11. A local grocery store has 7 different kinds of hot sauce that you would love try.
However, you only have enough money to purchase 5 of the different flavors. How
many of the flavors of hot sauce are possible for you to purchase?

The area of the shaded region is [ (36 * √3)/4 - 3 * (9 * √3)/4 ] square units = (36 * √3)/4 - 27 * √3/4 square units = 9 * √3/4 square units.

The area of a triangle can be found using the following formula:

Area = (base * height) / 2

The area of the shaded region can be found by subtracting the sum of the areas of three small equilateral triangles from the area of the original equilateral triangle.

Each of the small equilateral triangles has side length 3, since it is half the length of the original triangle's sides. The area of each small triangle is (3^2 * √3)/4 = (9 * √3)/4 square units.

The area of the original equilateral triangle is (6^2 * √3)/4 = (36 * √3)/4 square units.

Hence, the area of the shaded region is [ (36 * √3)/4 - 3 * (9 * √3)/4 ] square units = (36 * √3)/4 - 27 * √3/4 square units = 9 * √3/4 square units.

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The expressions are matched as;

1. Subtract m

2. subtract 2m

3. Add 1

4. subtract 1

5. subtract 2

6. add 2

Algebraic expressions are described as mathematical expressions that are composed of coefficients, factors, constants, variables and terms.

These expressions are also composed of arithmetic operations. These operations are;

From the information given, we have that;

2m = 1 + m

collect like terms

2m - m= 1

m = 1

2. 2m -1 = 3m

2m -3m = 1

-m = 1

m = -1

3. m - 1 = 2

m = 2 + 1

m = 3

4. 3 = 1 + m

collect like terms

m = 3 - 1 = 2

5. 2 + m = 3

m = 3 - 2

subtract 2

m = 1

6. -2 + m = 1

collect like terms

m = 1+ 2 = 3

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Answer:

Option 3

Step-by-step explanation:

Each value of x maps onto one value of y and vice versa.

The value of algebraic multiplicity will be 1 and geometric multiplicity will be 1

\($$\begin{aligned}& A=\left[\begin{array}{ccc}3 & -2 & 0 \\-2 & 4 & 4 \\1 & 0 & 2\end{array}\right] \\& \Rightarrow A=\left[\begin{array}{ccc}-1 & 1 & 0 \\0 & 0 & 0 \\1 & 1 & -2\end{array}\right]\end{aligned}$$\)

\($$Det(A-\lambda I) = Det A=\left[\begin{array}{ccc}(-1-\lambda) & 1 & 0 \\0 & -\lambda & 0 \\1 & 1 & (-2-\lambda)\end{array}\right]$$\)

\($$-(1+\lambda)\left|\begin{array}{cc}-\lambda & 0 \\1 & -2-\lambda\end{array}\right|-1\left|\begin{array}{cc}0 & 0 \\1 & -2-\lambda\end{array}\right|$$\)

\($$\begin{aligned}& =-(1+\lambda)\left(\lambda^2+2 \lambda\right) . \\& =-\lambda(1+\lambda)(\lambda+2) .\end{aligned}$$\)

So, for \(\lambda=-1\), eigen values are \(\lambda\)=0,-1,-2.

Hence, the value of algebraic multiplicity=1

\(AV=\lambda v \\& \Rightarrow A V=-V\\ \Rightarrow-V_1+V_2=-V_1\\ \Rightarrow V_2=0 \\& v_1+v_2-2 v_3=-v_3\\ \Rightarrow v_1+v_2-v_3=0\\ \Rightarrow v_1=v_3 \\\)

\($$\begin{aligned}& \Rightarrow \quad\left[\begin{array}{l}v_1 \\0 \\v_1\end{array}\right] \\& =v_1\left[\begin{array}{l}1 \\0 \\1\end{array}\right]\end{aligned}$$\)

So, the value of eigen vectors are: \(& =\left[\begin{array}{l}1 \\ 0 \\ 1\end{array}\right] \\\)

And the value of geometric multiplicity =1

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Answer:

Step-by-step explanation:

Since angles R and S are supplementary angles it means that the sum of their angles add up to 180°

To find R we must first find x

To find x , add angles R and S and equate them to 180

That's

R + S = 180

80 - x + 3x - 30 = 180

2x + 50 = 180

2x = 180 - 50

2x = 130

Divide both sides by 2

x = 65°

From the question

R = 80 - x

But x = 65°

Substitute the value of x into the expression

That's

R = 80 - 65

We have the final answer as

Hope this helps you

Answer:

152

Step-by-step explanation:

a = 3; b = -8

2b² − 4a + 4a² =

= 2(-8)² - 4(3) + 4(3)²

= 2(64) - 12 + 4(9)

= 128 - 12 + 36

= 116 + 36

= 152

Answer:

The exact value of the other leg is 10.

Step-by-step explanation:

Finding the exact value of x given a 45 degree angle and a side length of 10 can be done using trigonometry. In a 45-45-90 right triangle, the two legs are congruent and the hypotenuse is equal to the square root of 2 times the length of the legs.

Therefore, if one leg is 10, the hypotenuse is 10 times the square root of 2. To find the length of the other leg, we can use the Pythagorean theorem:

c^2 = a^2 + b^2, where c is the hypotenuse, a and b are the legs of the right triangle.

Substituting known values, we get:

(10√2)^2 = 10^2 + b^2

200 = 100 + b^2

b^2 = 100

b = 10

Therefore, the exact value of the other leg is 10.

Answer:

Step-by-step explanation:

r² means the length of the radius is multiplied by itself.

It is also a clue that area is expressed in square units.

Answer:

D-16

Step-by-step explanation:

Answer:

D. 16

Step-by-step explanation:

On one shelf, she can put 4 baskets.

So, on 4 shelves, she can put (4 x 4) 16 baskets.

Hope this helps :)

Answer:

6 =h

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh

12 = 1/2 (4) h

12 =2h

Divide each side by 2

12/2 = 2h/2

6 =h

The 95% confidence intervals are between 71.05 and 73.37.

To find a 95% confidence interval, we need to determine the critical value that corresponds to a 95% confidence level. This critical value is the z-score that separates the top 2.5% of the normal distribution from the rest of the distribution. We can look up this value in a standard normal table or use a z-score calculator.

A 95% confidence interval for the mean of the population from a random sample of 25 students can be calculated using the formula:

mean ± (standard error * critical value)

where standard error = standard deviation / square root of sample size

critical value = z-score corresponding to 95% confidence level

So,

standard error = 2.5 / √(25) = 0.6324555320336759

Using a z-table, the z-score corresponding to 95% confidence level is 1.96.

So, the 95% confidence interval is:

72.21 ± (0.6324555320336759 * 1.96) = (71.05, 73.37)

Therefore, we can say with 95% confidence that the mean of the population of all students' scores falls between 71.05 and 73.37.

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The amount of water tank  with water after 10 minutes will be 4950 liters.

To solve this problem, we need to keep track of the net flow of water into the tank over the course of 10 minutes. The tap filling water adds water to the tank, while the tap emptying water removes water from the tank.

Let's calculate the net flow rate of water per minute:

Flow rate = (filling tap flow rate) - (emptying tap flow rate)

Flow rate = 40 L/min - 25 L/min

Flow rate = 15 L/min

Now, we can calculate the net flow of water over 10 minutes:

Net flow of water = (flow rate) * (time)

Net flow of water = 15 L/min * 10 min

Net flow of water = 150 L

Therefore, over the course of 10 minutes, the net flow of water into the tank is 150 liters.

Initially, the tank had 4800 liters of water. Adding the net flow of water, we can determine the final amount of water in the tank:

Final amount of water = (initial amount of water) + (net flow of water)

Final amount of water = 4800 L + 150 L

Final amount of water = 4950 L

After 10 minutes, there will be 4950 liters of water in the tank.

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Answer:

-1.33333 < x

Step-by-step explanation:

subtract 5 from both sides

get -4<3x

divde 3 by both sides

-1.33< x

Hi, there!

