Which ordered pair is a solution to the system of inequalities?y > 3xy≤ x + 5O A. (2,6)OB. (2,5)O C. (1,8)O D. (1,5)← PREVIOUSSUBMIT

The triangle which could be drawn as per the given description is only option b. isosceles triangle with measure 20° and 80°.

An acute triangle with sides measuring 7, 4, and 2

In an acute triangle, the sum of the squares of the two shorter sides must be greater than the square of the longest side .

According to the Pythagorean Theorem.

Here, 7² is greater than (4² + 2²).

So this is not possible.

An isosceles triangle with angles measuring 20° and 80°

In an isosceles triangle, two angles are equal, so if two angle measures 20° and 80°,

Then the third angle measures is

180° - 20° - 80°= 80°

Two angles are congruent implies two sides are congruent.

It is possible to form isosceles triangle.

An obtuse triangle with sides measuring 5, 10, and 15

In an obtuse triangle, the longest side is opposite the largest angle.

Sum of squares of two shorter sides is less than square of longest side according to Pythagorean Theorem.

However, 15²is greater than (5²+ 10²),

so this is not possible.

A scalene triangle with angles measuring 110° and 35°

The sum of the angles of any triangle is 180°,

so the third angle must measure

180° - 110° - 35° = 35°.

Two angles are congruent so it is isosceles triangle.

It is not possible to form scalene triangle.

Therefore, the triangle possible to draw as per the given condition is only option b. isosceles triangle with measure 20° and 80°.

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a) The standard deviation of  1.45 mpg.

b)The margin of error for the mean estimate 3.03 mpg

c) A 95% confidence interval for μμ is (28.1 - 3.03, 28.1 + 3.03) or (25.07, 31.13) mpg, the mean highway mpg for this vehicle is  27 mpg.

a) Using the formula for the standard error of the mean, σx¯ = σ/√n, where σ is the standard deviation of the population, n is the sample size, we can calculate σx¯ = 6.5/√20 ≈ 1.45 mpg.

b) Using a 95% confidence level, we can find the critical value for the t-distribution with 19 degrees of freedom (n-1), which is 2.093. The margin of error for the mean estimate is then t*σx¯ = 2.093 x 1.45 ≈ 3.03 mpg.

c) The 95% confidence interval for μ is given by x¯ ± margin of error, which is (28.1 - 3.03, 28.1 + 3.03) or (25.07, 31.13) mpg. Since the vehicle sticker information states a highway average of 27 mpg, the results of this experiment are not consistent with the vehicle sticker, as the 95% confidence interval does not contain the value of 27 mpg. This suggests that the vehicle may not be performing as well as expected, or that the sample of mpg readings was not representative of the overall population.

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Answer:

The answer is D. -9 and -3

Step-by-step explanation:

since the graph starts at 1 and goes backwards, it cant be 1. so that rules out A. and B. then it requires the numbers to be negative because if they are a whole number over 1, they don´t fit the inequality. I hope this helps :))

Based on the set of transformations for trapezoid ABCD, the location of point A after the transformations are complete is: D. (−5, 1).

In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has the coordinates (-x, -y).

By applying a rotation of 180° to the given point, the coordinates of its image is given by:

(x, y)                           →               (-x, -y)

Points A = (-5, 1)        →     Points A' = (-(-5), -(1)) = (5, -1).

Next, we would reflect the given point over the x-axis as follows;

(x, y)                           →              (x, -y)

Points A' = (5, -1)        →     Points A' = (5, -(-1)) = (5, 1)

Lastly, we would reflect the given point over the y-axis as follows;

(x, y)                           →              (-x, y)

Points A' = (5, 1)        →     Points A' = (-(5), 1) = (-5, 1)

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Answer:

c. Both Tami and Vu performed equally well.

Step-by-step explanation:

To solve this question, we use z score

The formula for calculating a z-score is is z = (x-μ)/σ

where x is the raw score

μ is the population mean

σ is the population standard deviation.

a) For Tami , who took MCAT

We are told:

Scores on the MCAT follow a Normal distribution with a mean of 505.6 points and a standard deviation of 9.3 points.. If Tami earns 524.2 points on the MCAT.

x = 524.2 points

μ = 505.6 points

σ = 9.3 points

z = 524.2 - 505.6/9.3

= 2

The z score for Tami is 2

For Vu, who took LSAT

We were told:

Scores on the LSAT follow a Normal distribution with a mean of 150.7 points and a standard deviation of 10.2 points. Vu earns 171.1 points on the LSAT.

x = 171.1 points

μ = 150.7 points

σ = 10.2 points

z = 171.1 - 150.7/10.2

z = 2

The z score for Vu is also equal to 2

Therefore, we can say the bout Tami and Vu performed equally well.

