using the data on this scatter plot ​

Answer:

Therefore, the fully factorised form is 5a(1 + 3b).

Step-by-step explanation:

5a + 15ab as 5a(1 + 3b) by taking out the common factor of 5a from both terms.

The number of pounds of cookie dough needed is 1,440. Therefore, option B is the correct answer.

Given that,

Last year, they sold 1,080 pounds of cookie dough to 360 people.

This means that they sold an average of 3 pounds of cookie dough per person.

Number of pounds of cookie dough = 3 pounds/person × Number of people

Here, 3×460=1,380

3×500=1500

To get a more accurate estimate, we can take the average of these two numbers, which is 1,440 pounds of cookie dough.

Therefore, option B is the correct answer.

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The solution of the equation x - √x + 4 - 2√(x+3) =0 is given by x ≈ 0.449 or x = 2.

The expression is equal to,

x - √x + 4 - 2√(x+3) =0

By rearranging the terms and simplifying the expression as follows,

x - √x + 4 - 2√(x+3) = 0

⇒x + 4 = √x + 2√(x+3)

Square both sides to eliminate the square root,

⇒ (x + 4)² = (√x + 2√(x+3))²

⇒ x² + 8x + 16 = x + 4(x+3) + 4√x√x+3

⇒x² + 8x + 16 -x -4x -12 = 4√x√x+3

⇒ x² + 3x + 4 = 4√x√x+3

⇒x² + 3x + 4 = 4√x√(x+3)

⇒ x² + 3x + 4 = 4√(x²+3x)

Squaring both sides again gives,

⇒ (x² + 3x + 4)² = 16(x²+3x)

Expanding the left side gives,

x⁴ + 6x³ + 17x² + 24x + 16 = 16x² + 48x

Simplifying and rearranging the terms,

x⁴ + 6x³ + x² - 24x + 16 = 0

Factor this equation as follows,

(x² + 4x - 2)(x² + 2x - 8) = 0

The solutions are,

x²+ 4x - 2 = 0 or x² + 2x - 8 = 0

Solve each quadratic equation using the quadratic formula,

For x² + 4x - 2 = 0

x = (-4 ± √(4² - 4(1)(-2))) / (2(1))

⇒ x = (-4 ± √24) / 2

Simplifying the expression under the square root gives,

⇒ x = (-4 ± 2√6) / 2

⇒ x = -2 ± √6

For x² + 2x - 8 = 0

x = (-2 ± √(2² - 4(1)(-8))) / (2(1))

⇒x = (-2 ± √36) / 2

Simplifying the expression under the square root gives,

⇒ x = (-2 ± 6) / 2

⇒ x = -4 or x = 2

Discard the negative solution -2-√6 and -4

As it would lead to a negative value under the square root.

The final solutions are,

x ≈ 0.449 or x = 2

Therefore, the solution of the given equation is equal to x ≈ 0.449 or x = 2.

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The above question is incomplete , the complete question is:

Solve for x.

x - √x + 4 - 2√(x+3) =0

The time it will take the bird to travel 1.4 m is 0.5738 seconds.

In Science and Mathematics, velocity can be defined as the distance covered by an object per unit of time in a specific direction. This ultimately implies that, velocity is a vector quantity because it has both magnitude and direction.

In Mathematics and Science, the velocity of any a physical object can be calculated by using this formula;

Velocity = distance/time

244 cm/s to m = 244/100 = 2.44 cm/s

By making time the subject of formula, we have:

Time = distance/velocity

Time = 1.4/2.44

Time = 0.5738 seconds.

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Answer: correct answer is A 2/3x^2

Step-by-step explanation:Multiply each side of the equation by 2cos2θ to get 2rcos2θ=3sinθ.

Multiply each side of the equation by r to get 2r2cos2θ=3rsinθ. Using the relationships x=rcosθ and y=rsinθ, the equation becomes 2x2=3y.

Divide each side of the equation by 3 and reverse the order of the equation to find that y=2/3x^2

The measure of angle 1 is 107° suing the concepts of corresponding angles and linear pair of angles..

Given a line t which is a transversal line that cuts the two parallel lines m and n.

