The fastest roller coaster in the world is located in New Jersey. It travels 27 miles per hour.

Given

To find: The value of x.

Explanation:

It is given that,

That implies,

Hence, the value of x is 4.

Answer:

The equation of the line in the slope-intercept form is y = -5x + 79

Step-by-step explanation:

The slope-intercept form of the linear equation is y = m x + b, where

∵ The slope of the line is -5

∴ m = -5

∵ The form of the equation is y = m x + b

→ Substitute the values of m in the form of the equation

∴ y = -5x + b

→ To find b substitute x and y in the equation by the coordinates

   of any point on the line

∵ The line passes through the point (18, -11)

∴ x = 18 and y = -11

∵ -11 = -5(18) + b

∴ -11 = -90 + b

→ Add 90 to both sides to find b

∵ -11 + 90 = -90 + 90 + b

∴ 79 = b

→ Substitute it in the equation

∴ y = -5x + 79

∴ The equation of the line in the slope-intercept form is y = -5x + 79

From the given discrete probability distribution, we have that:

a) Because the sum of all probabilities is of 1, we can verify that this is a probability model.

b) P(3 or 4) = 0.229.

c) P(at least one) = 0.908.

d) P(4) = 0.035.

e) Since both P(X ≤ 4) and P(X ≥ 4) > 0.05, 4 is not an unusual event.

The probability distribution in this problem gives the probability of a household having a number of TV sets, given as follows:

For item a, we have to add all the probabilities, hence:

0.092 + 0.275 + 0.101 + 0.194 + 0.035 + 0.303 = 1.

Because the sum of all probabilities is of 1, we can verify that this is a probability model.

For item b, we take the probabilities from the table as follows:

P(3 or 4) = P(X = 3) + P(X = 4) = 0.194 + 0.035 = 0.229.

For item c, we follow a similar procedure to item b, taking the probabilities from the table as follows:

P(at least one) = 1 - P(X = 0) = 1 - 0.092 = 0.908.

For item d, from the table, we have that:

P(4) = 0.035.

For item e, we have that:

Since both P(X ≤ 4) and P(X ≥ 4) > 0.05, 4 is not an unusual event.

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Answer:

It's D

Step-by-step explanation:

for edge...just took the test and got 100;)

Answer:

Graph D

Step-by-step explanation:

Answer:

The probability that 2 or more of the original 5,100 components may fail during the useful life of the product is:

= 0.001

Step-by-step explanation:

Probability of operating without failure = 0.999

The probability of failed component = 0.001 (1 - 0.999)

The number of components of the electronic office product = 5,100

The number of components that may fail, given the above successful operation = 5.1 (0.001 * 5,100).

Therefore, the probability that 2 or more of the original 5,100 components may fail during the useful life of the product = 0.001

Probability of component failure is the likelihood that a component fails during the useful life of the product.  It is expressed as the number of likely failed components divided by the total number of components.  This result can be left in decimal form or expressed as a percentage.

Following are the solution to the given expression:

\(\to \text{p = p (failure)} = 1 -0.999 = 0.001 \\\\\)

We employ the binomial approximation of the normal distribution with mean.

\(\to \mu = np = 5100(0.001) = 5.1 \\\\ \to \text{standard deviation} \ (\sigma) = \sqrt{np(1-P)}\)

                                         \(= \sqrt{5100(0.001)(1-0.001)} \\\\ = \sqrt{5.1 \times (0.999)} \\\\= \sqrt{5.0949 } \\\\= 2.2572\)

It require \(p(x\geq 2)\) but we find \(p(x \geq 1.5)\),  because of \(0.5\) correction.

Here

\(\to z = \frac{X-\mu}{\sigma }\)

       \(=\frac{1.5-5.1}{2.2572} \\\\ =\frac{-3.6}{2.2572} \\\\ = -1.59 \\\\\)

Calculating the required probability:  

\(\to p(z \geq -1.59)\)

\(=1+ p(z< 1.59) \\\\= 1+ 0.9440826\) , by standard normal table  

\(= 1.9440826 \approx 1.944\)

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Answer:

y = x - 19

Step-by-step explanation:

Slope intercept form of a line is y = mx + b.

To find slope we use the formula \(\frac{y_2-y_1}{x_2-x_1}\)

Now, to find the y-intercept we take the values of a point and plug them into our equation so far.