Option c is the correct answer.

Answer:

6/11

Step-by-step explanation:

Fraction that are girls

girls/ total

6/11

Answer:

6/11

Step-by-step explanation:

5+6=11 girls =6 so 6/11

Answer:

4

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Since x= 3/4

To take the fraction on left hand side, inverse 4/3

Take π as denominator

Then cube root the entire equation on the left hand side.

Answer:

Step-by-step explanation:

Step-by-step explanation:

To calculate the probability of getting at least four hearts when dealing five cards from a standard deck, we can use the concept of combinations and probability.

There are a total of 52 cards in a standard deck, and 13 of them are hearts (assuming no jokers). So the probability of drawing a heart on the first card is 13/52, or 1/4.

Now, there are two possible scenarios that would result in at least four hearts:

Four hearts and one non-heart: This can happen in C(13,4) * C(39,1) ways, where C(n, k) is the number of combinations of n items taken k at a time. The first part C(13,4) represents choosing 4 hearts out of 13, and the second part C(39,1) represents choosing 1 non-heart out of the remaining 39 cards. The total number of ways to choose 5 cards from 52 is C(52,5).

Five hearts: This can happen in C(13,5) ways, where C(13,5) represents choosing all 5 hearts out of 13.

So, the total number of favorable outcomes is C(13,4) * C(39,1) + C(13,5), and the total number of possible outcomes is C(52,5). Therefore, the probability of getting at least four hearts is:

P(at least 4 hearts) = (C(13,4) * C(39,1) + C(13,5)) / C(52,5)

Plugging in the values and simplifying, we get:

P(at least 4 hearts) = (C(13,4) * C(39,1) + C(13,5)) / C(52,5)

= (715 * 39 + 1287) / 2,598,960

= 27,885 / 2,598,960

≈ 0.0107566

So, the probability of getting at least four hearts when dealing five cards from a standard deck is approximately 0.0107566 or about 1.08%.

Answer:

Step-by-step explanation:

Let's solve your equation step-by-step.

x2+4=3x+8

Step 1: Subtract 3x+8 from both sides.

x2+4−(3x+8)=3x+8−(3x+8)

x2−3x−4=0

Step 2: Factor left side of equation.

(x+1)(x−4)=0

Step 3: Set factors equal to 0.

x+1=0 or x−4=0

x=−1 or x=4

Answer:

x=−1 or x=4

FIFO - March cost of goods sold = $13,050. March 31 inventory = $7,350. LIFO - March cost of goods sold = $14,600. March 31 inventory = $5,800.

To calculate March cost of goods sold we need to add the given data for FIFO =

March cost of goods sold

= (2,800 + 3,700 + 6,550)

= 13,050

To calculate March cost of goods sold we need to add the given data for LIFO =

March cost of goods sold

= (3,400 + 4,400 + 6,800)

= 5,800

Sales data refers to the information collected and recorded about the transactions that occur when a business sells products or services to customers. This data typically includes details such as the date and time of the sale, the products or services sold, the quantity sold, the price paid, and the customer's information. Sales data is crucial for businesses as it helps them understand their sales performance, identify trends and patterns and make informed decisions about their pricing, marketing and inventory management strategies.

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Answer: A

Step-by-step explanation:

The three angles in a triangle add to \(180^{\circ}\). Therefore, each angle measures \(\frac{180^{\circ}}{3}=60^{\circ}\).

Answer: D

Step-by-step explanation:

1 in.=1488 milesx5=7440 miles.

Area= pi x r^2

=pi x (7440)^2 or option D.

Hope this helps :)

The area of the green region of the circle is 96.4 ft².

Area is the region bounded by a plane shape.

To calculate the area of the green region of the circle, we use the formula below

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

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The area of the green region in the circle given is expressed as approximately: a. 96.5 square feet.

The sector of a circle is calculated as:

A = ∅/360 * πr², where r is the radius and ∅ is the reference or central angle of the sector.

Given the following:

Central or reference angle (∅) = 180 - 27 = 153 degrees

Radius (r) = 17/2 = 8.5 feet

Plug in the values:

Area of the green region = 153/360 * π * 8.5²

Area of the green region ≈ 96.5 square feet.

