Select one answer choice For part A and select one answer choice for part B

Answer:

Step-by-step explanation:

<, > - dotted line

≤, ≥ - solid line

<, ≤ - shaded region below a line or to the left if is a vertical line

>, ≥ - shaded region above a line or to the right if is a vertical line

----------------------------------------------------------

We have x ≥ 4:

solid vertical line x = 4

shaded region to the right

Answer:

C.

Step-by-step explanation:

You are given 3x-4y<16 and we want to see which of the ordered pairs is a solution.

These ordered pairs are assumed to be in the form (x,y).

A. (0,-4) ?

3x-4y<16 with (x=0,y=-4)

3(0)-4(-4)<16

0+16<16

16<16 is not true so (0,-4) is not a solution of the given inequality.

B. (4,-1)?

3x-4y<16 with (x=4,y=-1)

3(4)-4(-1)<16

12+4<16

16<16 is not true so (4,-1) is not a solution of the given inequality.

C. (-3,-3)?

3x-4y<16 with (x=-3,y=-3)

3(-3)-4(-3)<16

-9+12<16

   3<16 is true so (-3,-3) is a solution to the given inequality.

D. (2,-3)?

3x-4y<16 with (x=2,y=-3)

3(2)-4(-3)<16

6+12<16

18<16 is false so (2,-3) is not a solution to the given inequality.

The aquarium, which has a volume of 770 cubic feet, can hold approximately 5,760 gallons of water when taking into consideration the conversion rate of 7.48 gallons per cubic foot.

To calculate the volume of water an aquarium can hold, we need to first calculate the volume of the aquarium itself, which is determined by multiplying the length, width, and height together. In this case, we have an aquarium that measures 11 feet wide, 10 feet long and 7 feet deep, so multiplying these dimensions together gives us a volume of 770 cubic feet.

Next, we need to convert this volume into gallons. We're given the conversion rate of 7.48 gallons per cubic foot of water, so we multiply our previously obtained volume by this rate. This gives us: 770 cubic feet * 7.48 gallons per cubic foot, which equals 5,759.6 gallons.

So, the aquarium can hold approximately 5,760 gallons of water.

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The solutions to the quadratic equation are x = -1/4 and x = -5.

First, we look at the coefficient of x², which is 4 in this case. We need to find two numbers whose product is 4 times 5 (the constant term) and whose sum is the coefficient of x (12 in this case). These numbers are 1 and 20, as 1 * 20 = 20 and 1 + 20 = 21.

Next, we rewrite the middle term (12x) of the quadratic expression as the sum of these two numbers:

4x² + 1x + 20x + 5 = 0.

Now, we group the terms in pairs:

(4x² + 1x) + (20x + 5) = 0.

Next, we factor out the greatest common factor from each group:

x(4x + 1) + 5(4x + 1) = 0.

Notice that we have a common binomial factor, (4x + 1), which we can factor out:

(4x + 1)(x + 5) = 0.

Now, we apply the zero-product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor to zero and solve for x:

   1. 4x + 1 = 0 => 4x = -1 => x = -1/4.

   2. x + 5 = 0 => x = -5.

Answer: x = -1/4, -5.

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3 to the 2nd power plus 3 to the 3rd power does not equal 3 to the 5th power. In actuality, 3^2 + 3^3 = 36, while 3^5 = 243.

No, 3 to the 2nd power plus 3 to the 3rd power does not equal 3 to the 5th power. This is a common misconception when dealing with exponents. To clear this up, let's look at what these expressions actually mean:

3 to the 2nd power (3^2) = 3*3 = 9

3 to the 3rd power (3^3) = 3*3*3 = 27

So, 3^2 + 3^3 = 9 + 27 = 36

However, 3 to the 5th power (3^5) = 3*3*3*3*3 = 243

So, as you can see, 36 does not equal 243.