Therefore, the answer is y = x - 19.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

By definition of tangent,

tan(θ - x) = sin(θ - x) / cos(θ - x)

Expand the sine and cosine terms using the angle sum identities,

sin(x ± y) = sin(x) cos(y) ± cos(x) sin(y)

cos(x ± y) = cos(x) cos(y) ∓ sin(x) sin(y)

from which we get

tan(θ - x) = (sin(θ) cos(x) - cos(θ) sin(x)) / (cos(θ) cos(x) + sin(θ) sin(x))

Also recall the Pythagorean identity,

cos²(x) + sin²(x) = 1

from which we have two possible values for each of cos(θ) and sin(x):

cos(θ) = ± √(1 - sin²(θ)) = ± 3/5

sin(x) = ± √(1 - cos²(x)) = ± 12/13

Since there are 2 choices each for cos(θ) and sin(x), we'll have 4 possible values of tan(θ - x) :

• cos(θ) = 3/5, sin(x) = 12/13 :

tan(θ - x) = -56/33

• cos(θ) = -3/5, sin(x) = 12/13 :

tan(θ - x) = 16/63

• cos(θ) = 3/5, sin(x) = -12/13 :

tan(θ - x) = -16/63

• cos(θ) = -3/5, sin(x) = -12/13 :

tan(θ - x) = 56/33

Now

cos(ø-x)

sin(ø-x)

So

tan(ø-x)

Answer:

When you multiply -3 to x and +2

Step-by-step explanation:

Answer:

Step-by-step explanation:

-3(x+2)=21

Multiple -3 to (x+2)

-3x-6=21

then add 6 to 21

-3x=27

Divide by -3 to get an x

Answer:

35 schools

Step-by-step explanation:

just add the side lengths

9+ 5+4+10+5+2

Answer:

35

Step-by-step explanation:

if you see where each bar it on the side and add them up you get your answer of how many schools

Answer:

This study is good because we have minimized sampling error.

Step-by-step explanation:

We are given that . The researcher has two groups.

The researcher classifies the students based on when they volunteer for the study.

The first 50 students who volunteer receive online instruction. The next 50 receive instruction by attending a class with a teacher.

A. This study is poor because the researcher did not use random sampling.

B. This study is poor because the researcher did used random sampling.

C. This study is good because we have minimized sampling error.

D. This study is good due to the equal sample size in each group.

Option C is true : This study is good because we have minimized sampling error.

Answer:

37

Step-by-step explanation:

3(3)(4)- -1

9(4)- -1

36- -1

36+1

37

Answer:

37

Step-by-step explanation:

Given : a = 3, b = -1, C = 4

3ac - b

= 3(3)(4) - (-1)

= 36 + 1

= 37

The triangle ΔBAE is congruent to the triangle ΔCDE by ASA postulate.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

If two lines intersects, then the opposite angle of the line will be congruent to each other.

In ΔBAE and ΔCDE,

AB = DC, (Given)

∠BAE = ∠CDE, (Right angle)

∠BEA = ∠DEC, (Opposite angle)

The triangle ΔBAE is congruent to the triangle ΔCDE by ASA postulate.

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The singer sold 512 music downloads.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".

Let's use the following variables:

CD = the number of CD singles sold

DL = the number of music downloads sold

From the problem, we know the following:

CD + DL = total number of singles sold

CD = 456

The profit from selling CD singles is 35p = £0.35 per CD single

The profit from selling music downloads is 17p = £0.17 per music download

The total profit is £246.64

Using the information above, we can set up two equations based on the profits earned from selling CD singles and music downloads:

0.35 * CD = profit from CD sales

0.17 * DL = profit from download sales

And we know that the sum of these two profits equals the total profit:

0.35 * CD + 0.17 * DL = 246.64

Substituting CD = 456, we get:

0.35 * 456 + 0.17 * DL = 246.64

Simplifying this equation, we get:

159.6 + 0.17 * DL = 246.64

0.17 * DL = 87.04

DL = 512

Therefore, the singer sold 512 music downloads.

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The length of the isosceles trapezoid height CE is 14 meters.

To find the length of the height CE of the isosceles trapezoid, we can use the Pythagorean theorem.

The isosceles trapezoid CE is the hypotenuse of the right triangle formed by height CE and distance AC. CE is also the height of the trapezoid. Let the length of CE be 'x'

The Pythagorean theorem states that the square of the length of the hypotenuse of a right triangle (CE) is equal to the sum of the squares of the lengths of the other two sides (AC and CE).

x² = AC² + CE²

We know that AC = 14 meters and CE = x.

So x² = 14² + x²

x² = 196 + x²

x² = x² + 196

0 = 196

x = √196 = 14

Therefore, the length of height CE is 14 meters.

