equal to its length times its width

We have given that,

The shape of garden is Square.

The area of garden , A = 4x² + 28x + 49

We know that , Area of square= Side × Side --(*)

where side is dimension of square. We have to find out the side of the square garden.

A = 4² + 28x + 49

Factorize the middle term such that sum of factors is 28x and multiply of factors is 196x².

A = 4x² + 14 x + 14x + 49

=> A = 2x( 2x + 7 ) + 7(2x + 7)

=> A = (2x+7)(2x+7)

comparing this Area with equation(*) we get,

Side = 2x+7

Hence, the required side is (2x+7) feet.

To learn more about Area of square, refer:

https://brainly.com/question/1658590

#SPJ4

The real part of Z₁+Z₂ is 8 and imaginary part of Z₁+Z₂ is -2, when Z₁ and Z₂ are added together and the result moves Z₁ 6 units right and 3 units down

A complex number is of the structure a + bi, a, b are real numbers, and I = √(- 1). Deciding the upsides of square underlying foundations of negative numbers is utilized. It is addressed in the direction plane with the real part on the x-hub and imaginary part b on the y-pivot, the arranged pair being (a, b).

In the inquiry, we are given two complex numbers,

Z₁ = 2 + i

Z₂ = 6 - 3i

These focuses are addressed on the direction plane as a circle and a triangle separately. We ascertain their total, z3.

To add Complex Numbers, the real parts are added to the genuine parts and the nonexistent to the imaginary.

∴ Z₃ =Z₁+Z₂ = (2 + i) + (6 - 3i) = (2+6) + (1-3)i = 8 - 2i.

This point is addressed as a square on the Direction plane.

Hence, we can say that real part is 8, and its imaginary part is - 2.

To know more about Complex Numbers, visit here:

brainly.com/question/10662770

#SPJ4

Answer: A. 16.7%

The probability of the letter C being chosen is 16.7% because there are 6 options and the probability will always be out of 100%. If you divide 100 by those 6 choices you will get 16.66 and rounded it is 16.7

Answer:

the answer is option B. 20%

a) The sampling distribution of the mean lifetime x is: Approximately normal with mean 55,000 and standard error 1591.

b) The probability that the sample mean lifetime is 51,800 miles or less if the lifetime distribution is unchanged is of 0.0222 = 2.22%. As the z-score has an absolute value greater than 2, it shows that this is an unusual measure, hence a conclusion could be drawn that there actually were changes in the distribution.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 55000, \sigma = 4500, n = 8, s = \frac{4500}{\sqrt{8}} = 1591[/tex]

The probability that the sample mean lifetime is 51,800 miles or less is the p-value of Z when X = 51,800, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (51800 - 5500)/1591

Z = -2.01.

Z = -2.01 has a p-value of 0.0222.

More can be learned about the normal distribution and the central limit theorem at https://brainly.com/question/25800303

#SPJ1

The equation that represents the relation between length and weight of a species of fish is y = 0.903 (1.087)^x.

What is exponential function?

A mathematical function with the formula f (x) = a^x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.

Given table is

Length(in.)    4            6       8        10          12

Weight(lb)     1.26      1.49   1.76    2.08       2.45

Assume the exponential function be:

y = ab^x

Putting x = 4 and y = 1.26 in the exponential function:

1.26 = ab⁴  ....(i)

Putting x = 6 and y = 1.49 in the exponential function:

1.49 = ab⁶  ...(ii)

Divide equation (ii) by (i)

1.49/1.26 = ab⁶/ab⁴

149/126 = b⁶/b⁴

149/126 = b⁶⁻⁴

149/126 = b²

b = 1.0874

b  ≈ 1.087

Putting b = 1.087 in equation (i)

1.26 = a(1.087)⁴

a = 1.26/(1.087)⁴

a = 0.9025

a ≈ 0.903

Therefore, y = 0.903 (1.087)^x

To learn more about exponential model, click on below link:

https://brainly.com/question/29193541

#SPJ1

Answer:

Step-by-step explanation:

95% of the given number is 285 if 75% of that number is 225 and 20% of the same number is 60.

In mathematics, a percentage is defined as a number or ratio that can be expressed as a fraction of 100.