Here the angle which is linear pair to angle 1 and the angle 73° are corresponding angles.

By the corresponding angle theorem, the corresponding angles formed by two parallel lines cut by a transversal are equal.

So,

Measure of angle which is linear pair to 1 = 73°

Now linear pair of angles are supplementary.

∠1 + 73° = 180°

∠1 = 180° - 73°

∠1 = 107°

Hence the measure of angle 1 is 107°.

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The rate of change for the cab ride is A = $3 per mile

Given data ,

Change in cost = $55 - $40 = $15

Change in distance = 15 miles - 10 miles = 5 miles

Now, we can divide the change in cost by the change in distance to get the rate of change or cost per mile:

Rate of change or cost per mile = Change in cost / Change in distance

A = $15 / 5 miles

A = $3 per mile

Hence , the rate of change or cost per mile for the cab ride is $3 per mile

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Answer:

The correct solutions to the equation 2x^2 = -10x + 12 are x = -2 and x = 3.

Step-by-step explanation:

The required rate of simple interest is 1.75%.

Here, we have,

(Principal + Interest) is a straightforward interest equation.

A = P(1 + rt)

Where: A is the sum of the accrued principal and interest.

Principal Amount is P.

I is the interest rate.

r is the annual percentage rate of interest, or R/100.

R is the annual percentage rate of interest; R = r * 100 t is the length of time involved in months or years.

Since I = Prt,

the initial formula A = P(1 + rt) evolved from A = P + I to A = P + Prt,

which may be represented as A = P(1 + rt).

Given: Principal is $1,300

Rate is 7% and the amount earned that is A-P is $159.25.

A = P(1 + rt)

Therefore substituting the values in the above mentioned equation, we get:

159.25= 1300(1+r×7)

On solving we get,

r= 1.75%

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complete question:

At the Blue Bank, Barry would earn $159.25 in simple interest in 7 years after depositing $1,300.

What rate of simple interest is offered at the

Blue Bank?

The area of the green region of the circle is 96.4 ft².

Area is the region bounded by a plane shape.

To calculate the area of the green region of the circle, we use the formula below

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

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The area of the green region in the circle given is expressed as approximately: a. 96.5 square feet.

The sector of a circle is calculated as:

A = ∅/360 * πr², where r is the radius and ∅ is the reference or central angle of the sector.

Given the following:

Central or reference angle (∅) = 180 - 27 = 153 degrees

Radius (r) = 17/2 = 8.5 feet

Plug in the values:

Area of the green region = 153/360 * π * 8.5²

Area of the green region ≈ 96.5 square feet.

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The trio of sides that will make a right triangle are the ones in the first option:

5, 12, and 13.

Remember that for any right triangle, the sum of the squares of the two shorter sides must be equal to the square of the longest side.

So for example, for the first option we would have:

5^2 + 12^2 = 13^2

25 + 144 = 169

169 = 169

The equation is true, thus, these sides make a right triangle.

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The biker needs to travel 45 km more to complete his journey.

Given that, a biker traveled 2/5 of the road on the first day, then traveled 5 kilometers less on the next day, which is equal to 3/8 of the road, we need to find how much he need to cover more,

Let the total distance of the road be x,
So,

2x/5 - 5 = 3x/8

2x/5 - 3x/8 = 5

Solving for x,

Multiply by 40 to both sides,

16x-15x = 200

x = 200

Therefore, the total distance of the road is 200 km.

Since, he travelled =

200 (2/5) = 80 km + 200 (3/8) = 75 km = 155 km

Therefore, he needs to travel 200-155 = 45 km more.

Hence, the biker needs to travel 45 km more to complete his journey.

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To produce 60 liters of a 55% acid solution, we need 18 liters of a 50% acid solution and 42 liters of a 60% acid solution.

Let x be the number of liters of the 50% acid solution needed, and y be the number of liters of the 60% acid solution needed.