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Answer:

1/32

15/32

Step-by-step explanation:

For a fair sided coin,

Probability of heads, P(H) = 1/2

Probability of tails P(T)  = 1/2

For a coin tossed 5 times,

P( All heads)

= P(HHHHH),

= P (H) x P(H) x P(H) x P(H) x P(H)

= (1/2) x (1/2) x (1/2) x (1/2) x (1/2)

= 1/32 (Ans)

For part B, it is easier to just list the possible outcomes for

"at most 2 heads" aka "could be 1 head" or "could be 2 heads"

"One Head" Outcomes:

P(HTTTT), P(THTTT) P(TTHTT), P(TTTHT), P(TTTTH)

"2 Heads" Outcomes:

P(HHTTT), P(HTHTT), P(HTTHT), P(HTTTH), P(THHTT), P(THTHT), P(THTTH), P(TTHHT), P(TTHTH), P(TTTHH)

If we count all the possible outcomes, we get 15 possible outcomes representing "at most 2 heads)

we know that each outcome has a probability of 1/32

hence 15 outcomes for "at most 2 heads" have a probability of

(1/32) x 15  = 15/32

Answer:

x = 7.5

Step-by-step explanation:

Given

- 15 = [tex]\frac{x}{-0.5}[/tex]

Multiply both sides by - 0.5

- 0.5 × - 15 = x, hence

x = 7.5

Answer:

7.5.

Step-by-step explanation:

-15 = x / -0.5

Cross multiplying:

x =  -15 * -0.5

= 7.5.

Answer:

see explanation

Step-by-step explanation:

81[tex]a^{6}[/tex] - 100 ← is a difference of squares which factors in general as

a² - b² = (a - b)(a + b)

81[tex]a^{6}[/tex] = (9a³ )² ⇒ a = 9a³ and 100 = 10² ⇒ b = 10

Hence

81[tex]a^{6}[/tex] - 100

= (9a³)² - 10²

= (9a³ - 10)(9a³ + 10)

Answer:

C

Step-by-step explanation:

Unit Test Is a pain I know

Answer:

The correct answer option is C. [tex]y>\frac{2}{3}x+3[/tex].

Step-by-step explanation:

We are given a graph and we are to determine whether which linear  inequality is represented by the graph.

We know that the grey part on the graph represents the the region which is not included in the inequality.

Also, when x = 0, the values of y can only be less than 3.

So we choose two points on the graph and we find the slope.

For example, we take the points [tex](0,3)[/tex] and [tex](3,5)[/tex].

Slope = [tex]\frac{5-3}{3-0} =\frac{2}{3}[/tex]

which makes the equation of the line [tex]y=\frac{2}{3}x+3[/tex] and inequality [tex]y>\frac{2}{3}x+3[/tex].

[tex]\bf \cfrac{1+cot^2(\theta )}{1+csc(\theta )}=\cfrac{1}{sin(\theta )} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1+cot^2(\theta )}{1+csc(\theta )}\implies \cfrac{1+\frac{cos^2(\theta )}{sin^2(\theta )}}{1+\frac{1}{sin(\theta )}}\implies \cfrac{~~\frac{sin^2(\theta )+cos^2(\theta )}{sin^2(\theta )}~~}{\frac{sin(\theta )+1}{sin(\theta )}}\implies \cfrac{~~\frac{1}{sin^2(\theta )}~~}{\frac{sin(\theta )+1}{sin(\theta )}}[/tex]

[tex]\bf \cfrac{1}{\underset{sin(\theta )}{~~\begin{matrix} sin^2(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }}\cdot \cfrac{~~\begin{matrix} sin(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{sin(\theta )+1}\implies \cfrac{1}{sin^2(\theta )+sin(\theta )} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cfrac{1+cot^2(\theta )}{1+csc(\theta )}\ne \cfrac{1}{sin(\theta )}~\hfill[/tex]

Answer: So the sum of all of the measures of the interior angles of a 16-sided polygon is 2520 degrees.

The sum of the interior angles of a 16-sided polygon is 2520 degrees.

The sum of the interior angles of a 16-sided polygon, or hexadecagon, is 2520 degrees, which can be calculated using the formula (n-2) x 180 degrees.

