Mowing the lawn is one of Jeremy's jobs at home. But, Jeremy's dad offered to help him this week. His dad drew the following diagram of the lawn and told Jeremy to choose one of the parts to mow. If Jeremy wants to mow the rectangle with the smaller area, which one should he choose?

Answer:

The lower, middle, and upper quartiles of this data are 80.5, 98 and 118 respectively.

Step-by-step explanation:

The given data set is

122, 164, 71, 98, 84, 147, 114, 111, 98, 85, 104, 71, 77

Arrange the data set in ascending order.

71, 71, 77, 84, 85, 98, 98, 104, 111, 114, 122, 147, 164

Divide the data set in equal parts.

(71, 71, 77, 84, 85, 98), 98, (104, 111, 114, 122, 147, 164)

Now divide each parenthesis in two equal parts.

(71, 71, 77), (84, 85, 98), 98, (104, 111, 114), (122, 147, 164)

Lower quartile is

[tex]Q_1=\frac{77+84}{2}=80.5[/tex]

Middle quartile is

[tex]Median=Q_2=98[/tex]

Upper quartile is

[tex]Q_3=\frac{114+122}{2}=118[/tex]

Therefore, the lower, middle, and upper quartiles of this data are 80.5, 98 and 118 respectively.

The probability that 10 or more will show that the above three food items were ordered is 0.403.

The binomial distribution summarises the number of trials or observations where each trial has the same chance of achieving a specific value. The binomial distribution indicates the likelihood of observing a given number of successful outcomes in a given number of trials.

Given:

n= 15

p= 0.6

q= 1-0.6= 0.4

r= 10

Now, P(10<=x<=15) = 1 - binomcdf (15,0.6,9) = 0.4032

Then, P (x≥0) =  [tex]\sum_{x=0}^n[/tex][tex]^{15}C_{10}(0.6)^{10}(0.4)^{10}[/tex]

                       = [tex]\sum_{x=0}^{15[/tex]  3003 x (0.0060466176) (x 0.0001048576)

                       = 0.403

Hence, the probability is 0.403.

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Final answer:

Mora ate a total of 45.9 ounces of yogurt after consuming 8.5 containers, with each container holding 5.4 ounces.

Explanation:

The student asked how many ounces of yogurt Mora ate after consuming 8.5 containers, with each container holding 5.4 ounces. Mora ate 8.5 containers of yogurt, with each container holding 5.4 ounces of yogurt. To calculate the total amount of yogurt consumed, we multiply the number of containers by the amount of yogurt each container holds.

To solve this, simply calculate 8.5 containers × 5.4 ounces/container = 45.9 ounces of yogurt in total. This is the total amount of yogurt Mora ate during that week.

The area of the shaded region is 4π/3 square units.

We have given that x= center diameter =wz w and z end over line radius=2

Triangle XYZ is equilateral,

What is the central angle of equilateral ?

120 degrees

so the central angle of the sector is 120°,

In radian

=120×[tex]\pi[/tex]/180

=2π/3 radians.

The area of a sector of central angle β is given by,

[tex]A = (1/2)r^2(\beta )[/tex] . . . . . . β in radians

[tex]A = (1/2)*2^2*(2\pi /3)[/tex]    

 = 4π/3 . . . . square units

Therefore the area of the shaded region is 4π/3 square units.

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it's C: It is the graph of y = log2x translated 9 units down and 3 units to the left.

the correct answere is B

To find out how many plants are needed, we calculate the perimeter of the square flower bed, convert that to inches, and then divide by the spacing of the plants. In this case, about 48 plants would be needed.

This problem can be solved using the properties of a square and unit conversion. Since a square has four equal sides and each side of the square flower bed is 22 feet long, the total perimeter of the flower bed would be calculated as 22 feet * 4, which is 88 feet. Next we need to convert these feet to inches since the plants are spaced 22 inches apart. There are 12 inches within a foot, so 88 feet equals 1,056 inches (88*12).

Once you have the total length in inches, you can determine the number of plants by dividing the total length in inches by the distance each plant is to be spaced. Thus, 1,056 inches divided by 22 inches gives us approximately 48 plants.

So, if you want to space your plants 22 inches apart around a square flower bed where each side is 22 feet, you will need 48 plants.