We can set up two equations based on the amount of acid and the total volume:

0.50x + 0.60y = 0.55(60)

x + y = 60

Simplifying the first equation:

0.50x + 0.60y = 33

5x + 6y = 330 (multiplying both sides by 10)

We can solve for one variable in terms of the other in the second equation, and substitute into the first equation:

y = 60 - x

5x + 6(60 - x) = 330

Simplifying:

x = 18

So we need 18 liters of the 50% acid solution, and:

y = 60 - x = 42

So we need 42 liters of the 60% acid solution.

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11, - 6, -1, 4, 9, 14, 19, ... are mapped onto 4. ... A;-l = (-ltQn (mod N),. (A5.34) ... 131 2, 14, 34, 38, 42, 78, 90, 178, 778, 974(1000).

Step-by-step explanation:

the nearest .1/2 incp, we say the 'unit 131/2 incl. 1.4 a measUrement is-stated tp- be 546 inch, this UM= the

The relationship between the distance that birds fly in relation to the time they do so, is positive.

There are about 3 outliers but for the most part, the relationship is positive.

The graph which shows the distance that birds fly in relation to the time they do, shows that there is a positive relationship because as the time increases, the distance that the birds have flown also increases.

There are some outliers such as the bird that flew 1 mile in 7 hours but in general, as the time increases, the distance increases as well. There are two clusters of distance as well.

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time tables on the map mannnnn

Step-by-step explanation:

well, the combination of all set elements.

FYI : if some elements appear in both sets, we only use these once for the result set (this is not the case here, but it might be in other questions).

the combination of both sets is then

{b, c, d, e, g, h}

The lengths of the two legs of the right triangle are 58 and 839, in increasing order.

We have,

The formula given is incorrect.

The correct formula for Pythagorean triples with a given integer z is:

(z² - 1², 2z, z² + 1²)

Using this formula, we can find the two legs of the right triangle with hypotenuse 29 as follows:

z² + 1² = 29²

z² + 1 = 29²

z² = 29² - 1

z² = 840

z = √840

z = 28.98

Since z must be an integer, we can try integer values close to 28.98 to find one that works.

Trying z = 29,

a = z² - 1² = 840 - 1 = 839

b = 2z = 58

c = z² + 1² = 840 + 1 = 841

Therefore,

The lengths of the two legs of the right triangle are 58 and 839, in increasing order.

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The pairs of supplementary angles are;

B. <SQT and <SQR

C. <TQP and <RQP

D. <SQR and <RQP

F. <SQT and <TQP

Two or more angles are referred to as supplementary angles if they add up to 180^o. Therefore the sum of angles is equal to the sum of angles on a straight line.

Thus, the pair of supplementary angles in the given diagram are;

B. <SQT and <SQR

C. <TQP and <RQP

D. <SQR and <RQP

F. <SQT and <TQP

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The system of inequalities that represents this real-world scenario is:

x + y ≤ 450  (The total people cannot be greater than 450)

7x + 4y ≤ 1150  (total price cap of $1,150)

A group of two or more simultaneously true inequalities is referred to as a system of inequalities. A system of inequalities can be solved by finding the set of values that satisfies every one of the inequalities in the system.

Therefore, The system of inequalities that represents this real-world scenario is:

x + y ≤ 450 (The total people cannot be greater than 450)

7x + 4y ≤ 1150 (total price cap of $1,150)

Where x is the number of adults and y is the number of campers.

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The composition of functions is solved and gof ( -7 ) = 1,286

Given data ,

Let the first function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = 13 - 2x

Let the second function be represented as g ( x )

Now , the value of g ( x ) is

g ( x ) = 2x² - 6x - 10

Now , g o f ( x ) = 2 ( 13 - 2x )² - 6 ( 13 - 2x ) - 10

On simplifying , we get

g o f ( x ) = 2 ( 169 + 4x² - 52x ) - 78 + 12x - 10

g o f ( x ) = 250 + 8x² - 92x

Now , the composition of function is

g o f ( -7 ) = 8 ( -7 )² - 92 ( -7 ) + 250

g o f ( -7 ) = 392 + 894

g o f ( -7 ) = 1,286

Hence , the function is g o f ( -7 ) = 1,286

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Answer:

60

Step-by-step explanation:

The area of a parallelogram is base x hight.