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Answer:

Step-by-step explanation:

The thousand mark is the 4th number when going from right to left. So it would be the {6},976. When it comes to rounding, you go "5 and above, give it a shove, 4 and below, let it go. 6,976 rounded to the nearest thousand is 7,000,  3,983 rounded to the nearest thousand is 4,000,  13,560 rounded is 14,000.

7,000 + 4,000+ 14,000 = 25,000

a) The mean of the sampling distribution would be 12, the standard deviation would be 2, and the shape would be normal.

The sampling distribution for the sample mean would be a normal distribution with a mean equal to the population mean (12) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (4 / sqrt(9) = 2).

b) We can use a standard normal table or a normal calculator function to find the probability of a person having moved at most 5 times. We need to first standardize the random variable by subtracting the population mean (12) and dividing by the population standard deviation (4):

z = (5 - 12) / 4 = -2.5

Using a standard normal table or a normal calculator function, we find that the probability of a person having moved at most 5 times is 0.0062.

c) To find the value such that 85% of the people will have moved at least that many times, we need to find the 85th percentile of the normal distribution.

We can use a normal calculator function to find the inverse standard normal value for 0.85. Let x be the number of moves.

z = (x - 12) / 4

x = 12 + 4 * invNorm(0.85)

Using a normal calculator function, we find that invNorm(0.85) = 0.841. So,

x = 12 + 4 * 0.841 = 16.164

Rounding to the nearest whole number, we find that 85% of people from the United States will have moved at least 16 times in their lifetime.

d) To find the probability that a random sample of 9 people will have a mean number of moves greater than 17, we need to standardize the sample mean:

z = (17 - 12) / (2) = 2.5

Using a standard normal table or a normal calculator function, we find that the probability of a standard normal random variable being greater than 2.5 is 0.0062.

So, the probability that a random sample of 9 people will have a mean number of moves greater than 17 is 0.0062.

e) To find the probability that a random sample of 9 people will have a mean number of moves less than 9, we need to standardize the sample mean:

z = (9 - 12) / (2) = -1.5

Using a standard normal table or a normal calculator function, we find that the probability of a standard normal random variable being less than -1.5 is 0.0668.

So, the probability that a random sample of 9 people will have a mean number of moves less than 9 is 0.0668.

f) To find the middle 50% of sample means, we need to find the 25th and 75th percentiles of the normal distribution of sample means. We can use a normal calculator function to find the inverse standard normal values for 0.25 and 0.75.

Let x be the number of moves.

z = (x - 12) / (2)

x = 12 + 2 * invNorm(0.25) or x = 12 + 2 * invNorm(0.75)

Using a normal calculator function, we find that invNorm(0.25) = -0.675 and invNorm(0.75) = 0.675. So,

x = 12 + 2 * -0.675 = 11.35 or x = 12 + 2 * 0.675 = 13.

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Answer: 30

Step-by-step explanation:

You multiply the base by the height, so 10*6=60

You then take that and divide it by 2 to get 30.

You do this because you assume that the triangle is half of a square.

Answer:

16 for the first one. each segment is 4

40 for the second. each segment is 8

Answer:

0, 4, 8, 12, 16

8, 16, 24, 32, 40, 48

Step-by-step explanation:

The first number line has 6 parts. 24÷6=4. Each vertical line will increase by 4.

So starting at 0, the parts of the number line are:

0, 4, 8, 12, 16, 20, 24

The specific part being asked for is 0, 4, 8, 12, 16

The second number line has 8 parts. 64÷8=8. Each vertical line will increase by 8.

Starting at 0, the parts of the number line are:

0, 8, 16, 24, 32, 40, 48, 56, 64

The specific part being asked for is 8, 16, 24, 32, 40, 48

Answer:

Step-by-step explanation:

If it is not Monday, then there are students in the gym.

Negation: It is not Monday and there are not students in the gym.

Statement: It is Monday or there are students in the gym.

Equivalent: If there are not students in the gym, then it is Monday.

Neither: There are not students in the gym or it is not Monday.

Answer:

x=10

Since 4×2=8

Then automatically 5×2=10

(1) The value of x is determined as 16.8.

(2) The measure of length VX is calculated as 4.1.

(3) The measure of angle UWV is 69.5⁰.