Let assume the number is x

So, according to first statement, we are given that 75 percentage of x=225,it means

=>(75/100) × x=225

=>(3/4) × x=225

=>x=(225 × 4) /3

=>x = (75 × 4)

=>x = 300

Now, check for same number whether 20% is 60 or not

=>20% of x=60

=>(20/100) × x=60

=>(1/5) × x =60

=>x= 60 × 5

=>x = 300

So, our assumption is correct.

Now,95% of the same number is 95% of x

=(95/100) ×300

=95 × 3

=285

Hence,95% of 300 is 285.

To know more about percentages, visit here:

https://brainly.com/question/24159063

#SPJ4

The upper limit and lower control limits will be 56 and 44 respectively.

What is statistical process control ?

When the process is under control, there will be a high possibility that the value of the sample mean will fall between the two control limits, which is why the lower line, also known as the lower control limit, was chosen.

Mean = 50

Sample size = 16

Standard deviation = 8

We need to find the upper and lower control limits.

So, Lower limit would be

= x - 3×σ÷

= 50 - 3×8÷

= 50 - 3×2

= 50 - 6

= 44

Upper limit would be

= x + 3×σ÷

= 50 + 3×8÷    

= 50 + 3×2

= 50 + 6

= 56

The upper and lower control limits of process will be 56 and 44 respectively

To learn more about the statistical process visit: brainly.com/question/18914915

#SPJ4

The total number of items collected for relief is 200.

In order to write a linear equation first find the quantity of which the value is not given. Then, relate the value of this quantity with all the known values to form an equation.

Suppose the number of relief items are x.

The following equation can be written according to the problem,

10% of x = 20

=> 10/100 × x = 20

=> x = (20 × 100)/10

=> x = 200

Hence, the items collected by Hurricane Relief Foundation is given as 200.

To know more about linear equation click on,

https://brainly.com/question/11897796

#SPJ1

Hence, a temperature increase of  

9

5

​

 degree Fahrenheit is equivalent to a temperature increase of  

81

25

​

 degree Celsius.

the total way the committee formed is 3080.

What is combination?

A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The quantity of k-combinations for a set with n components

The available candidates from a group are 8 Democrats and 11 Republicans.

Three Democrats and two Republicans must be included on the committee that we choose.

Thus, from a pool of 11 Republicans and 8 Democrats, we must select 3 each.

Both 8C3 and 11C2 approaches are viable for achieving this.

8C3 * 11C2 = 3080 are the total ways to form this committee.

Hence the total way the committee formed is 3080.

Learn more about combination, by the following link.

https://brainly.com/question/11732255

#SPJ4

Answer:

Line C

Step-by-step explanation:

Given:

Create the equation for the line using the given information:

[tex]\implies y=\dfrac{1}{2}(x-4)[/tex]

Distribute:

[tex]\implies y=\dfrac{1}{2}x-2[/tex]

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Compare the found equation with the slope-intercept formula:

The y-intercept is the y-value of the point at which the line crosses the y-axis.  Therefore, the line crosses the y-axis at y = -2.

The slope tells us how much y increases as x increases.  Given the slope is ¹/₂, the line increases by one y-value for every two x-values.

Therefore, the line that represents the given information is line C.

Probability that that sum of the two dice outcomes is 6 is 5/36

What is probability?

We know,

Probability = Number of events / Total no. of favourable outcomes

If we through two dice then ,

Total number of favourable outcomes = 36

Here, we need the sum of the two outcomes is 6 is

(1, 5) , (2, 4), (3, 3), (4, 2), (5, 1)

So, the number of events = 5

P(of getting sum 6) = 5/ 36

Hence, Probability that that sum of the two dice outcomes is 6 is 5/36

To read more about Probability.

https://brainly.com/question/25870256

#SPJ4

The measures of x are obtained with the Pythagorean Theorem, as follows:

1. x = 10.2.

2. x = 7.2.

3. x = 13.7.

4. x = 36.2.

5. x = 10.7.

The Pythagorean Theorem is a geometry axiom which states that for a right triangle, the length of the hypotenuse squared is equals to the sum  of the lengths of the sides squared.

Hence, for item 1, we have that:

x² + 16² = 19²

x = square root(19² - 16²)

x = 10.2.

For item 2, we have that:

x² + 12² = 14²

x = square root(14² - 12²)

x = 7.2.

For item 3, we have that:

x² + 9.2² = 16.5²

x = square root(16.5² - 9.2²)

x = 13.7.