 _______

The first step is:

» Subtract both sides by 5

\(\sf{-4 < 3x}\)

Now divide each term by 3:

\(\sf{-\dfrac{4}{3} < x}\)

We can flip it over:

\(\sf{x > -\dfrac{4}{3}}\)

Hope the answer - and explanation - made sense,

happy studying!!

If a 4-yard dumpster cost $95.00 monthly, the total cost for the year is $1,140.

The total cost for the year of the dumpster is the product of the multiplication of the monthly cost and 12.

Multiplication is one of the four basic mathematical operations, including addition, subtraction, and division.

In any multiplication, there must be the multiplicand (the number being multiplied), the multiplier (the number multiplying the multiplicand), and the product (or the result).

The monthly cost of the 4-yard dumpster = $95.00

1 year = 12 months

The total annual cost = $1,140 ($95 x 12)

Thus, using the multiplication operation, we can find that none of the options is correct as the total annual cost but $1,140.

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Answer:

x=7

Step-by-step explanation:

(3x+7)=4x

Subtract 3x from each side

(3x+7) -3x=4x-3x

7 = x

The distance between the start of the walkway and the middle person is 52 feet.

It is given that a 100 foot long moving walkway moves at a constant rate 6 feet per second.

AI steps into the start of the walkway and stands this means speed of AI is 6 feet per second.

Bob steps onto the start of  he walkway two second later and stolls forward along walkway 4 feet per second that means 10 feet [per seconds.  

And CY reaches the starts of the walkway and walks briskly forward beside the walkway at a rate of 8 feet per second.

At the time s we gave that,

\(\frac{8(s-4)+10(s-2)}{2}\) = 6s

\(\frac{8s -32 + 10s - 20}{2}\)  = 6s

      18s - 52 = 12s

              6s  = 52

                s  = \(\frac{26}{3}\)

At the time AI has travels,  

6* \(\frac{26}{3}\) = 52 feet.

Therefore distance between the start of the walkway and the middle person is 52 feet.

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Based on the information, there would be 89 items left in inventory, the total cost spent on new items would be $2,160, and the expected selling price for the new items is $3,059.

To calculate the total cost of purchases we must multiply the unit value of the items purchased by the number of items purchased and then add the total value of each item.

To calculate the number of items available for sale we must add all the items available and subtract the number of items sold.

To calculate the cost of the items available for sale we must multiply the unit cost by the number of units and then add the costs of each set of items.

To calculate ending inventory we must identify the number of items we have left for sale, the price they earned us, and the price we expect to sell them for.

Note: This question is incomplete. Here is the complete information

Attached image

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Answer:

The equation of this line is y = -4.

Answer:

y=-4

Step-by-step explanation:

zero slope m=0

y-y1=m(x-x1)

y-(-4)=0(x-(-9))

y+4=0

y=-4

The values of x for the tangent segments to the circles are: (25). x = 2 and (26). x = 4

A theorem of tangents to a circle states that if from one exterior point, two tangents are drawn to a circle then they have equal tangent segments.

(25). 2x - 1 = x + 1 {equal tangent segments}

2x - x = 1 + 1 {collect like terms}

x = 2

(26). 2x - 4 = x {equal tangent segments}

2x - x = 4 {collect like terms}

x = 4

Therefore, the values of x for the tangent segments to the circles are: (25). x = 2 and (26). x = 4

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The greater unit rate is 6. Therefore, option C is the correct answer.

The given equation is y=10/3 x+8.

Here, rate of change is 10/3 and the y-intercept is 8

From the graph we have (1, 6) and (2, 12)

Unit rate = (12-6)/(2-1)

= 6

Here, the greater unit rate is 6.

Therefore, option C is the correct answer.

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The correct answer is, by choosing a = -2 and b = 1, we satisfy both inequalities .a < b:

To make both inequalities true, we need to select values for a and b that satisfy the given conditions:

a < b: This inequality means that the value of a should be less than the value of b.

|b| < |a|: This inequality means that the absolute value of b should be less than the absolute value of a.