The sum of the interior angles of any polygon can be found using the formula (n-2)  imes 180 degrees, where n is the number of sides of the polygon. A 16-sided polygon is known as a hexadecagon. Using the formula, we have:

Sum of interior angles = (16-2)  imes 180 degrees

Sum of interior angles = 14  imes 180 degrees

Sum of interior angles = 2520 degrees

Therefore, the sum of the interior angles of a 16-sided polygon is 2520 degrees.

Answer:

see explanation

Step-by-step explanation:

Using the exact values of the trigonometric ratios

sin30° = [tex]\frac{1}{2}[/tex], cos30° = [tex]\frac{\sqrt{3} }{2}[/tex]

Then

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{17}{y}[/tex] = [tex]\frac{1}{2}[/tex]

Cross- multiply

y = 2 × 17 = 34

cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{y}[/tex] = [tex]\frac{x}{34}[/tex] and

[tex]\frac{x}{34}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2x = 34[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

x = 17[tex]\sqrt{3}[/tex]

Hence

x = 17[tex]\sqrt{3}[/tex] and y = 34

Step-by-step explanation:

pt C is (-4,-4)

pt D is (2,-4)

length of CD is 6 units

to form a rectangle AB must be parallel to CD, AC must be parallel to BD and AC and BD must be 6 units

Therefore...A =(-4, 2) and B = (2, 2)

Answer:

1. 24

2. 30

3. 20

4. 12

5. 6

Answer:

y = - 3x + 3

Step-by-step explanation:

The equation of a line in slope intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 3, hence

y = - 3x + c ← is the partial equation of the line

To find c substitute (- 1, 6 ) into the partial equation

6 = 3 + c ⇒ c = 6 - 3 = 3

y = - 3x + 3 ← equation of line

Answer: A

Step-by-step explanation:

FLVS Question, the answer is A !!

Answer:

Rosa is closer to the correct depth.  

Step-by-step explanation:

To show that two measurements are nearly equivalent, we must convert one of the measurements to the other unit.

1 m = 3.281 ft

[tex]\text{Depth } = \text{1644 ft} \times \dfrac{\text{1 m}}{\text{3.281 ft}} = \textbf{501.1 m}[/tex]

Neither is correct but Rosa is closer to the correct depth.

Answer:

7.6 inches

Step-by-step explanation:

First of all we have to define range.

Range gives us the difference of two values between which the data is spread.

the formula for range is:

Range = Highest value - lowest value

By observing the diagram, we can see that

The highest value is = 8.5 inches

The lowest value is: 0.9 inches

So,

Range = 8.5 - 0.9

= 7.6 inches

So, the range is 7.6 inches ..

Answer:

11/16

Step-by-step explanation:

You could list all the possible fractions you will get:

Here are the's with 4 as the numerator:

4/4

4/5

4/6

4/7

Here are the one's with 5 as the numerator:

5/4

5/5

5/6

5/7

Here are the one's with 6 as the numerator:

6/4

6/5

6/6

6/7

Here are the one's with 7 as the numerator:

7/4

7/5

7/6

7/7

There are 4(4) different numerator-denominator combinations we can get.

Let's see which of these are bigger than 5/6.

If you think it is easier to look at the decimals of all these you can.

5/6=0.8333333333

----

4/4 =1

4/5 =0.8

4/6  =0.6666666666

4/7  =0.5714 (approximately)

There is only 1 bigger than 5/6 in this section.

5/4 =1.25

5/5  =1

5/6  =0.83333333333

5/7  =0.714 (approximately)

There is 2 bigger than 5/6 in this section.

6/4  =1.5

6/5   =1.2

6/6   =1

6/7   =0.857 (approximately)

There is 4 bigger than 5/6 in this section.

7/4

7/5

7/6

7/7

All of these are 1 or bigger because the numerator is bigger than or equal to the denominator so all 4 of these are bigger than 5/6 in this section.