For item 4, we have that:

x² = 15² + 33²

x = square root(15² + 33²)

x = 36.2.

For item 5, first we find the side of the top right triangle, hence:

h² + 16² = 25²

h = square root(25² - 16²)

h = 19.2.

Then the value of x is obtained as follows:

x² + 19.2² = 22²

x = square root(22² - 19.2²)

x = 10.7.

More can be learned about the Pythagorean Theorem at https://brainly.com/question/28853425

#SPJ1

Margin of error is statistical expressing the amount of a random sampling error in survay results not the error term from biased sampling method. So, correct answer is False.

Margin of error in statistics represents the amount of random sampling error in the survey results. The larger the margin of error, the less confident that the survey results reflect the results of the census of the entire population. It is denoted by E or MOE. It is calculated by dividing the square root of the sample size by the standard deviation of the population. 99% level is the most conservative, 90% level is the least conservative. The sampling error is a statistical error that occurs when the analyst does not select a sample that is representative of the entire data population.

False - Margin of error only account for sample variability (the fact that my sample differs from many others' samples and therefore provides different statistics.

To learn more about margin of error , refer:

https://brainly.com/question/10218601

#SPJ4

The speed of the each train = 63

Speed is defined as : The rate of change of position of an object in any direction.

Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.

There are four types of speed and they are:

1. Uniform speed

2. Variable speed

3. Average speed

4. Instantaneous speed

Given that

The passenger train travels23mphr faster than the coal train

In 4 hours the two trains are 412 miles apart

Let the speed of  train = x

4*x+4*(x+23)=412

4x + 4x + 92 = 412

8x = 320

x = 40

the speed of the each train = x + 23 = 40 + 23 = 63

Given that

The passenger train travels 23mphr faster than the coal train

In 4 hours the two trains are 412 miles apart

let the speed of  train = x

4*x+4*(x+23)=412

4x + 4x + 92 = 412

8x = 320

x = 40

the speed of the each train = x + 23 = 40 + 23 = 63

To learn more about speed:

https://brainly.com/question/28224010

#SPJ4

The scale factor tells at what ratio a figure has been changed from other figures

Shapes in various dimensions can be scaled using the Scale Factor.

The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger.

K is the scaling factor for x in the equation y = Kx. This expression can also be visualised in terms of proportionality:

y ∝ x

K can therefore be regarded as a proportionality constant in this context.

The scale factor tells a particular percentage increment or to calculate the percentage of an amount.

Also , To compare 2 Similar geometric figures: When we compare two similar geometric figures by the scale factor, it gives the ratio of the lengths of the corresponding sides.

To know more about Scale factor here

https://brainly.com/question/29464385

#SPJ4

Answer: A, C, 57

Step-by-step explanation:

I multiply by 0.40 for the first one, and then multiply by 1.0625. 0.40 = 40% and multiplying by 1.0625 is the same as adding 6.25%. For the second, I multiply by 0.70 because that is 70%. For the last, I multiply by 0.95 for the same reason.

Greater than 0.05 is the p-value, which indicates that it is greater than the significance level.

When determining whether the available data are sufficient to support a given hypothesis, one method of statistical inference is known as a statistical hypothesis test. Making probabilistic claims about a population parameter is possible through hypothesis testing.

given

a 95% confidence interval with bounds for the inference's outcome (-0.0509,0.04273).

As the value p1-p2=0 is included in the interval and is one of the possible values of the genuine difference between the proportions, this confidence interval indicates that the difference (p1-p2) is not substantially positive at the level of significance utilized in the study.

The null hypothesis would then not be rejected by a test of hypothesis performed with the same data and level of significance because the proportional difference is not significant.

In this example, the P-value is more than 0.05, which indicates that it is greater than the significance level.

To know more about hypothesis visit:-

https://brainly.com/question/29519577

#SPJ4

Answer: 1.06 cm

Step-by-step explanation:

Take 2.7 divided by 2.54 = 1.062cm

Rounded the nearest hundredth, so it will be 1.06 cm

The weight of the piknits can be used to predict the number of gogles as there is Linear equation in variables may be defined as a linear courting among x and y, that is, variables.

In this case, x is the impartial variable, and y relies upon on it, so y is known as the established variables.

linear courting (or linear association) is a statistical time period used to explain a straight-line courting among variables. Linear relationships may be expressed both in a graphical layout or as a mathematical equation of the shape y = mx + b.