One possible solution that satisfies both conditions is:

a = -2

b = 1

With these values, we have:

-2 < 1 (a < b)

|-1| < |2| (|b| < |a|)

Therefore, by choosing a = -2 and b = 1, we satisfy both inequalities.a < b:

This inequality states that the value of a should be less than the value of b. In other words, a needs to be positioned to the left of b on the number line. To satisfy this condition, we can choose a to be any number that is less than b. In the example I provided, a = -2 and b = 1, we can see that -2 is indeed less than 1, fulfilling the requirement.

|b| < |a|:

This inequality involves the absolute values of a and b. The absolute value of a number is its distance from zero on the number line, always resulting in a non-negative value. The inequality states that the absolute value of b should be less than the absolute value of a. To satisfy this condition, we can choose b to be any number with a smaller absolute value than a. In the example I provided, |1| is less than |(-2)|, as 1 is closer to zero than -2, fulfilling the requirement.

By selecting a = -2 and b = 1, we satisfy both inequalities: a < b and |b| < |a|. The specific values of -2 and 1 were chosen as an example, but there are multiple other values that would also satisfy the given conditions. The important aspect is that a is indeed less than b, and the absolute value of b is smaller than the absolute value of a.

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Final speed after slowing down by 15 miles per hour and reducing the speed by one third is 25 miles per hour.

Let's break down the steps to determine the final speed:

Step 1: Convert the speed from miles per minute to miles per hour.

Since you're driving one and a half miles per minute, we need to convert it to miles per hour. There are 60 minutes in an hour, so we multiply 1.5 by 60 to get 90 miles per hour.

Step 2: Slow down by 15 miles per hour.

Subtract 15 from the initial speed of 90 miles per hour, resulting in 75 miles per hour.

Step 3: Reduce the speed by one third.

To find one third of 75 miles per hour, we divide it by 3, which gives us 25 miles per hour.

Therefore, the final speed after slowing down by 15 miles per hour and reducing the speed by one third is 25 miles per hour.

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(a) The maximum height of the ball above the ground is 12.5 m and the time of motion is 1.43 s.

(b) The time taken for the ball to contact the other player at 0.5 m above the ground is 3.0 s.

The maximum height reached by the ball is calculated as follows.

At maximum height, the final velocity, v = 0

dh/dt = v = 0

dh/dt = -2(4.9)t + 14

0 = -9.8t + 14

9.8t = 14

t = 1.43 s

H(1.43) = -4.9(1.43)² + 14(1.43) + 2.5

H(1.43) = -10.02 + 20.02 + 2.5

H(1.43) = 12.5 m

12.5 = -4.9t² + 14t + 2.5

4.9t² - 14t + 10 = 0

t = 1.43 s

0.5 = -4.9t² + 14t + 2.5

4.9t² - 14t + - 2 = 0

t = 3.0 seconds

The complete question is below:

In a volleyball match Hanein serves the volleyball at 14 m/s, from a height of 2.5 m above the court. The height of the ball in flight is estimated using the equation, h = -4.9t² + 14t + 2.5, where t is the time in second and h is height above ground, in metres.

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Since you cannot really factor this problem easily, we are going to resort to the quadratic formula!

x= -b+or- sqrt(b^2-4ac)    / 2a

x=-17+ or - sqrt(17^2-4*50)   /2

x=-17+ or - sqrt89 /2

Now we just need estimate sqrt 89 which is about 9.43 and I will not bother to show the step I did to estimate its about 9.43.

So x= -17+ or -9.43 /2

x= -26.43/2 or -7.57/2

x=-13.215 or -3.785

Round to nearest tenth digit.

x= -13.2 or -3.8

Hope this helps any questions just ask in the comments.

Step-by-step explanation:

To differentiate the function f(x) = 1/x^3, we can use the power rule of differentiation. Here's the step-by-step process:

Write the function: f(x) = 1/x^3.

Apply the power rule: For a function of the form f(x) = x^n, the derivative is given by f'(x) = nx^(n-1).

