I went into a store with a 70% off sign on the door. I found a pair of pants that were originally $49.99 for $30.00 I didn't think this was 70% off so I had to make sure. What were the real percentage off?

The inequality representing the problem is 5x+32y≤400

A relationship between two expressions or values that are not equal to each other is called inequality.

Given that, A solar panel can generate power at a maximum rate of 400 kilowatts per day. When it is cloudy, it can only generate 5 kilowatts per hour and when the sky is clear, 32 kilowatts per hour.

According to question,

5x+32y≤400

Hence, The inequality representing the problem is 5x+32y≤400

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The value of a in this question is 1.

Here, we've been given the matrix A=[2 0 1; 0 2 0; a 0 2]

For eigenvalues, the characteristic polynomial of A -

= det(A-  λI) = 0

= Let [(2 0 1; 0 2 0; a 0 2) - (λ 0 0; 0 λ 0; 0 0 λ)] = 0

= [2-λ 0 1; 0 2-λ 0; a 0 2-λ] = 0

= (2-λ)(2-λ)² - a[+(2-λ)] = 0

= 8+2λ² -8λ-4λ-λ³ +4λ²-2a+aλ = 0

= -λ³ +6λ² +(a-12)λ+8-2a = 0

For the given eigenvalues 1,2, and 3, the characteristic polynomial must have the roots at λ=1,2,3

= -(λ-1)(λ-2)(λ-3)

=-λ³+6λ²-11λ+6

Hence, -λ³+6λ²-11λ+6 = -λ³ +6λ² +(a-12)λ+8-2a

From equating these, we get-

a = 1

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The equation of a line given two points in point slope form is:

y - y1 = (y2-y1 / x2-x1)(x-x1).

Given:

Two points (x1,y1) and (x2,y2)

we know that,

slope m = y2-y1 / x2-x1

the equation passes through (x1,y1).

we know that:

Point slope form is y - y1 = m(x-x1)

substitute m value

y - y1 = (y2-y1 / x2-x1) (x-x1)

Therefore The equation of a line given two points in point slope form is:

y - y1 = (y2-y1 / x2-x1)(x-x1).

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The pair of triangles in the option B are congruent by AAS congruence theorem.

What is AAS congruence theorem ?

The Triangles Are Congruent Theorem (AAS) states that if two angles and a non-included side in one triangle are congruent to two angles and the matching non-included side in another triangle.

AAS congruence theorem full form is Angle Angle Side .

This means 2 angles 1 side have to be same for the two triangles to be congruent.

So, in the option B, the 2 angles and 1 side same for the two triangles .

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The simplified equation is 2x y²√y + 2x y√y when the actual equation is √x²y³ +2√x³y⁴ +x y√y. Option -B is correct.

Given that,

The equation is

√x² y³ +2√x³y⁴ +x y√y

We have to simplify the equation.

We know that,

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.

Take the equation

√x²y³ +2√x³y⁴ +x y√y

x y√y +2√x³y⁴ +x y√y

2√x³y⁴ + 2x y√y

2x y²√y + 2x y√y

Therefore, The simplified equation is 2xy²√y + 2x y√y when the actual equation is √x²y³ +2√x³y⁴ +x y√y. Option -B is correct.

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Answer:

B on edge

Step-by-step explanation:

Number of degrees of freedom should we​ use for sample size of 15 at 95% confidence interval is 14.

Given:

Suppose we are making a​ 95% confidence interval for the population mean from a sample of size 15.

Degrees of freedom:

Degrees of freedom indicate the number of independent pieces of information used to calculate a statistic; in other words - they are the number of values that are able to be changed in a data set.

we know that,

Degrees of freedom df = n - 1.

where n = sample size

df = sample size - 1

= n - 1

= 15 - 1

= 14

Therefore number of degrees of freedom should we​ use for sample size of 15 at 95% confidence interval is 14.

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There is a probability of 66.5 % chance of it landing on a 5 at least once in 6 dice.

Because there are six faces on a die, you have an even chance of the dice landing on one of these faces each time you roll:

This means that each time that you roll, there is a 5/6 chance that you will not roll a 5.

The probability of not rolling a 6 twice is 5/6 or 69.4%.

Roll the die six times, and the probability of not rolling a 5 is

(5/6) * (5/6) * (5/6) * (5/6) * (5/6) * (5/6) * (5/6)

= (5/6)⁶

= 33.5%

Therefore, the probability of rolling a 5 at least once in 6 dice

= 100%  - 33.5%

= 66.5%

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The cost for  [tex]1\frac{3}{4}[/tex] pounds of milk chocolate is $ 6.16 more than the cost for  [tex]1\frac{3}{4}[/tex] pounds of caramels.

Two or more expressions with an Equal sign is called as Equation.

