For any two integers A and B, A minus b is equal to a plus additive inverse of b is equal to a + Dash

Step-by-step explanation:

SAS ================

What it says:

If two sides and the angle between them on one triangle are congruent to the corresponding two sides and the angle between them on the other, the triangles are congruent.

Required information:

Two sets of congruent sides with a congruent angle between them

ASA ================

What it says:

If one side and both connected angles on one triangle are congruent to one side and both connected angles on the other, the triangles are congruent.

Required information:

One set of congruent sides with two sets of congruent angles on the sides

AAS ==================

What it says:

If two angles and the non-included side on one triangle are congruent to two angles and the non-included side on the other, the triangles are congruent.

Required information:

Two sets of congruent angles and one set of congruent non-included sides

HL =================

What it says:

If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg on the other, the triangles are congruent.

Required information:

Congruent hypotenuse and congruent leg

Answer:

C

Step-by-step explanation:

The integral: S1 0 (-x³ - 2x² - x + 3)dx is -1/12

An integral is a mathematical operation that calculates the area under a curve or the value of a function at a specific point. It is denoted by the symbol ∫ and is used in calculus to find the total amount of change over an interval.

To evaluate the integral:

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx $\)

We can integrate each term of the polynomial separately using the power rule of integration, which states that:

\($ \int x^n dx = \frac{x^{n+1}}{n+1} + C $\)

where C is the constant of integration.

So, we have:

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx = \left[-\frac{x^4}{4} - \frac{2x^3}{3} - \frac{x^2}{2} + 3x\right]_0^1 $\)

Now we can substitute the upper limit of integration (1) into the expression, and then subtract the result of substituting the lower limit of integration (0):

\($ \left[-\frac{1^4}{4} - \frac{2(1^3)}{3} - \frac{1^2}{2} + 3(1)\right] - \left[-\frac{0^4}{4} - \frac{2(0^3)}{3} - \frac{0^2}{2} + 3(0)\right] $\)

Simplifying:

\($ = \left[-\frac{1}{4} - \frac{2}{3} - \frac{1}{2} + 3\right] - \left[0\right] $\)

\($ = -\frac{1}{12} $\)

Therefore,

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx = -\frac{1}{12} $\)

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Answer:

  \(\textbf{A. }0.25^{3/2}\)

Step-by-step explanation:

Perhaps your answer choices are ...

  \(\textbf{A. }0.25^{3/2}\\\textbf{B. }(\sqrt[3]{4})^2\\\textbf{C.}\sqrt[3]{16}\\\textbf{D. }0.25^{-2/3}\)

Of these, the one that is not equivalent to 4^(2/3) is ...

  \(\boxed{\textbf{A. }0.25^{3/2}}\)

The value of this is ...

  \(\left(\dfrac{1}{4}\right)^{3/2}=\sqrt{\dfrac{1}{4^3}}=\dfrac{1}{8}\ne4^{2/3}=\sqrt[3]{16}=(\sqrt[3]{4})^2\)

Answer:

Both cans have a volume of less than 18 cubic inches.

Step-by-step explanation:

Answer:

im going to say 15.5 is the answer

Step-by-step explanation:

Answer:

Answer is 17

Step-by-step explanation:

7 - 2 = 5

12 + 5 = 17

Answer:

They use collected data to recognize trends, predict outcomes, and plan for the future.

Step-by-step explanation:

This represents the direction and degree of rotation utilised to make the image, which is 90 degrees anticlockwise.

When an item or form is rotated about a fixed point, generally the origin or a specified point in the plane, the amount of rotation that takes place is referred to as the degree of rotation. Angles are measured in degrees, where one full rotation equals 360 degrees. The amount of angle shift, expressed in degrees, that occurs when an item or shape is rotated is known as the degree of rotation. A shape has been turned a quarter of a full rotation anticlockwise, for instance, if it is rotated 90 degrees in that direction. Similar to this, a form has completed one-half of a full rotation if it is rotated 180 degrees.

given

The graph suggests that the image was rotated 90 degrees anticlockwise and in the other manner to make.

Compare the figure's initial placement (the grey triangle) to its final placement to see this (the red triangle).

One of the vertices on the grey triangle is pointing upward, and the other two are pointing to the right and left.

The red triangle's up-pointing vertex remains after the transformation, but the other two vertices now point down and up-left, respectively.

This represents the direction and degree of rotation utilised to make the image, which is 90 degrees anticlockwise.

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Answer:

Step-by-step explanation:

Answer:

=The opposite angles of a parallelogram are equal

=(3x+4)

=(5x-2)

=-2x=-6

=x=6+2

=x=3=

1st angle=3x+4=13

3rd angle=5x-2=13

=sum of adjacent side of angle is 180°

=Let the adjacent (2nd angle ) be y=

y+13°=180°

=y=180°-13°

=y=167°=

2nd angle=4th angle

=2nd angle=167° 

=4th angle=167°

Step-by-step explanation:

This might be confusing, but I hope it helps <3

The number of classes should be an integer and this value will typically be a fraction. The limit needs to be raised in order to take into account all observations when this calculation yields an integer.

