For the pair of supply-and-demand equations, where x represents the quantity demanded in units of 1000 and p is the unit price in dollars, find the equilibrium quantity and the equilibrium price.
p = −0.3x + 6 and p = 0.05x + 2.5
equilibrium quantity
units
equilibrium price $

We can conclude that we have sufficient data to reject the null hypothesis and that the mean breaking strength is different from 8000 at 5% of significance if we compare the p value and the significance threshold, for example, α = 0.05.

The information provided and notation

X = 7750 indicate the sample's mean breaking strength, which is 145.

n = 6 sample size μ o= 8000 reflect the sample standard deviation indicate the quantity we want to test, and

α = 0.05 denotes the level of significance for the hypothesis test.

The statistic (interesting variable) would be represented by t, and the test's p value would be represented by P u (variable of interest)

Name the prevailing and competing hypotheses.

It is a test with two tails.

We wish to determine whether or not the genuine mean is equal to 8000.

Null hypothesis μ = 8000.

Alternate hypothesis μ₀ ≠ 800

Determine the test statistic.

\(t = \frac{X-\mu}{\frac{s}{\sqrt{n} } }\)

t-test: "enables the comparison of group means. One of the most widely used tests, it is used to assess whether the mean is (greater, lower, or not equal) to a given value ".

Determine the statistic.

We can substitute the following information in the above formula

\(t = \frac{7750-8000}{\frac{145}{\sqrt{6} } } = -4.22\)

Give the test's appropriate conclusion -

To begin with, we must determine the degrees of freedom indicated by: df = n-1 = 6-1 = 5.

Given that the test has two possible outcomes, the p value is

Pv = 2 ×  P(t(5) < -4.22) = 0.0083.

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Step-by-step explanation:

√2x² + 7x +√2=0

2x + 7x + √ 2 =0

√2=9x

x = o.15713484

Step-by-step explanation:

3x = 6y - 30

6y = (6y - 30)+ 30

6y - 6y = -30 + 30

0 = 0

y = {any rational number}

Step-by-step explanation:

there is something severely wrong with the problem definition.

when the Hypotenuse = 9, there is no 30-60-90 triangle with a leg = 6.

and when we are just focusing that this is a right-angled triangle with the Hypotenuse = 9, then 6 cannot be the longer leg.

it is also not clear what the solution is supposed to be. the 2nd leg ? the area ? the perimeter ? the height(s) ? ...

what ?

so, all I can do here is to show you why I said what I said :

30-60-90 triangle with Hypotenuse = 9

then the longer leg is opposite of the 60° angle and therefore sin(60)×9 = 7.794228634...

the shorter leg is opposite of the 30° angle and therefore sin(30)×9 = 0.5×9 = 4.5

a right-angled triangle with Hypotenuse = 9, one leg = 6 gives us per Pythagoras for the other leg

9² = 6² + leg²

81 = 36 + leg²

45 = leg²

leg = sqrt(45) = 6.708203932...

so, you see, as stated above, there is no leg with the length 6 in such a 30-60-90 triangle.

and in a more general right-angled triangle, if one leg = 6, then the other leg is actually longer.

therefore, there is everything wrong with the problem definition.

The angle measure of the angle in the diagram is 62°.

From the question, we are to determine the angle measure of the angle shown in the diagram.

The angle shown is an acute angle.

An acute angle is an angle whose measure is less than 90°.

To determine the measure of the angle, we will read the angle from the side which the angle is closer to zero (0). We will read from 0 to the line that indicates the angle.

Reading the angle:

Reading the angle as explained above, the measure of the angle is 62°

Hence, the angle measure is 62°.

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Answer:

true

Step-by-step explanation:

Answer:

x =23

Step-by-step explanation:

1) \(\frac{7x}{20x-4}\) = \(\frac{3}{2x+2}\)

2) Cross multiply - 14x+14=60x-12

3) Combine like terms - 46x=2

4) Divide - x=23

Answer:

score >= 30

Step-by-step explanation:

Add 20 to 10 to get 30

Make an inequality since they use the word "at least"

Hope this helps!

Answer:

Joshua score = x

x+10 ≥ 20

The possibilities could be from numbers 1-10, does it have any more info?

Answer: when I chip my nail -5 percent then rip off the rest -2 then add +3 coats of nail polish to hide my pain would equal -4 because that's how much i cried in the end or how much it costs out of my budget

Step-by-step explanation:

this was silly sorry lol

Answer:

only allow 3 decimals

90.284 is the answer we removed all others except for 3

The values of the angles are m∠AOB = 27°, m∠BOC = 48° and m∠COD = 27°.