Differentiate the function: In our case, n = -3, so the derivative is:

f'(x) = -3 * x^(-3-1) = -3 * x^(-4) = -3/x^4.

Therefore, the derivative of the function f(x) = 1/x^3 is f'(x) = -3/x^4.

Answer:

Probabilities:

1-5:1/7

6: 2/7

Probability of even number: 4/7

Probability of odd number: 3/7

Step-by-step explanation:

We are told that the probability in each throw is as follows. Probability of getting 1 to 5 is the same and the probability of 6 is twice the probability of getting 1. Let us call c the probability of having a 1. So, the probability of having 2,3,4,5 is also c. In this case, the probability of having 6 is 2*c. Since all of this outcomes are mutually exclusively, then we must have the following

\( c+ c + c+ c +c + 2c = 1= 7c\)(since the probabilities of mutually exclusive events that cover all outcomes of the experiment must add to 1)

This implies that \(c = \frac{1}{7}\). Then, the probability of having a 6 is 2/7 and to have any other number is 1/7.

Each roll is independent of each other, so the probability of having an odd or even number doesn't depend of the other trials.

To calculate the probability of having an even number, we add the probabilties of getting a 2,4,6. In this case, that is 1/7+1/7+2/7 = 4/7. To calculate the probability of an odd number we add the probabilities of 1,3,5 which 1/7+1/7+1/7 = 3/7.

Answer:

Olivia is in the Engineering and Design pathway and Camile is in the Science and Meteorology pathway.

Step-by-step explanation:

Engineering & Design pathway⇒ A methodological series of steps that are used by engineers in creating functional products and processes.

Science & Methodology pathway⇒ Steps used by scientists to create explanations based on the evidence which they have gathered.

Hence, [A] Olivia is in the Engineering and Design pathway and Camile is in the Science and Meteorology pathway is the correct answer.

[RevyBreeze]

Answer:

A - Olivia is in the Engineering and Design pathway and Camile is in the Science and Meteorology pathway.

Step-by-step explanation:

1. false

2. open

3. 5

hope dis helps

The area of the archway is (π + 24) square meters, as the total area of the two rectangular pillars is 24 square meters, area of semicircle is (9π) / 2 square meters.

Radius is a term used in geometry to refer to the distance from the center of a circle or sphere to its edge. It is usually represented by the symbol "r". In a circle, all points on the edge, also called the circumference, are at the same distance from the center. This distance is equal to the radius. The radius is half the length of the diameter, which is the distance across the circle passing through its center.

To determine the area of the archway, we need to calculate the area of the two rectangular pillars and the semicircle top arch, and then add them together.

The area of each rectangular pillar is:

Area of each pillar = length x width

= 4 meters x 3 meters

= 12 square meters

So the total area of the two rectangular pillars is:

Total area of pillars = 2 x 12 square meters

= 24 square meters

Now we need to calculate the area of the semicircle top arch. The radius of the semicircle is half of the distance between the two pillars, which is:

Radius of semicircle = (6 meters / 2) = 3 meters

The area of the semicircle is:

Area of semicircle = (π x r²) / 2

= (π x 3²) / 2

= (9π) / 2 square meters

We also need to subtract the area of the rectangle sections at the top of each pillar from the semicircle to get the area of the archway. Each of these rectangles has a length of 3 meters and a height of the difference between the radius of the semicircle and the height of the pillars, which is:

Height of rectangle = (3 meters - 4 meters) = -1 meter

Since we can't have a negative height, we take the absolute value of this difference:

|Height of rectangle| = 1 meter

The area of each rectangle is:

Area of each rectangle = length x width

= 3 meters x 1 meter

= 3 square meters

So the total area of the two rectangles is:

Total area of rectangles = 2 x 3 square meters

= 6 square meters

Therefore, the area of the archway is:

Area of archway = Area of pillars + Area of semicircle - Area of rectangles

= 24 square meters + (9π) / 2 square meters - 6 square meters

= (π + 24) square meters

Hence, the area of the archway is (π + 24) square meters.

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