The fixed and variable costs can be determined by solving the system of equations if the variable cost is a fixed charge per unit and the fixed costs stay the same. The high-low method can, however, produce more or less accurate findings based on the distribution of values between the highest and lowest monetary values or quantities, therefore it is important to use caution when applying it.

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Answer:

depends on how long he spent on homework

Step-by-step explanation:

Answer:

It depends on how long David used the computer to do homework.

You didn't give us any numbers to calculate with.

Answer:2.9

3

Step-by-step explanation:

The geometric series is 6, -30, 150, -750, 3750, -18750 and the sum of the geometric series is -15624.

A geometric series is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio.

The geometric series that starts with 6, ends with -18,750, and has a common ratio of -5 is:

6, -30, 150, -750, 3750, -18750.

The sum of the geometric series is the sum of all the terms in the series. To find the sum of the series, you can use the formula:

S = a(1 - rⁿ)/(1 - r)

Where:

S is the sum of the series

a is the first term of the series

r is the common ratio

n is the number of terms in the series

In this case, a = 6, r = -5 and n = 6. Thus:

S = 6(1 - (-5)⁶)/(1 - (-5))

S = 6(1 - 15625)/(1 + 5)

S= 6(-15624)/6

S = -15624

Thus, the sum of the geometric series is -15624.

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Answer:

First Answer is correct

Step-by-step explanation:

The probability that both will experience allergies to pollen is 0.0484, and the probability that at least one will is 0.9516.

The following information is provided in the question:

A large country has a pollen allergy rate of about 22%.

As a result, the probability of people has a chance of having an allergy is  0.22.

P(allergic) = 0.22

P(Not allergic) = 1 - 0.22 = 0.78

If A and B are independent even, then,

P(A∩B) = P(A) × P(B)

Two people are randomly selected.

a) P( both will be allergic to pollen)

Since these are independent events,

P(both will be allergic to pollen)= P(allergic)*P(allergic)

= 0.22*0.22 =  0.0484

b) P(at least one person is allergic to pollen)

= 1 - P(both are not allergic to pollen)

= 1 - P(P(not allergic)*P(not allergic))

= 1 - (0.22*0.22)

= 0.9516

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Answer:

48

Step-by-step explanation:

4^2=16×3=48

hope this helps

The approximate standard deviation of the sampling distribution of the proportion is 3.8%.

A standard deviation (or) is a measure of how widely distributed the data is in reference to the mean.

A low standard deviation indicates that data is clustered around the mean, whereas a high standard deviation implies that data is more spread out.

Now, as per the questions;

Whenever the population size is so very large, the PQ/N factor approaches zero, and the standard deviation equation becomes:

σp = √( PQ/n)

We don't know how so many listeners this same radio station has in this case, but we can assume it's a large number.

P = probability of listening at work, is 14% or 0.14

Q = probability of not listening at work, is (100- 14)% = 86% = 0.86

N = sample size, is 85

The sample standard deviation is then

σp = √(14×.86/85)

σp = 0.0376

σp = 3.8% (approximately)

Therefore, the approximate vale of the standard deviation is found to be 3.8 %.

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The correct question is-

If 14% of the listeners of a radio station listen to it while they are at work, what is the approximate standard deviation of the sampling distribution of the proportion for samples of size 85?

Yes, the laws of exponents hold for positive and negative numbers, fractional exponents, and even irrational exponents such as π.

The laws of exponents apply to both positive and negative numbers. For example, when multiplying or dividing numbers with exponents, the exponents can be added or subtracted, respectively, regardless of the sign of the base. Similarly, when raising a number with an exponent to another exponent, the exponents can be multiplied. These rules hold true for positive and negative numbers, allowing consistent manipulation of expressions involving exponents.

Yes, the laws of exponents also hold for fractional exponents. The most common law, the power rule, states that when raising a number to a fractional exponent, the exponent can be expressed as a quotient of integers. This allows us to extend the laws of exponents to include fractional exponents and perform calculations accordingly. For example, we can multiply numbers with fractional exponents by adding the exponents and divide them by subtracting the exponents.

Yes, the laws of exponents also hold for irrational exponents, including numbers like π. Although irrational exponents cannot be expressed as exact fractions or decimals, we can still apply the laws of exponents. When working with irrational exponents, the calculations typically involve approximations or infinite series representations. However, the fundamental rules of exponentiation, such as adding, subtracting, or multiplying exponents, remain valid for irrational exponents as well.

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Answer:

y >= x/2 - 1

Step-by-step explanation:

the slope (rise/run) is 1/2 and the y-intercept is -1 so in point-slope form

y = x/2 - 1 but everything above the line (unshaded part) is valid so y is equal to or greater than.

Total Seeds required 9.33 kg  and she has 10 kg.so, she has enough grass seed to make a lawn 10m by 14 m.

If you're fortunate enough to have a rectangular lawn, determining the size is straightforward. Multiply the length and breadth measurements together to get the total. You now have your region/area.