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Applying angle relationships, the measures of the numbered angles are:

m∠1 = 90°

m∠2 = 68°

m∠3 = 112°

m∠4 = 112°

m∠5 = 68°

m∠6 = 56°

m∠7 = 124°

m∠8 = 124°

To calculate angle measurements that are formed by a transversal and parallel lines, we can apply the knowledge of the angle relationships that exist between the angle pairs in concerned. Some angle relationships are:

m∠1 = right angle [corresponding angles is the angle relationship]

m∠1 = 90°

m∠2 = 180 - m∠1 - 22 [triangle sum theorem]

Substitute

m∠2 = 180 - 90 - 22

m∠2 = 68°

m∠3 = 180 - m∠2

Substitute

m∠3 = 180 - 68

m∠3 = 112°

m∠4 = m∠3

m∠4 = 112°

m∠5 = 180 - m∠4

m∠5 = 180 - 112

m∠5 = 68°

m∠6 = 1/2(180 - m∠5)

m∠6 = 1/2(180 - 68)

m∠6 = 56°

m∠7 = 180 - 56

m∠7 = 124°

m∠8 = m∠7 [alternate interior angles is the angle relationship]

m∠8 = 124°

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\(\huge\bf\underline{Answer}\)

\(\boxed{\huge \sf{TSA = 6a²}}\)

Let the Side of a cube be 'x'

\(\sf{:⇒6(x) ^{2} } = 1944cm^{2} \)

\(\sf{:⇒ {x}^{2} = \dfrac{1944}{6} }\)

\(\sf{:⇒ {x}^{2} = 324}\)

\(\sf{:⇒x = \sqrt{324} }\)

\(\sf{:⇒x = 18cm}\)

Answer:

If you mean what is the square root of 36, then the answer is 6.

6 × 6 = 36.

Remeber sqaure root means what two numbers multplied together equal another number. It is irrational when the number doesn't repeat or terminate.

Hope this helps!!

Derrick and Janis together plant a total of 30 + 90 = 120 strawberry plants on the first day.

To find out how many strawberry plants Derrick and Janis planted on the first day, we need to calculate the sum of the plants they individually planted.

Derrick planted 20% of the 150 strawberry plants:

20% of 150 = (20/100) * 150 = 30 strawberry plants.

Janis planted 60% of the 150 strawberry plants:

60% of 150 = (60/100) * 150 = 90 strawberry plants.

Therefore, on the first day, Derrick and Janis planted a total of 30 + 90 = 120 strawberry plants.

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Step-by-step explanation:

Supplementary angles are either of two angles whose sum is 180°.

Those are:

<1 and <2

<3 and <4

<5 and <6

<7 and < 8...

Vertical angles are each of the pairs of opposite angles made by two intersecting lines.

Those are:

<1 and <4

<2 and <3

<5 and <8

<7 and <6

Answer:

Step-by-step explanation:

This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.

The set of values {A = 0, B = 1, and C = 2} to have a completely horizontal line.

A horizontal line is defined as a line with slope m = 0 that is parallel to the x-axis.

A horizontal line across (-4,2) informs us of two things.

A horizontal line with slope m = 0 is parallel to the x-axis.

The line crosses the point (-4,2).

Ax + By = C has m = B/A = 0 slope and intersects point (-4,2).

Then, B = A×0 indicates that any constant A will work, and the Ax term disappears.

Ax + By = C then becomes y = C. To find C, use the point (-4,2).

⇒ C = 2

This line's equation is y = 2, and any point (x,2) matches the equation.

Therefore, the set of values {A = 0, B = 1, and C = 2} to have a completely horizontal line.

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Answer:

Step-by-step explanation:

17

Answer:

23100 ways

Step-by-step explanation:

We have 8 men and 11 women

Number of ways of choosing a subcommittee of 4 men and 7 women

8C4 x 11C7

8!/(8-4)!4! x 11!/(11-7)!7!

= 8!/4!4! x 11!/4!7!

= (40320/24*24) x (39916800/24x5040)

= (40320/576) x (39916800/120960)

=70 x 330

= 23100 ways

We can select a subcommittee of 4 men and 7 women in 23100 ways.

The two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).

To solve the system of equations, let's assign variables to the two integers. Let the first integer be represented by 'x' and the second integer by 'y'.