"There is no linear relationship between the weight of the and the number of glasses"

"There is a linear relationship.

A. Yes, because the scatterplot shows a linear pattern.

C. Yes, because a random sample was taken from Piknits for the scatterplots of the 4th and 5th residuals is.

Read more about number;

https://brainly.com/question/251701

#SPJ4

By using percentage, it can be calculated that

Percentage reduction on the portable cd player  [tex]= 18.76 \%[/tex]

What is Percentage?

Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.

For example 9% means [tex]\frac{9}{100}[/tex]. Here, 9 is expressed as a fraction of 100.

Original price of the CD player = $79.95

Selling price = $64.95

Reduction in price = $(79.95 - 64.95) = $15

Percentage reduction on the portable cd player = [tex]\frac{15}{79.95} \times 100 = 18.76 \%[/tex]

To learn more about percentage, refer to the link-

https://brainly.com/question/24304697

#SPJ4

The area of a plane figure is the region enclosed by the figure's boundary . Here the area is measured in square units of length such as a square meter   or square centimeter

The area of plane figures is a mathematical concept that is used to measure the size of two-dimensional shapes. It is the amount of space inside the figure and can be calculated by multiplying the length and width of the figure. The measurement of the area is usually measured in square units, such as inches, centimeters, or meters. The area is a fundamental concept in geometry and is used in many areas of mathematics, such as calculus and trigonometry.

To know more about plane figures refer to the link  brainly.com/question/1872483

#SPJ4

Answer:

Step-by-step explanation:

12.33(4)+24= 73.32

then add the extra 30$ that was spent

73.32+30= $103.32

The required probabilities of the given parts are a) 56%, b) 6% , c) 94%.

The probability is the proportion of the probability of an occasion to occur. It estimates the conviction of the occasion. The recipe for probability is given by; P(E) = Number of Good Results/Number of absolute results.

a) These two occasions are autonomous, consequently, the probability of both is the increase of the probabilities of every, accordingly:

0.56 = 56% probability that the two offers are fruitful.

b) E1 has a 1 - 0.7 = 0.3 probability of being ineffective, while E2 has a 0.2

likelihood, thus:

0.06 = 6% probability that neither one of the bids is effective.

c) 1 - 0.06 = 0.94

0.94 = 94% probability that the firm is effective in no less than one of the two bids.

Thus, required probabilities are a) 56%, b) 6% , c) 94% .

To know more about Probability visit:

brainly.com/question/15124899

#SPJ4

Its -14  :>

Randoml spam letters bc it asked me to

Answer:

D

Step-by-step explanation:

C is the point - 4

the opposite of a number is its negative , that is

- (- 4) = + 4

the opposite of point C is therefore 4

The slope of the line passing through points (3, -3) and (0, -3) is equal to zero.

If we look at the general meaning of slope then we find out that Slope is nothing but the elevation or the steepness of any curve plotted on a graph paper. Now, the formula for finding the slope between two points (x₁, y₁) and (x₂, y₂) is expressed as

m = (y₂ - y₁)/(x₂ - x₁)

where m is the slope between the points, (y₂ - y₁) is difference between the y coordinates and (x₂ - x₁) is the difference between the x coordinates.

We have the values as (x₁, y₁) = (3, -3) and (x₂, y₂) = (0, -3)

So, the slope will be expressed as

m = (-3 + 3)/(0 - 3)

m = 0/-3

m = 0 which is the required slope.

Learn more about Slope at:

brainly.com/question/1734258

#SPJ4

Complete Question:

What is the slope of the line that passes through (3, -3) and (0, -3).

if they work together it takes 12/7 hours to mow one lawn

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

jake can mow a lawn in 3 hours.

kellie can mow a lawn in 4 hours.

1/3 lawns can be cut per hour by Jake.

kellie has a 1/4 hour cutting rate for lawns.

They can cut 7/12 lawns per hour by working together at a rate of 1/3 + 1/4.

One lawn can be mowed in 12/7 hours at a rate of 7/12 lawns per hour.

Hence if they work together it takes 12/7 hours to mow one lawn.

Learn more about arithmetic, by the following link.

https://brainly.com/question/13181427

#SPJ4

Answer:

( a + 5 ) ( a + 6 )

? maybe

Step-by-step explanation:

I really don't know how to explain