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The length of each side of the square can be represented by the equivalent expressions 30x + 80, 10(3x + 8), and 2(15x) + 2(40), with the first expression being in the simplest form and containing only two terms.

The student is provided with an expression for the side length of a square and is asked to write equivalent expressions representing the lengths of the other three sides. Since all four sides of a square are equal, we simply need to simplify the given expression and use it to represent each side. The given expression is 6(3x+8)+32+12x.

First, we can simplify this by distributing and combining like terms:

6(3x+8) becomes 18x + 48

Adding the 32 gives us 18x + 48 + 32

Finally, add the 12x to get 18x + 12x + 48 + 32

Combining like terms results in 30x + 80.

Now we have our simplified expression, which is 30x + 80, to represent the length of each side of the square. For different but equivalent forms:

As two terms: 30x + 80 (this meets the requirement of containing only two terms)

Factored form: 10(3x + 8)

Expanded form by distributing a common factor: 2(15x) + 2(40)

These are three different equivalent expressions we can use to represent the lengths of each side of the square.

Answer: There is approximately 8.2 amount of radioactive material that will remain after 10 hours.

Step-by-step explanation:

Since we have given that

[tex]f(x)=10(0.98)^x[/tex]

where, f(x) represents the amount of radioactive material that will remain after x hours in the container.

Since we have given that x = 10 hours.

So, our equation becomes,

[tex]f(10)=10\times (0.98)^{10}\\\\f(10)\approx 8.17\\\\f(10)\approx 8.2[/tex]

Hence, there is approximately 8.2 amount of radioactive material that will remain after 10 hours.

Answer:

C. 42

Step-by-step explanation:

Answer: x = 3, x= - 3

Step-by-step explanation:

x^2 - 9 = 0

=> x^2 = 9

=> x = 3, x= - 3

To find the measure of angle OPQ, set up an equation using the given angles in triangle NOP. Simplify the equation and solve for x. Substitute the value of x back into the expression for angle OPQ to find the measure of the angle.

To find the measure of angle OPQ, we can set up an equation using the given angles in triangle NOP:
(x+17) + (2x-4) + (5x-17) = 180
Simplifying the equation, we get: 8x - 4 = 180
From this, we can solve for x: 8x = 184, x = 23.
Now that we have the value of x, we can substitute it back into the expression for angle OPQ: 5(23) - 17 = 108 degrees.
Thus, the measure of angle OPQ is 108 degrees.

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The smallest possible value for the width of the rectangle is 9 meters, given that the perimeter must be greater than or equal to 108 meters and the length is 5 times the width.

The question asks for the possible values of the width of a rectangle where the length is 5 times the width and the perimeter is greater than or equal to 108 meters.

Step-by-step explanation:

Let's call the width of the rectangle w. The length is then 5w. The perimeter P of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width.

In this case, P = 2(5w) + 2w = 10w + 2w = 12w. Now, we know that P >= 108, so 12w >= 108.

To find the smallest value for w, we divide both sides by 12: w >= 9. Thus, the width of the rectangle must be at least 9 meters.

Answer: Congruent

Step-by-step explanation:

If two chords are the same distance from the center of a circle, then they are congruent, the correct option is B.

Suppose it is given that two triangles ΔABC ≅ ΔDEF

Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.

The order in which the congruency is written matters.

For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.

Thus, we get:

[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex]

(|AB| denotes length of line segment AB, and so on for others).

We are given that;

The distance between the chords is same

Now,

According to 1 and 2, if two chords are the same distance from the center of a circle, then they are congruent. This means they have the same length and subtend equal angles at the center.

Therefore, the answer will be congruent.

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Final answer:

There are 1326 different 2-card hands possible when drawing without replacement from a standard deck of 52 playing cards, using combinations to calculate it.

Explanation:

To determine how many different 2-card hands are possible from a standard deck of 52 playing cards when drawing without replacement, we need to consider combinations since the order of the cards does not matter. Using the combination formula C(n, r) = n! / (r!(n - r)!), where n is the total number of items and r is the number of items to choose, we calculate C(52, 2).

We have:

n = 52 (total number of cards)

r = 2 (number of cards to choose)

Therefore, the calculation is as follows:

C(52, 2) = 52! / (2!(52 - 2)!) = 52! / (2! * 50!) = (52 * 51) / (2 * 1) = 1326.

So, there are 1326 different 2-card hands possible when drawing without replacement from a standard deck of cards.