According to the given information:

a. Fourteen more than twice the first integer gives the second integer:

This can be expressed as: 2x + 14 = y

b. The second integer increased by one is the square of the first integer:

This can be expressed as: y + 1 = x^2

Now, we have a system of equations:

1) 2x + 14 = y

2) y + 1 = x^2

To solve this system, we can substitute the value of 'y' from equation 1) into equation 2):

2x + 14 + 1 = x^2

2x + 15 = x^2

Rearranging the equation, we have:

\(x^2 - 2x - 15 = 0\)

Factoring the quadratic equation, we get:

(x - 5)(x + 3) = 0

Setting each factor equal to zero:

x - 5 = 0   -->   x = 5

x + 3 = 0   -->   x = -3

Substituting the values of 'x' back into equation 1), we can find the corresponding values of 'y':

For x = 5:

2(5) + 14 = y

10 + 14 = y

y = 24

For x = -3:

2(-3) + 14 = y

-6 + 14 = y

y = 8

Therefore, the two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).

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The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

2000000000 ants would equal 1 elephant.

Step-by-step explanation:

8 x 10^6 = 8000000

4 x 10^-3 = 0.004

8000000 ÷ 0.004 = 2000000000

I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

Step-by-step explanation:

first the theoretical maximum number :

the big block is 25cm×20cm×15cm.

so, the volume is 25×20×15 = 7500 cm³

we want to cut this note into pieces of 2.5cm×2cm×1cm with a volume of 2.5×2×1 = 5 cm³

so, we can get 7500/5 = 1500 such lumps out of the big block.

now, a quick check, if we can cut full pieces until the last bit, or if the shape of the big block will not allow us to fully cut it into the desired pieces, and we get some remains (too small to be lumps of the desired size and shape).

and we do this by checking, if each dimension of the big block can be divided by the dimensions of the small lumps without remainder (whole number results).

25 / 2.5 = 10, and no remainder here.

=> 10 cuts of 2.5 cm perpendicular to the length.

20 / 2 = 10, and no remainder here.

=> 10 cuts of 2cm perpendicular to the width.

15 / 1 = 15, and no remainder here.

=> 15 cuts of 1 cm perpendicular to the height.

so, yes, we can achieve the theoretical maximum number of 1500 lumps also in reality and cut the big block without remaining material into these small blocks.

Answer:

z = 3(-6x + 4y + 3)/6y and + 1

Step-by-step explanation:

z = 9 - 3x × 2 - 3y × 2 and z - 6x × 2 + 6y × 2

z = 9 - 3 × 2x - 3 × 2y and z - 6 × 2x + 6 × 2y

z = 9 - 6x - 6y and z - 12x + 12y

z = 3(-6x + 4y + 3)/6y and + 1

Given:

A circle with a center at C.

Required:

We need to find the names of the given parts.

Explanation:

Recall that radius is a line segment extending from the center of a circle to the circumference.

Line segment AC extends from the center C of a circle to the circumference.

Recall that the arc of a circle is defined as the part of the circumference of a circle.

AE is the part of the circumference of a circle.

Recall that a straight line segment joins and is included between two points on a circle.

D and E are two points on a circle.

A straight line DE line segment joins and is included between two points D and E on a circle.

Recall that meeting a curve or surface in a single point if a sufficiently small interval is considered a straight line tangent to a curve.

AB is tangent.

Recall that an inscribed angle is an angle with its vertex "on" the circle, formed by two intersecting chords.

Recall that a central angle is an angle formed by two radii with the vertex at the center of the circle.

Recall that an angle formed by an intersecting tangent and chord has its vertex "on" the circle.

Final answer:

Answer:

-13/2

or

-6.5

Step-by-step explanation:

yeah-ya.......... right?

Answer:

\(P(X = 5) = 0.166\)

Step-by-step explanation:

Given

\(Mean = 4.3\)

\(x = 5\)

Required

Determine the probability that the order is 5

This question can be answered using Poisson distribution.

\(P(X = x) = \frac{\alpha ^x e^{-\alpha}}{x!}\)

Where

\(\alpha\) is used to represent the mean

and

\(\alpha = 4.3\)

\(x = 5\)

\(e = 2.71828\) ---- Euler's constant

So, we have:

\(P(X = x) = \frac{\alpha ^x e^{-\alpha}}{x!}\)

\(P(X = 5) = \frac{4.3^5 * 2.71828^{-4.3}}{5!}\)

\(P(X = 5) = \frac{4.3^5 * 2.71828^{-4.3}}{5* 4 * 3 * 2 *1}\)

\(P(X = 5) = \frac{4.3^5 * 2.71828^{-4.3}}{120}\)

\(P(X = 5) = \frac{1470.08443 * 0.01356859825}{120}\)

\(P(X = 5) = \frac{19.9469850243}{120}\)

\(P(X = 5) = 0.1662248752\)

\(P(X = 5) = 0.166\) Approximated