The value of the missing lengths of the triangle is calculated by applying the following formula;

(1) For the two similar triangles, the value of x is calculated as follows;

20 / (28 - x) = 30 / x

20x = 30 (28 - x )

20x = 840 - 30x

20x + 30x = 840

50x = 840

x = 840 / 50

x = 16.8

(2) The measure of length VX is calculated by applying trig ratios.

tan 63 = 8 / VX

VX = 8 / tan 63

VX = 4.1

(3) The measure of angle UWV is calculated as follows;

angle T = 360 - (94 + 127) = 139

angle UWV = ¹/₂ x 139 (angle at circumference is half of angle at center)

angle UWV = 69.5⁰

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Answer:

C.  \(x=-9 \textsf{ and }x=1\)

Step-by-step explanation:

\((x+4)^2=25\)

\((x+4)(x+4)=25\)

expand the brackets:

\(x^2+8x+16=25\)

subtract 25 from both sides:

\(x^2+8x-9=0\)

factor:

\(x^2+9x-x-9=0\)

\(x(x+9)-1(x+9)=0\)

\((x-1)(x+9)=0\)

solve for x:

\(x-1=0 \implies x=1\)

\(x+9=0 \implies x=-9\)

To make 10 to add 8 + 8 is 10 - 2 + 10 - 2 that is 16

Make 10, or Add up using 10 is a derived facts strategy. That means children need to know some facts by hear before they can use a make 10 strategy. The key facts for using a make 10 strategy are 8+2=10 and 9+1=10.

We need to make 10 to add 8 + 8.

8  + 8 = (10 - 2) + (10 - 2)

8 + 8 = 10 - 2 + 10 - 2

8 + 8 = 20 - 4

8 + 8 = 16

Thus, to make 10 to add 8 + 8 is 10 - 2 + 10 - 2 that is 16

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1 cm = 10 mm. Length of book : 28 cm. Length of book = 280 mm. This shows that measurements in mm are the same but look to have a higher number .

The conversion factor provided states that 1 cm is equal to 10 mm, which means that 1 cm is made up of 10 individual millimeters.

The length of my book in when measured in millimeters is 280 mm.

In centimeters, this is therefore:

= 280 mm / 10 cm /mm

= 28 cm

Although the numerical value appears higher when expressed in millimeters, it is important to note that the actual length of the book remains the same.

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The probability of rejecting the null when the alternative is true is d. 0.67

Given :

If α=.10 and β=.33, then the probability of rejecting the null when the alternative is true is .

Probability :

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

Null hypothesis :

A null hypothesis is a type of statistical hypothesis that proposes that no statistical significance exists in a set of given observations.

we know that ,

probability = 2 * 0.33 + 0.01

= 0.66 + 0.01

= 0.67

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Answer:

Step-by-step explanation:

Let x = base side length

y = side height

volume V = x²y

y = V/x²

surface area

A = x² + 4xy

A = x² + 4x(V/x²)

A = x² + 4V/x

Solving for volume

V = (A - x²)(x/4)

V = ¼(Ax - x³)

a maximum will occur when the derivative equals zero

V' = ¼(A - 3x²)

0 = ¼(A - 3x²)

0 = A - 3x²

3x² = A

3x² = 1100

x² = (1100 / 3)

x = √(1100/3)

V = (A - x²)(x/4)

V = (1100 - √(1100/3))²(√(1100/3)/4)

V = 3,510.56606...

V = 3510.6 cm³

The box height will be half of the base side length.

y = ½√(1100/3)

Answer:

As = 256\(\pi\) or 804.25cm

Step-by-step explanation:

By formula As = \(4\pi r^{2}\)

As = 256\(\pi\) or 804.25cm

The intersection points are (6, 6) and (-6, -6).

What is Intersection points?

The point at which two lines or curves intersect is referred to as the point of intersection. The point at which two curves intersect is crucial because it is the point at which the two curves take on the same value.

The given curves are the polar equations of two circles with radii 6. To find their intersection points, we can set the two equations equal to each other and solve for Ф.

6 sin(Ф) = 6 cos(Ф)

Dividing both sides by 6 and rearranging terms, we get:

tan(Ф) = 1

This equation has infinitely many solutions, but we are only interested in those that lie in the interval [0, π/2].

Ф = π/4 satisfies this condition and corresponds to the point (6, 6) in Cartesian coordinates.

Since the two curves are circles, they are symmetrical about the origin. Therefore, we can deduce that the other intersection point is (-6, -6).

Therefore, the intersection points are (6, 6) and (-6, -6).

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