Congruency may be defined as the property between two shapes or figures which shows same behavior in their shape and size. The symbol for congruency is given by '≅'. If one image is mirror image of another, then also both are said to be congruent. From the figure ∠AOB is congruent to ∠COD. We have the value of m∠AOB = 6x - 3 and m∠COD = 3x + 12. Equating these two values we get

6x - 3 = 3x + 12

3x = 15

=> x = 5

Now, the value of m∠AOB = 6x - 3 = 27°, value of m∠BOC = 6x + 18 = 48° and of value m∠COD = 3x + 12 = 27°.

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Answer:

1)Solving the expression \(1-2(2x+1)=1-(x-1)\) we get \(\mathbf{x=-\frac{1}{3}}\)

2) solving the equation \(3.6x-6.1=5.9-2.4x\) we get \(\mathbf{x=2}\)

Step-by-step explanation:

We need to solve the expressions:

1) \(1-2(2x+1)=1-(x-1)\\\)

Solving

\(1-2(2x+1)=1-(x-1)\)

First solving the brackets

\(1-4x-2=1-x+1\)

Simplifying

\(-1-4x=-x\)

Adding 4x on both sides

\(-1-4x+4x=-x+4x\\-1=3x\)

Switching the sides

\(3x=-1\)

Divide both sides by 3

\(\frac{3x}{3}=-\frac{1}{3}\\x= -\frac{1}{3}\)

So, Solving the expression \(1-2(2x+1)=1-(x-1)\) we get \(\mathbf{x=-\frac{1}{3}}\)

2) \(3.6x-6.1=5.9-2.4x\)

Solving:

\(3.6x-6.1=5.9-2.4x\)

Adding 6.1 on both sides

\(3.6x-6.1+6.1=5.9-2.4x+6.1\\3.6x=12-2.4x\)

Adding 2.4x on both sides

\(3.6x+2.4x=12-2.4x+2.4x\\6x=12\\\)

Divide both sides by 6

\(\frac{6x}{6}=\frac{12}{6}\\x=2\)

So, solving the equation \(3.6x-6.1=5.9-2.4x\) we get \(\mathbf{x=2}\)

N is the midpoint of MO and NO is 5, so MN would also be 5

MP = MN + NP = 5 + 9 = 14

Answer:

Step-by-step explanation:

y = -8x - 49

y = -x

Because it is more robust, or unaffected by the specific numerical values of those outliers, the median is typically a better indicator of the center when there are extreme values or outliers.

What is mean, median and mode?

The sum of the numbers is added, and the result is divided by the total number of numbers in the list to determine the arithmetic mean. An average usually refers to anything like this. In a list with values ranging from smallest to largest, the median is the middle value. On the list, the mode appears the most frequently.

As given, a high school basketball player is creating a scout summary of their sophomore season.

The points are,  29, 24, 32, 20, 0, 22, 28, 29 33, 34, 30, and 27.

Arrange these numbers in ascending order,

0, 20, 22, 24, 27, 28, 29, 29, 30, 32, 33, 34.

So,

Mean = (0 + 20 + 22 + 24 + 27 + 28 + 29 + 29 + 30 + 32 + 33 + 34) / 12

Mean = 308 / 12

Mean = 28

Median = 29

Mode = 29 (2 times repeating)

Because it is more robust, or unaffected by the specific numerical values of those outliers, the median is typically a better indicator of the center when there are extreme values or outliers.

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Answer:

1997 > y

Step-by-step explanation:

The inequality that presents year before 1997 is y<1997

Inequality shows relation between two expression which are not equal to each others.

According to given condition,

The emoji were introduced in the year 1997,

There can be infinite year before 1997, when emoji were not introduced.

The year y that describes inequality the year before 1997 can be represented as,

y<1997

The required inequality is y<1997.

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The area of the square is 1084 square inches.

The area of a square can be calculated as the square of the sides of a given figure. A square is always a rectangle, parallelogram, a rhombus and a quadrilateral but its reverse statement may or may not be true.(ie it is not always necessary that a rectangle is a square or a parallelogram is a square or a rhombus is a square).

The area of a square = side x side

Given;

One side of square= 33inches

Area of square= A^2

=33x33

=1089

Therefore, the area will be 1089m^2

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Using Scale Factor, the value of x = 33.6.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

Scale factor = Dimension of the new shape / Dimension of the original shape is the fundamental formula used to calculate it.

