Factor completely.

3x squared + 2xy - y squared

Answer: Squash plant is the right answer to fill the blank.

Step-by-step explanation:

Since we have given that

Number of tomato plants = 9

Number of pepper plants = 5

Number of squash plants = 3

Number of pumpkin plants = 6

Since the ratio of tomato plants to squash plants is 9 : 3 = 3 : 1.

So, for every 3 tomato plants in Sunny's garden, there is 1 squash plant.

Hence, Squash plant is the right answer to fill the blank.

In this question, we will use Pythagoras theorem in order to find the height of the tent.

The center height of tent is 8.1 feet.

Right triangle is defined as a triangle which one angle is a right angle or two sides are perpendicular.

A right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

perpendicular² + base² = hypotenuse²

Given,

Side length of each triangle = 4 feet

Hypotenuse of each triangle = 9 feet

Shared side = x

Given the triangles are right angled,

According to Pythagoras theorem,

a² + b² = c²

Here, a = 4 , b = x , c= 9

Substitute the values in Pythagoras theorem,

4² + x² = 9²

16 + x² = 81

x² = 81 - 16

x² = 65

Taking square root on both sides

x = √65

x = 8.062

x = 8.1 (Rounding nearest tenth)

Hence, the center height of tent is 8.1 feet.

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The required 1/8 divided by 6 is equal to 1/48.

To solve 1/8 divided by 6, we can rewrite it as a fraction. The reciprocal of 6 is 1/6, so the division problem becomes (1/8) * (1/6). To multiply fractions, we multiply the numerators together and the denominators together.

Step 1 is given as:
= (1/8) * (1/6)

Step 2(simplification) is given as:

= 1 * 1 / 8 * 6
= 1/48

Therefore, the required 1/8 divided by 6 is equal to 1/48.

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The correct statement is that if two polygons are similar, their corresponding sides are proportional while their corresponding angles are congruent. Similar polygons have the same shape but can have different sizes, and this applies across various geometrical figures and principles, like the Pythagorean theorem in the context of right triangles.

The correct statement among the given options is: If two polygons are similar, then the corresponding sides are proportional and the corresponding angles are congruent. When polygons are similar, this means their shapes are geometrically the same but they may differ in size. The ratios of the lengths of corresponding sides of similar polygons are equal, which is true for any pairs of similar polygons, not just triangles. The corresponding angles, on the other hand, are congruent, which means they have the same measure in both polygons.

To explain this concept, we use different examples in geometry. For instance, in similar triangles, not only are the three angles in one triangle congruent to the three angles in the other, but also the sides are proportional, which can be expressed as the ratio of any two corresponding sides in the two triangles being equal. This proportional relationship is a key characteristic of similarity in geometry.

Moreover, a statement like the Pythagorean theorem applies to right triangles, stating that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This theorem is connected to similarity because one can generate a family of similar right triangles by scaling a single right triangle.

John deposits $5,250 into his savings account every month, which is 75% of his monthly salary.

The student's question is about how much money John deposits into his savings account from his monthly salary. To solve this, we calculate 0.75 (or 75%) of John's monthly salary of 7,000.

Calculation: 0.75  imes 7,000 = 5,250

So, John deposits $5,250 into his savings account every month.

The Ratio of the square feet to the per flower type is 14 : 1.

A Ratio shows the relative size of two or more value.

According to the question,

Area of a flower garden = 70 square feet

Number of flower plants varieties = 5

Formula for Perimeter of square = 4a where 'a' is sides of a square

4(a) = 70

a=70/4

a=15

To find the Ratio of the square feet to the per flower type

70 : 5

14 : 1.

Hence,  the Ratio of the square feet to the per flower type is 14:1

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Answer:

Correct answer is option C (√61)

Step-by-step explanation:

in this question we have given a right triangle in which

∠C=[tex]90^{0}[/tex]

BC = 6 and AC = 5

we have to find the length of the hypotenuse, AB=?

To find the the hypotenuse we will apply Pythagoras theorem (According to Pythagoras theorem, "in a right angle triangle, square of hypotenuse is equal to the sum of square of other two sides")

In ΔABC by Pythagoras theorem

[tex]AB^{2}=AC^{2}+BC^{2}[/tex]...................(1)

put values of BC and AC in equation 1

[tex]AB^{2}=5^{2}+6^{2}[/tex]

[tex]AB^{2}=25+36[/tex]

[tex]AB^{2}=61[/tex]

AB=√61

Answer:

C.) $10 per shirt

Step-by-step explanation:

have a nice day

The option C is more simplified answer for given condition, unit rate is $10.

When comparing two different kinds of numbers with distinct units, a rate is a ratio that is employed. The unit rate, on the other hand, shows how many units of one quantity are equal to one unit of another. When the rate's denominator is 1, we refer to the rate as a unit rate.