So, Maisie knows that she needs 3 kg of grass seed to make a rectangular lawn 5 m by 9m.

Grass seed is sold in 2 kg boxes,

Maisie wants to make a rectangular lawn 10 m by 14 m,

She has 5 boxes of grass seed

To Find, Has Maisie got enough grass seed to make a lawn 10m by 14 m

Solution:

3 kg of grass seed to make a rectangular lawn 5 m by 9m.

=> 3 kg  of grass seed  needed for 5 x 9 = 45 m²

=>  1 m² required  = 3/45  kg seed

a rectangular lawn 10 m by 14 m,

area = 10 x 14 = 140 m²

Hence 140 m² required = 140 x  3/45  =  9.33 kg

Grass seed is sold in 2 kg boxes,

She has 5 boxes of grass seed

Hence total seeds = 5 x 2 = 10 kg

Therefore, total seeds required 9.33 kg  and she has 10 kg.so, she has enough grass seed to make a lawn 10m by 14 m.

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Answer:

Step-by-step explanation:

Answer:

( 1, 35 )

Step-by-step explanation:

y=mx+c

c= y-intercept ( where the graph line crosses the cross line)

c=0

mx = gradient ( rise/run, up/across )

mx = 175/5 ( you could have picked any point in the graph )

mx = 35

the m is useless now so we discard it

y= 35x+0

if x = 1

then y = 35(1)+0

y= 35

at the coordinate x=1 y is 35

Probability distributions according to the number of occurrences of green cards. Probabilities are:

P(x=0) =  0.1

P(x=1) = 0.15

P(x=2) = 0.45

P( x= 3) = 0.2

P ( x=4) = 0.1

Probability is absolutely how probably something is to take place. whenever we're unsure about the outcome of an occasion, we can speak approximately the chances of certain outcomes—how possibly they're. The evaluation of occasions governed by probability is referred to as facts.

P(x=0) = 12/120 = 1/10 = 0.1

P(x=1) = 18 /120 = 3/20 = 0.15

P(x=2) = 54 / 120 = 9/20 = 0.45

P( x= 3) = 24 / 120 = 0.2

P ( x=4) = 12 / 120 = 1 /10 = 0.1

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In an experiment, a deck of cards containing different colored cards is shuffled. Four cards are randomly selected and the number of green cards selected is recorded. One hundred twenty trials of the experiment are run.

The table shows the frequency of 0, 1, 2, 3, or 4 green cards occurring in the trials.

Number of green cards 0 1 2 3 4

Frequency 12 18 54 24 12

Create a probability distribution for the discrete variable.

Answer:

root 50

Step-by-step explanation:

Pythagorean theorem d is the hypotenuse

Answer:

5/2

Step-by-step explanation:

/50 if you do a2+b2=c2 and c=d

“My mother always used to say: The older you get, the better you get, unless you’re a banana.”

—Rose (Betty White), The Golden Girls

When a population is growing logistically the change in population size (dn/dt) is greatest  is given by  option c. when k/2 is equal to n.

Population size = n

Time = t

Change in population size over time = dn/dt

Option a,

This occurs because when the population is small .

There are fewer individuals to reproduce and contribute to the population growth.

Option b,

As the population approaches the carrying capacity  the growth rate slows down.

Because of environmental limitations on resources, space, and other factors.

At the carrying capacity, the population growth rate is zero, and the population remains stable.

The fastest population growth rate occurs when the population size is at an intermediate level.

Around half of the carrying capacity.

When the population size n is approximately half of the carrying capacity k of the environment.

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(5) The area of trapezium is 833.85 m².

(6) The area of the square is 309.76 mm².

(7) The area of the parallelogram is 148.2 yd².

(8) The area of the semicircle is 760.26 in².

(9) The area of the rectangle is 193.52 ft².

(10) The area of the right triangle is 183.74 in².

(11) The area of the isosceles triangle is 351.52 cm².

The area of the figures is calculated as follows;

area of trapezium is calculated as follows;

A = ¹/₂ (38 + 13) x 32.7

A = 833.85 m²

area of the square is calculated as follows;

A = 17.6 mm x 17.6 mm

A = 309.76 mm²

area of the parallelogram is calculated as follows;

A = 19 yd  x 7.8 yd

A = 148.2 yd²

area of the semicircle is calculated as follows;

A = ¹/₂ (πr²)

A =  ¹/₂ (π x 22²)

A = 760.26 in²

area of the rectangle is calculated as follows;

A = 16.4 ft x 11.8 ft

A = 193.52 ft²

area of the right triangle is calculated as follows;

based of the triangle = √ (29.1² - 14.6²) = 25.17 in

A = ¹/₂ x 25.17 x 14.6

A = 183.74 in²

area of the isosceles triangle is calculated as follows;

height of the triangle =  √ (30² - (26/2)²) = √ (30² - 13²) = 27.04 cm

A =  ¹/₂ x 26 x 27.04

A = 351.52 cm²

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