P(fraction being greater than 5/6)=[\tex]\frac{\text{ the numbers I listed bigger than } \frac{5}{6}}{\text{ all the fractions I listed }}[/tex]

P(fraction being greater than 5/6)=[\tex]\frac{4+4+2+1}{4(4)}=\frac{11}{16}{/tex]

11/16

Answer:

1/6 or 11/16

Step-by-step explanation:

If you spin a spinner with the first spin giving the numerator and the second spin giving the denominator of a fraction, the probability of the fraction will be greater is 1/6 or 11/16.

6 - 5/6 = 1/6

However, there are 4 possible spots you could land on so, it would change to 11/16.

Answer:

The correct option is A

Step-by-step explanation:

(x^2+x+9)+(7x^2+5)​

Open the parenthesis:

=x²+x+9+7x²+5

Now add the like terms:

=8x²+x+14

Therefore the correct option is A...

Answer:

A

Step-by-step explanation:

Answer:

D. Linear decay.

Step-by-step explanation:

The data decays and lowers.

Answer with explanation:

If you will look at the graph of function, it is not a straight line.

Horizontal Asymptote is, y=0.

There is no vertical Asymptote.

Either it can be growth function or decay function.

But , if you will look at the graph of growth function, it begins from negative infinity and then starts increasing.

In this case graph is decreasing function.

So, The function represents

Option C:→ Exponential Decay

Answer:

x = 4.2, LJ = 14.2

Step-by-step explanation:

When 2 chords of a circle intersect, then the product of the measures of the parts of one chord is equal to the product of the measures of the parts of the other chord, that is

10x = 6 × 7 = 42 ( divide both sides by 10 )

x = 4.2

Hence LJ = 10 + x = 10 + 4.2 = 14.2

Elisa's distance from home (in miles) equals her walking speed (2 mph) multiplied by time spent walking (t hours).

To model Elisa's distance from home based on the time spent walking, we can use the formula for distance, which is:

[tex]\[ \text{Distance} = \text{Rate} \times \text{Time} \]\\[/tex]

Given that Elisa walks at a steady pace of 2 miles per hour, her rate (or speed) is 2 miles per hour. Let's denote this rate as [tex]\( r = 2 \)[/tex] mph.

The time Elisa spends walking can vary, so let's denote it as [tex]\( t \)[/tex] (in hours).

Now, to find Elisa's distance from home, we'll substitute the values into the formula:

[tex]\[ \text{Distance} = r \times t \]\[ \text{Distance} = 2 \times t \][/tex]

Since Elisa's distance from home is what we're interested in, this equation models her distance from home based on the time spent walking. It shows that her distance from home increases linearly with time as she walks at a steady pace.

Multiply the bracket by 5

I used PEMDAS

P= parenthesis

E= exponents

M=multiplication

D= division

A= addition

S= subtraction

7r+2= 5(r-4)

7r+2= 5r-20

Move 5r to the left hand side . Positive 5r changes to negative 5r

7r-5r+2= 5r-5r-20

2r+2=- 20

2r+2-2= -20-2

Move positive 2 to the right hand side. Changes to negative -2

2r+2-2= -20-2

2r= -22

Divide by 2 for 2r and -22

2r/2= -22/2

r= -11

Answer is r= -11

Answer:

r = (-11)

Step-by-step explanation:

7r + 2 = 5(r – 4) ​

7r + 2 = 5r – 4 * 5

7r + 2 = 5r – 20

7r - 5r = -20 - 2

     2r = -22

       r = -22/2 = (-11)

Answer:

6x + 8y

Step-by-step explanation:

Distribute 2:

Note: This means to multiply 2 with the numbers inside the parentheses.

2 * 3x = 6x

2 * 4y = 8y

Our answer would be 6x +8y

Answer:

I think A and C are because they all go back to the original equation.

Step-by-step explanation:

Hope my answer has helped you and if not i'm sorry.