The cost of each pounds of Caramels = $ 9.28,

So, the cost of [tex]1\frac{3}{4}[/tex]  pounds of caramels =  [tex]1\frac{3}{4}[/tex]×9.28

=7/4×9.28=$16.24

The cost of each pounds of milk chocolate = $ 12.80

So, the cost of [tex]1\frac{3}{4}[/tex]  pounds of milk chocolate = [tex]1\frac{3}{4}[/tex]  ×12.8

=$22.24

∵ 22.4 > 16.24,

the cost of  [tex]1\frac{3}{4}[/tex] pounds of milk chocolate  > The cost of   [tex]1\frac{3}{4}[/tex]pounds of caramels

22.4-16.24=6.16

Hence, the cost for  [tex]1\frac{3}{4}[/tex] pounds of milk chocolate is $ 6.16 more than the cost for  [tex]1\frac{3}{4}[/tex] pounds of caramels.

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There exists infinitely many solutions for the given equation 12x + 1 = 3(4x + 1) – 2  

Here, we are given an equation as follows-

12x + 1 = 3( 4x + 1 ) – 2

Let us solve the equation to get the value of the variable x.

12x + 1 = 12x + 3 – 2

12x + 1 = 12x + 1

Thus, here, we see that the Left hand side is exactly equal to the right hand side. This means that the given equation has infinitely many solutions.

Therefore, there exists infinitely many solutions for the given equation 12x + 1 = 3(4x + 1) – 2  

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Answer:

C

Step-by-step explanation:

The problem states:

"The second anthill has one and one-third the amount of ants of the first hill."

Answer: C

Properties used in the given equation is Commutative property, Associative property, Additive inverse, Identity property.

In a commutative property multiplication and addition which posses commutative property takes place without considering the order of arrangement of data.

12.2 + 18.6 + -4.3 + (-18.6)

12.2 + -4.3 _ 18.6 + (-18.6)

The second step results into the presence of a commutative property.

12.2 + -4.3 + [18.6 + (-18.6)] is an associative property because here, regrouping of numbers which gives the same result.

[18.6 + (-18.6)] is an additive inverse since the result is zero. Additive inverse occurs when the addition of a number to another number results into zero.

12.2 + -4.3 + (0) is an identity property.

This property occurs when the addition of any number with zero eventually resulted into that number.

So here we used 4 properties which are

Commutative property,

Associative property,

Additive inverse,

Identity property.

Given question is written in wrong language.

Here is the given question 12.2 + 18.6 + -4.3 + (-18.6)12.2 + -4.3 + 18.6 + (-18.6)12.2 + -4.3 + [18.6 + (-18.6)]12.2 + (-4.3) + (0)12.2 + -4.3 7.9

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No they are not the same . AAS stands for Angle Side Angle and SAA stands for Side Angle Angle .

After 35 minutes there will be 40 bacteria remaining.

The process of a constant percentage rate decrease in an amount over time is referred to as "exponential decay." The formula to calculate exponential decay is given as, [tex]N_t=N_0\left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}}[/tex]. Here, Nt is the quantity after time t, N0 is the initial quantity, t1/2 is the half-life, and t is time.

For the first situation, Nt=360, N0=900, t=10 minutes. Therefore, substituting the given values get the value of t1/2. So,

[tex]\begin{aligned}360&=900\left(\frac{1}{2}\right)^{\frac{10}{t_{1/2}}} \\\frac{360}{900}&=\left(\frac{1}{2}\right)^{\frac{10}{t_{1/2}}}\\0.4&=\left(\frac{1}{2}\right)^{\frac{10}{t_{1/2}}}\\ \ln(0.4)&=\frac{10}{t_{1/2}}\ln(0.5)\\t_{1/2}&=10\times\frac{\ln(0.5)}{\ln(0.4)}\\&=7.6\end{aligned}[/tex]

Now, for the second situation,  Nt=40.  We have to find the time at which there will be 40 bacteria remaining. Then,

[tex]\begin{aligned}40&=900\left(\frac{1}{2}\right)^{t/7.6}\\0.04&=\left(\frac{1}{2}\right)^{t/7.6}\\\ln(0.04)&=\frac{t}{7.6}\ln(0.5)\\t&=7.6\times\frac{\ln(0.04)}{\ln(0.5)}\\&=7.6\times4.64\\&=35.26\\&\approx35\end{aligned}[/tex]

The answer is 35 minutes.

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The radical expression as an expression with a rational exponent is A- seven to the five fourths power.

An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.

Given, the fourth root of 7 to the fifth power, we have to write the radical as a rational exponent.

The formula to change a radical to a rational exponent is given by:

= a ^(m/n)

Now, cube root of the seventh power can be written as:

4✓7^5

Therefore, the rational exponent is A.

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The critical value used is (10 – 2.5, 10 + 2.5) when, the mean is 10 and confidence level is 89%.

The confidence interval for a population with a known standard deviation is based on the fact that the sample means follow an approximately normal distribution. Suppose

mean = 10

as, we have 89% confidence interval (5, 15)

where EBM = 5.

To get 89% confidence interval,

mean = 10 of the normal distribution.

Then, the critical value we use is

(10 – 2.5, 10 + 2.5).

So, the critical value used is (10 – 2.5, 10 + 2.5) when, the mean is 10 and confidence level is 89%.

Hence, the critical value used is (10 – 2.5, 10 + 2.5) when, the mean is 10 and confidence level is 89%.

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Answer: D. y = 2 x + 1

Step-by-step explanation:

The angle of inclination of the ramp is approx. 4°.

Define the angle of inclination.

The angle formed between a line and the x-axis's positive direction is known as the inclination angle. This angle has a value between 0° and 180°. From the positive direction of the x-axis, it is measured counterclockwise.

Added definitions include The positive angle, measured counterclockwise from the x-axis to the line, with a value less than 180 degrees, which is the inclination of a non-horizontal line.

Solution Explained:
Given in question,

length (l) = 6.10m and height(h) = 0.45m

So the angle of inclination can be found using,

sin θ = h/l

sin θ = 0.45/6.10

θ = sin^-1(0.45/6.10)

θ ≈ 4°

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Interpreting the graph, it is found that the function has two real solutions

The number of different real solutions that a function has is given by the number of times it crosses the x-axis(also known as the horizontal axis) on the graph. If the graphs of the equations intersect, then there is one solution that is true for both equations.

In this problem, the function crosses the x-axis, at 0 and -4

Using the above we find that the given graph has solution at the x intercepts.

X intercepts are 0 and -4

Hence the solutions are two real and they are x=0 and x =-4

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In the given function f(x) = 3ˣ, a function table is created from -2 to 2 which is represented on a graph.

A function table is a visual table with columns and rows that displays the function with regards to the input and output. Younger students will also know function tables as function machines. Every function has a rule that applies and represents the relationships between the input and output.

In the function given;

f(x) = 3ˣ

The values of y from x = -2 to 2 are

f(-2) = 1/9

f(-1) = 1/3

f(0) = 1

f(1) = 3

f(2) = 9

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Answer: 110°

Step-by-step explanation: We know that a quadrilateral is always 360° in total, and two of the angles are right angles, which both equal 90°. We also know that one of the angles is 70° so, with this information, we can set up an equation. 90+90+70+x=360 To solve this, add 90, 90, and 70 together. This equals 250. Now we subtract 360 and 250, which equals 110°.

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According to the histogram, the percentage of the tournament participants are under the age of 20 is 50%.

A histogram approximately represents a distribution of grouped data with numerical values.

It uses rectangular bars to show the frequency of data items in successive numerical intervals of equal sizes.

Age Group (year)  Number of People

0 to 19                            30

20 to 39                         20

40 to 59                         10

60 to 79                         0

Total                             60

Percentage of ages 0-19  =  30/60 x 100 = 50%

Thus, using the histogram, we can assure the percentage of the tournament participants are under the age of 20 is 50%.

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The correct answer is Yes, past age 85 years of age, for every 100 men, there are 200 women.

Given,

In the question:

Your grandmother is 87 years old and she has remarked to you that nearly all of her friends are women. She told you that it is rare to see a man older than age 85. She is correct because, after age 85, for every 100 men, there are __________.

Now, According to the question:

Your grandmother is 87 years old and she told you that all of her friends are women. There is no single man in her circle of friends. She also told that it is rare to see a man over the age of 85. It is because of the fact that women are more in number than man above the age of 85 and this ratio is like 100 men per 200 women, which means the chances of getting a male friend is almost half after the age of 85. So women are more in number than men.

Hence, The correct answer is Yes, past age 85 years of age, for every 100 men, there are 200 women.

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Answer:

b₂ = [tex]\frac{2A}{h}[/tex] - b₁

Step-by-step explanation:

A = [tex]\frac{b_{1}+b_{2} }{2}[/tex] × h ( multiply both sides by 2 to clear the fraction )

2A = h(b₁ + b₂ ) ← divide both sides by h

[tex]\frac{2A}{h}[/tex] = b₁ + b₂ ( subtract b₁ from both sides )

[tex]\frac{2A}{h}[/tex] - b₁ = b₂

The solution is, the formula to find the base b₂ is : b₂ = 2A/h - b₁.

Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

here, we have,

given that,

The area of a trapezoid is calculated using the formula below, where A is the area of the trapezoid, b₁ and b₂ are the bases of the trapezoid, and h is the height of the trapezoid.

A = (b1+b2)/2 × h

( multiply both sides by 2 to clear the fraction )

2A = h(b₁ + b₂ )

← divide both sides by h

2A/h = b₁ + b₂

( subtract b₁ from both sides )

2A/h - b₁ = b₂

Hence, The solution is, the formula to find the base b₂ is : b₂ = 2A/h - b₁.

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Answer:

21

Step-by-step explanation:

rate of baskets *total shots = shots made

3/5*35=21

Number expressed in the form a+ bi is complex number.

A number system is defined as a system of writing to express numbers.

The number is expressed in the form a + bi

A complex number is a number of the form a + bi, where a and b are real numbers, and i is an indeterminate satisfying i² = −1.

The number a+bi, in which a is real number and b is imaginary number.

Hence, number expressed in the form a+ bi is complex number.

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The height of the rocket at the end of the 25 seconds is 275 ft.

We have given that,

a rocket rises at 5 ft/s between 0 and 10 seconds,

therefore

V₁ = 5 ft/s

T₁ = 10 seconds

Height in first 10 seconds = ?

we know the formula to find the height,

i.e Height = velocity × time

⇒ H₁ = V₁ × T₁

        = 5 × 10

   H₁ = 50 ft

Therefore height of the rocket in the first 10 seconds is 50 ft.

Now it given that, rocket rises at 25 ft/s for another 15 seconds.

i.e V₂ = 15 ft/s

    T₂ = 15 seconds

    H₂ = ?

H₂ = V₂ × T₂

    = 15 × 15

H₂ = 225 ft

Therefore height of the rocket in next 15 seconds is 225 ft.

Now we will find the height of the rocket at the end of the 25 seconds.

i.e H = H₁ + H₂

       = 50 + 225

    H = 275 ft

Hence the height of the rocket at the end of 25 seconds is 275 ft.

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The equation of the line that shown in the graph is;

y = x + 3

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

We know that Point-Slope Form:

y - y₁ = m(x - x₁)  

Where x₁ - x coordinate and y₁ - y coordinate

m - slope

Point are (3, 6) and (4,5)

Then Slope m = 1

Now Write the equation as;

y - 6 = 1(x- 3)

y = x - 3 + 6

y = x + 3

Hence, the equation of the line that shown in the graph is;

y = x + 3

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x-intercept and y-intercept of the line y = 4x+5 is -5/4 and 5 respectively.

What is the equation straight line?

The given equation Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.

The equation of the line is y = 4x+5

So the y-intercept is (x=0)

y = 5

And the x-intercept is (y=0)

4x +5 =0

x = -5/4

Hence, the x-intercept and y-intercept of the line y = 4x+5 is -5/4 and 5 respectively.

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The following are the two lines: y = 4x - 1. y = -1.25x + 10.5.

Their point of intersection is: (2.19, 7.76).

The two vertices through which the line y = 4x - 1 pass are as follows:

(2.19, 7.76) and (3,11).

The slope is:

m = (7 - 3)/(2 - 1) = 4.

Hence:

y = 4x + b.

When x = 1, y = 3, the intercept b is calculated as follows:

3 = 4 + b

b = -1.

The first line is then: y = 4x - 1.

The points for the second line are (2,7) and (6,2).

As a result, the slope is m = (2 - 7)/(6 - 2) = -5/4 = -1.25.

The solution is y = -1.25x + b.

When x = 2, y = 7, therefore the intercept b is as follows:

7 = -1.25(2) + b

b = 10.5.

As a result, the second line is:

y = -1.25x + 10.5.

The intersection's x-coordinate is as follows:

4x - 1 = -1.25x + 10.5

5.25x = 11.5

x = 11.5/5.25

x = 2.19.

The intersection's y-coordinate is:

y = -1.25(2.19) + 10.5 = 7.76.

Another position where the line y = 4x - 1 intersects is:

y = 4(3) - 1 = 11.

As a result, point (3,11).

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The probability the class average is less than 79 is 0.1587.

What is Normal Distribution ?

Given that,

Normally distributed with a mean μ = 80

sample standard deviation σ = 6

In a class, number of students n = 30   (This may be 36 in ques but we take 30 as mentioned in question )

Let, x = be the individual score

∑x = be the class average

It's given, class average is less than 79.

Now, the probability that the class average is less than 79.

P(∑x < 79) = P( (∑x - μ) / (σ/√n)  < (79 - 80) / (6 /√30) )

                = P( (∑x - μ) / (σ/√n)  < (-1) / 1.09 )

                = P( (∑x - μ) / (σ/√n)  < -1 )     [Round off the Denominator it gives 1]

we know, Standard normal distribution Z = (∑x - μ) / (σ/√n)

so,

P(∑x < 79) = P( Z < -1 )

By Standard normal distribution table,

P( Z < -1 ) = 0.1587

Hence, the probability the class average is less than 79 is 0.1587.

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