A = bh

10(b) x 6(h) = 60

The instantaneous velocity of the train at t = 9 seconds is approximately 6.8 m/s

To estimate the instantaneous velocity of the train at t = 9 seconds, we can consider the average velocities over several small intervals of time that include the point t = 9. This is an approximation of the slope of the tangent line to the curve s(t) at t = 9, which is the instantaneous velocity.

We can calculate the average velocity over each interval by dividing the change in displacement by the change in time:

Average velocity from [8.5, 9] = (s(9) - s(8.5)) / (9 - 8.5) = (8√9 + 1 - 8√8.5 + 1) / 0.5 = 6.34 m/s (approx.)

Similarly, we can calculate the average velocities over the other intervals:

[8.7, 9]: 6.48 m/s (approx.)

[8.9, 9]: 6.60 m/s (approx.)

[8.99, 9]: 6.66 m/s (approx.)

[9, 9.01]: 6.67 m/s (approx.)

[9, 9.1]: 6.74 m/s (approx.)

[9, 9.3]: 6.87 m/s (approx.)

[9, 9.5]: 7.00 m/s (approx.)

As we consider smaller intervals closer to t = 9, the average velocities approach a limit, which is the instantaneous velocity at t = 9. In this case, we see that the average velocities are increasing as we approach t = 9, indicating that the instantaneous velocity at t = 9 is also increasing.

Based on these calculations, we can estimate that the instantaneous velocity of the train at t = 9 seconds is approximately 6.8 m/s (averaging the average velocities from [8.99, 9] to [9, 9.5]).

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The Area of Kitchen is 120 square feet.

We have,

Area of living room = 144 square feet

So, the dining room

= 1/3 (area of living room)

= 1/3 (144)

= 48 square feet

and, Area of Dining room = 2/5 x Area of kitchen

48 =  2/5 x Area of kitchen

Area of kitchen = 48 x 5/2

Area of Kitchen = 24 x 5

Area of Kitchen = 120 square feet

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The equation that is the inverse of 5y+4= (x+3)²+12 is y = -3 ± √(5x - 8)

From the question, we have the following parameters that can be used in our computation:

5y+4= (x+3)²+12

Swap x and y in the equation

So, we have

5x + 4= (y + 3)² + 12

When we make the vairiable y the subject, we have

y = -3 ± √(5x - 8)

Hence, the equation that is the inverse of 5y+4= (x+3)²+12 is y = -3 ± √(5x - 8)

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The volume of the triangular base prims is 21.6 inches cube.

A triangular base prism is a prism with a triangular base. Therefore, let's find the volume of the triangular prism.

volume of a triangular prism = base area × height

Therefore,

base area = 1 / 2 bh

where

Therefore, the triangular base has angles 45, 45 and 90 degrees. Using trigonometric ratios let's find the other legs.

tan 45 = opposite / adjacent

tan 45 = x / 6

x = 6 inches

Therefore,

base area = 1 / 2 × 6 × 6

base area = 36  /2

base area = 18 inches²

Hence,

volume of the triangular base prism = 18 × 1.2

volume of the triangular base prism = 21.6 inches³

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The expected joint frequencies are

From the question, we have the following parameters that can be used in our computation:

The table of values

Also, we have

People = 160

This means that

Male and Drama = 12.5% * 160

Male and Drama = 20

Male and Comedy = 25% * 160

Male and Comedy = 40

Female and Drama = 46.9% * 160

Female and Drama = 75

Female and Comedy = 15.6% * 160

Female and Comedy = 25

In conclusion, we have

Because the expected and the joint frequencies are not the same, gender is not independent of movie type

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Answer:

12 • (17 • 23) = (12 • 17) • 23

The given shape of the distribution is not symmetric.

Given that, a box plot shows donations in dollars to charity.

We need to describe the shape of the distribution.

Donations to Charity ($) =

20 40 60 80 100 120 140 160 180 200 220

so, as we can see,

The shape of the distribution is not symmetric since the lengths of each box and whisker are not the same. There is an outlier at 220.

Hence, the given shape of the distribution is not symmetric.

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