Answer:

f(x)=x^3-3x^2+25x-75

Step-by-step explanation:

Solve for x:

x^3 - 3 x^2 + 25 x - 75 = 0

The left hand side factors into a product with two terms:

(x - 3) (x^2 + 25) = 0

Split into two equations:

x - 3 = 0 or x^2 + 25 = 0

Add 3 to both sides:

x = 3 or x^2 + 25 = 0

Subtract 25 from both sides:

x = 3 or x^2 = -25

Take the square root of both sides:

Answer:  x = 3 or x = 5 i or x = -5 i

Answer:

[tex]\large\boxed{y=\dfrac{15}{14}x+1.5}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

------------------------------------------------------------------------

You must solve the system of equations:

[tex]\left\{\begin{array}{ccc}4x-3y+4=0&(1)\\x+2y=5&(2)\\y=mx+1.5&(3)\end{array}\right\qquad\text{substitute (3) to (1) and (2)}\\\\\left\{\begin{array}{ccc}4x-3(mx+1.5)+4=0\\x+2(mx+1.5)=5\end{array}\right\qquad\text{use the distributive property}\\\left\{\begin{array}{ccc}4x-3mx-4.5+4=0\\x+2mx+3=5&\text{subtract 3 from both sides}\end{array}\right\\\left\{\begin{array}{ccc}4x-3mx-0.5=0&\text{add 0.5 to both sides}\\x+2mx=2\end{array}\right\\\left\{\begin{array}{ccc}4x-3mx=0.5&\text{multiply both sides by 2}\\x+2mx=2&\text{multiply both sides by 3}\end{array}\righ[/tex]

[tex]\underline{+\left\{\begin{array}{ccc}8x-6mx=1\\3x+6mx=6\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad11x=7\qquad\text{divide both sides by 11}\\.\qquad x=\dfrac{7}{11}\\\\\text{Put the value of}\ x\ \text{to the second equation:}\\\\\dfrac{7}{11}+2m\left(\dfrac{7}{11}\right)=2\qquad\text{multiply both sides by 11}\\\\7+2m(7)=22\qquad\text{subtract 7 from both sides}\\\\14m=15\qquad\text{divide both sides by 14}\\\\m=\dfrac{15}{14}[/tex]

Answer:

2.25

Step-by-step explanation:

Answer:

x = 2.25

Step-by-step explanation

using process of elimination the only viable answer is 2.25

Answer:

Option A (Causation cannot be proven because lower test scores can occur for other reasons, such as not studying or poor attendance).

Step-by-step explanation:

Correlation is a concept which explains a linear relationship between two variables. The correlation constant lies between -1 and 1. 0 lies in the center of the interval. A negative correlation means an inverse relationship, and a positive correlation means a direct relationship. 0 technically means no linear relation between the variables. Further the correlation constant lies from 0, more the strength of the relationship. It is important to note that correlation shows a relationship between the two variables but it cannot determine the causation i.e. it cannot be concluded that one variable caused the other variable to occur. Even though having a strong correlation does not mean causal relationship. Therefore, correlation does not prove causation. This is because there are several other lurking and unobserved variables which affect the observed variables. The former class of variables are not accounted for in the correlation. Therefore, the exact magnitude of the causal relationship cannot be determined. Therefore, Option A is the correct choice!!!

Answer:

OPTION A: Causation cannot be proven because lower test scores can occur for other reasons, such as not studying or poor attendance.

Step-by-step explanation: I got it right on the test.

Answer:

6 Hours

Step-by-step explanation:

360 is half of 720, so it would take half the time to travel. half of 12 is 6

At a constant speed of 60 miles per hour, it would take 6 hours to travel 360 miles, which is a reasonable answer since the time required is halved when the distance is halved.

The question involves calculating the time it would take to travel a certain distance given a constant speed which is a basic concept in mathematics, more specifically in the topic of rates and ratios.

If you travel 720 miles in 12 hours, you are traveling at a speed of 720 miles / 12 hours = 60 miles per hour. Now, to find out how long it would take to travel 360 miles at this constant speed, you divide the distance by the speed to get the time: 360 miles / 60 miles per hour = 6 hours. So, it would take 6 hours to travel 360 miles if you maintain the same speed.

When you check if the answer is reasonable, consider if the distance is halved, the time should also be halved if the speed remains constant. Since 360 miles is half of 720 miles, and 6 hours is half of 12 hours, the answer is indeed reasonable.