Given

There are 5 shirts in the image given to us composed of 3 white shirts and 2 black shirts.

A rate with 1 as its denominator is known as a unit rate.

Option A: A ratio of 3:2 or a fraction of 3/2 is indicated by 3 white shirts and 2 white black shirts.

The denominator is not 1, hence this cannot be a unit rate.

Option B: 5 white shirts to 2 black shirts. This cannot be a unit rate because the fraction 2/5 will not have 1 as the denominator.

Choice C: $10 for each shirt. Because it represents a ratio of 10:1 or a fraction of 10/1, this rate is a unit rate. Therefore, the price of 5 shirts will be $50.

D: $50 for each shirt. Because option C has provided us with a more straightforward sum of $10, which we must accept as we are dealing with unit rates, this would not be a unit rate in this question.

Hence Option C is most suitable answer.

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The complete question is in image.

Answer: Permutation

Permutation is a way, in which a set or number of things can be ordered or arranged. It is a listing where order matters and each thing in the list of things appears only once.

 In Mathematics, permutation is the action of changing the arrangement of a set of items. .It is also called an "arrangement number" or "order 

Given mean = 24.5 and standard deviation = 1.7

Within 1 standard deviations, x ∈ [24.5 - 1.7 , 24.5 + 1.7] or [22.8 , 26.2].

Within 2 standard deviations, x ∈ [24.5 - 2(1.7) , 24.5 + 2(1.7)] or [21.1 , 27.9].

Within 3 standard deviations, x ∈ [24.5 - 3(1.7) , 24.5 + 3(1.7)] or [19.4 , 29.6].

Given values are 24, 23, 28, 23, 24, and 25.

So {24, 23, 23, 24, 25} fall within 1 standard deviation and {28} falls within 3 standard deviations.

The expression that is equal to the rational expression when x does not equal to 5 or -1 is; (x - 7)/(x -5)

We want to simplify the algebraic expression;

(x - 7)(x + 1)/(x + 1)(x - 5)

Now, looking at the given expression, we see that (x + 1 ) is common to both numerator and denominator and as such they will cancel out to leave us with;

(x - 7)/(x -5)

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0.0003840

Written in scientific notation!

Move the decimal point.

.00384 x 10^1

.0384 x 10^2

.384 x 10^3

3.84 x 10^4

38.4 x 10^5

The lowest marks that a student can have and still be awarded a passing grade is 44.

Step-by-step explanation:

Given :

Mean, [tex]\mu = 62[/tex]

Standard Deviation, [tex]\sigma = 11[/tex]

Calculation :

z score is given by,

[tex]z = \dfrac{x-\mu }{\sigma}[/tex] ----- (1)

Value of z corresponds to 5% is,

[tex]z =-1.65[/tex]

from equation (1) we get,

[tex]-1.65=\dfrac{x-62}{11}[/tex]

[tex]x=43.85[/tex]

[tex]\rm x = 44 \;\;(Approx)[/tex]

The lowest marks that a student can have and still be awarded a passing grade is 44.

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In the given set, the mean is 64, the median is 66, there is no mode, and the range is 62.

To find the mean, median, mode, and range of the given set of numbers: 83, 75, 74, 40, 85, 64, 23, 68.

1. Mean:

[tex]\[ \text{Mean} = \frac{\text{Sum of all numbers}}{\text{Total number of numbers}} \][/tex]

[tex]\[ \text{Mean} = \frac{83 + 75 + 74 + 40 + 85 + 64 + 23 + 68}{8} \][/tex]

[tex]\[ \text{Mean} = \frac{512}{8} \][/tex]

[tex]\[ \text{Mean} = 64 \][/tex]

2. Median:

The median is the middle number when the numbers are arranged in ascending order.

Arranging the numbers in ascending order: 23, 40, 64, 68, 74, 75, 83, 85

Since there are 8 numbers, the median is the average of the two middle numbers:

[tex]\[ \text{Median} = \frac{64 + 68}{2} \][/tex]

[tex]\[ \text{Median} = 66 \][/tex]

3. Mode:

The mode is the number that appears most frequently.

In this set, there is no number that appears more than once.

So, there is no mode.

4. Range:

The range is the difference between the largest and smallest numbers.

[tex]\[ \text{Range} = \text{Largest number} - \text{Smallest number} \][/tex]

[tex]\[ \text{Range} = 85 - 23 \][/tex]

[tex]\[ \text{Range} = 62 \][/tex]

So, for the given set of numbers, the mean is 64, the median is 66, there is no mode, and the range is 62.

Answer:

[tex]41\%[/tex]

Step-by-step explanation:

we have the ratio

[tex]\frac{41}{100}[/tex]

To write as percent, multiply the ratio by 100

so

[tex]\frac{41}{100}*100=41*100/100=41\%[/tex]