The formula is expressed as Scale factor = Larger figure dimensions Smaller figure dimensions in the event that the original figure is enlarged.

Dimension of the large triangle divided by the little triangle is the formula to utilize.

Based on the accompanying figure,

The little triangle's corresponding side length is 28, whereas the giant triangle's side length is x.

Scale factor = 6/5 Scale factor = 6/5 = 28

x = 33.6

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Complete Question -

If the figures below are similar with a scale factor of 6:5, find the value of x

Answer:

120 and 40

Step-by-step explanation:

Given

\(\angle 1 = 160\)

\(\angle 2 = 80\)

Rotation = 180 degrees

Translation = 40 units down

Required

A measure of the resulting angles

180 degrees rotation

Rotation only affects the positioning of angles and does not change the measure of the angles.

So, the measure of both angles remain unchanged.

40 units down translation

This will reduce the measure of both angles by 40 degrees.

So:

\(\angle 1 = 160 - 40 = 120\)

\(\angle 2 = 80 - 40 = 40\)

Answer: B i think

Step-by-step explanation:

A term can be a number, a variable, product of two or more variables or product of a number and a variable. An algebraic expression is formed by a single term or by a group of terms.

Answer: it is D

Step-by-step explanation:

Answer:

Step-by-step explanation:

To check whether the given credit card number is valid or not, we need to apply the Luhn algorithm or the mod-10 algorithm. The Luhn algorithm works by adding up all the digits in the credit card number and checking if the sum is divisible by 10 or not. If it is, then the credit card number is considered valid, otherwise, it is invalid.

Let's apply the Luhn algorithm to the given credit card number:

Step 1: Starting from the rightmost digit, double every second digit

| 5 | 4 | 2 | 4 | 9 | 8 | 1 | 3 | 2 | 7 | 2 | 0 | 0 | 0 | 8 | 5 |

|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

| | 8 | | 8 | | 16| | 6 | | 14| | 0 | | 0 | | 10|

Step 2: If the doubled value is greater than 9, add the digits of the result

| 5 | 4 | 2 | 4 | 9 | 8 | 1 | 3 | 2 | 7 | 2 | 0 | 0 | 0 | 8 | 5 |

|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

| | 8 | | 8 | | 7 | | 6 | | 5 | | 0 | | 0 | | 1 |

Step 3: Add up all the digits in the credit card number, including the check digit

5 + 4 + 2 + 4 + 9 + 8 + 1 + 3 + 2 + 7 + 2 + 0 + 0 + 0 + 8 + 5 + 1 = 61

Step 4: If the sum is divisible by 10, then the credit card number is valid, otherwise, it is invalid.

61 is not divisible by 10, therefore the given credit card number is invalid.

Hence, it can be concluded that 5424 9813 2720 0085 is an invalid MASTERCARD credit card number.

First, we have to get rid of the parenthesis, to do that, we just multiply signs to get

Now, we sum these numbers since they have the same signs

Therefore, the answer to (a) is -56.

We get rid of the parenthesis

Then, we subtract these numbers since they have different signs

Therefore, the answer to (b) is 10.

We just subtract these numbers since they have different signs

Therefore, the answer to (c) is 3.

We just subtract

Therefore, the answer to (d) is -5.

We just sum

Therefore, the answer to (e) is 96.

Answer:

Step-by-step explanation:

Common difference

Difference of first two

Difference of second two

Difference of last two

Now comparing d:

and

Eliminating a:

Finding a:

So the first term is:

Common difference:

The 6th term:

Answer:

x+100

Step-by-step explanation:

x^2-10,000/x-100

x^2-10000 is a difference in squares and can be factored.

x^2-10000 = (x+100)(×-100).

(x+100)(x-100)/(x-100)

(x-100) cancel each other.

x+100 remains.

4.2 x 10^8 is  2*10^6  times the value of 2.1 x 10^2 when division is performed.

The concept that will be used to solve the question is division operation.

We were given 4.2 x 10^8 which is greater than  2.1 x 10^2

The operation can be expressed as :

4.2 x 10^8 =( n *2.1 x 10^2)

where n = the number of times that 4.2 x 10^8  is greater than 2.1 x 10^2

Then make n the subject of the formular which is

n = 4.2 x 10^8/2.1 x 10^2

n = 2*10^6

Therefore, the values of 4.2 x 10^8 is greater than 2.1 x 10^2 in 2*10^6 times.

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Answer:

0.698, 6.9, 9.68, 80.69

Answer:

Step-by-step explanation: