When the research hypothesis predicts the direction of a relationship, the test is ______. a. direct b. two-tailed c. one-tailed d. positive

The required factorized form of the given expression is 50(x+2), where 50 is the greatest common factor (GCF).

Factorization, also known as factoring, is the breakdown of one element into a product of other objects, or factors, which when multiplied together generate the original. For example, the number 21 factors into primes as 3 × 7, and the polynomial x² − 9 factors as (x+3)(x-3).

We have been given that the expression below as

50x + 100

We have to determine the factor of the expression 50x + 100

First, we have to find the Greatest Common Factor (GCF).

GCF = 50

2 Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

50(50x/50 + 100/50)

Simplify each term in parentheses.

50(x+2)

Therefore, the required factorized form of the given expression is 50(x+2).

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C. 2916 Mice

Step-by-step explanation:

4 x 3^6 = 2916

Because as the mice increases, you triple that amount, instead of tripling 4 & multiplying by 6.

So, you're doing this instead:

4 x 3 = 12 (1 wk)

12 x 3 = 36 (2 wk)

36 x 3 =108 (3 wk)

108 x 3 = 324 (4 wk)

324 x 3 = 972 (5 wk)

972 x 3 = 2916 (6 wk)

Hope this helps!

The number of children who disliked the smoothie is 9, total children is 27, and conditional relative frequency is 33%

It is defined as the frequency that can be evaluated by the two-way frequency table. Usually, we can obtain this frequency by dividing the frequency that is not in the total frequency cell to total frequency.

From the data given in the table:

The number of children who disliked the smoothie = 9

The total number of children = 27

To find the conditional relative frequency that a customer disliked the new smoothie(if the person is a child)

It is the ratio of total number of children who disliked the smoothie to total number of children, mathematically:

= 9/27

= 0.3333

= 0.3333×100

= 33.33 ≈ 33%

Thus, the number of children who disliked the smoothie is 9, total children is 27, and conditional relative frequency is 33%

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Answer:

9, 27, 33

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

Check out the attached photo

Answer:

I think it's A I hope this helps!!

Step-by-step explanation:

Answer:

  a. 0.41

  b. 0.22

Step-by-step explanation:

The sum of probabilities over all outcomes is 1. This fact can be used to fill the table. The other questions can be answered by reference to the table.

__

The total of all probabilities is 1:

  k +0.23 +0.18 +0.26 +2k = 1

  3k = 0.33 . . . . . . . collect terms, subtract 0.67

  k = 0.11 . . . . . . . divide by 3

  2k = 0.22 . . . . find 2k

Then the table is ...

  [tex]\begin{array}{c|ccccc}n&1&2&3&4&5\\p(n)&0.11&0.23&0.18&0.26&0.22\end{array}[/tex]

Landing on 2 or 3 are mutually exclusive outcomes, so the probability of one or the other is the sum of their individual probabilities:

  p(2 or 3) = 0.23 +0.18

  p(2 or 3) = 0.41

__

The table tells us ...

  p(5) = 0.22

Answer:

It is also known as E: random cause

Considering that the data has no outliers, the mean of 3.2 inches should be used to describe the center of the data represented in this line plot.

It depends if the data-set has outliers or not.

The dot plot gives the number of times each measure appears. Since there is no outliers, that is, all values are close, the mean should be used. It is given by:

M = (2 x 1 + 3 x 2 + 2 x 3 + 1 x 5 + 1 x 6 + 1 x 7)/(2 + 3 + 2 + 1 + 1 + 1) = 3.2 inches.

The mean of 3.2 inches should be used to describe the center of the data represented in this line plot.

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Answer: median 2.5

Step-by-step explanation:

Answer:

  1680

Step-by-step explanation:

To find the product of the two numbers, you can work out the values of the numbers, or you can work directly with the sum and difference figures.

__

We note that the square of a sum is ...

  (a +b)² = a² +2ab +b²

and the square of a difference is ...

  (a -b)² = a² -2ab +b²

The difference of these squares is ...

  (a +b)² -(a -b)² = (a² +2ab +b²) -(a² -2ab +b²) = 4ab

__

That is, dividing the difference of the squares of the sum and difference by 4 will give the desired product:

  P = (83² -13²)/4 = (6889 -169)/4 = 6720/4 = 1680

The product of the two numbers is 1680.

_____

Additional comment

If we factor the formula we derived, we find ...

  P = ((a +b)² -(a -b)²)/4 = ((a +b) +(a -b))/2 × ((a +b) -(a -b))/2

This simplifies to ...

  (2a)/2 × (2b)/2 = a × b

In short:

Using this fact, we find a=(83+13)/2 = 48; b=(83-13)/2 = 35, and the product is (48)(35) = 1680, as above.

The dot plot with the least number of sites has the least frequency

The dot plot has the least number of sites is the Shield Darter

To determine the dot plot with the least number of sites, we simply calculate the total frequency of each dot plot

So, we have:

Shield Darter = 3 + 1 + 4 + 2 + 3 + 1 + 1

Shield Darter = 15

Calico Crayfish = 1 + 1 + 3 + 4 + 1 + 2 + 4 + 2

Calico Crayfish = 18

Zebra Mussel = 1 + 3 + 2 + 5 + 1 + 1 + 2 + 3 + 2

Zebra Mussel = 20

Blue back Herring = 3 + 3 + 2 + 1 + 3 + 1 + 4

Blue back Herring = 17

From the computation above, the least frequency is

Shield Darter = 15

Hence, the dot plot has the least number of sites is the Shield Darter

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Answer:

If x2 + 6x + c = (x + d)2, then d =What value of c makes x2 + 6x + c a perfect square trinomial? c =

Divide the x-term coefficient by 2: 6/2 = 3

Now square 3: 3^2 = 9

c = 9

If x^2 + 6x + c = (x + d)^2, then d =

x^2 + 6x + 9 = (x + 3)^2 = (x + d)^2, so d = 3

Step-by-step explanation:

Answer:

c = +9.

Step-by-step explanation:

x^2 + 6x + c.

Divide 6 by 3 then square it

- so c = 3^2 = 9.

x^2 + 6x + 9 = (x + 3)^2.

remember

SOH CAH TOA

sin(θ) is the ratio of the opposite side to the hypotenuse

sin(θ) = opposite/ hypotenuse

sin 50 = 0.766

sin 50 = x / 16

0.766 = x/ 16

0.766 × 16 = x

x = 12.256

Answer:

no

Step-by-step explanation:

Answer:

The distributive property states that you can "distribute" the contents of one parentheses into the other to find an answer.

Let's first break down the larger number in the second parentheses:

400 + 10 + 5.

Then, let's multiply all those numbers by 3.

400 x 3 = 1200. 10 x 3 = 30. 5 x 3 = 15.

Then add up all the numbers and you get 1245.

Answer:

1245

Step-by-step explanation:

400+10+5

400×3=1200. 10×3=30. 5×3=15

Answer:

240 cm²

Explanation:

The shape given above is a parallelogram.

Area of parallelogram = base × perpendicular height

Identify the following:

So here area = b × h = 20 × 12 = 240 cm²

Answer:

80°

Step-by-step explanation:

2x+20=180°

2x= 180°-20°

x=160/2

x=80°

Answer:

the area of rectangle should be 1/8 square

Step-by-step explanation:

1/6*3/4

=1/8

Step-by-step explanation:

4) 42

5) -9

6) 27

7) x=3,y=27

8) x=6,y=13

9) x=2,y=(-3)

I hope I have helped you

pls mention any doubts in comment

Answer:

  B)  When you're finished, you have a line that bisects your segment

Step-by-step explanation:

An angle bisector is a ray that divides a given angle into two congruent parts. There is no line segment involved.

__

The statement that is not true about this construction is ...

  B) When you're finished, you have a line that bisects your segment

_____

Additional comment

The construction effectively creates an arc of a circle, then creates the perpendicular bisector of the chord of that arc. The center of the circular arc is the vertex of the angle being bisected. The constructed perpendicular bisector of the chord also bisects the angle. (The chord is never actually drawn, and the "circular arc" may be two short arcs across the rays of the angle being bisected.)

Step-by-step explanation:

Let the angle of triangle be x , so each angle will be 1x , 2x , 3x respectively.

We know that sum of all angles in triangle is 180°

So ,

1x + 2x + 3x = 180°

6x = 180°

x = 30°

Therefore , each angle would be 30° , 60° , 90° respectively.

Step-by-step explanation:

seems to be multiplication, because the differences between the numbers change.

so, let's find the factor.

2 × f = 5

f = 5/2

5 × f = 5 × 5/2 = 25/2

ok, the factor 5/2 is confirmed.

a1 = 2

a2 = a1 × 5/2 = 2 × 5/2 = 10/2 = 5

a3 = a2 × 5/2 = a1 × 5/2 × 5/2 = 2 × 5/2 × 5/2 = 25/2

an = an-1 × 5/2 = a1 × (5/2)^(n-1) = 2 × (5/2)^(n-1)

a9 = 2 × (5/2)⁸ = 2 × 390,625/256 =

= 390,625/128 = 3,051.7578125

The geometric sequence's 9th term will be 3,051.7578.

A geometric sequence is one in which each term is obtained by multiplying the previous term by the same number throughout the series.

Let a₁ represent the first term and r represent the common ratio. The geometric sequence's nth term is then given as,

aₙ = a₁ x (r)ⁿ⁻¹

The sequence is given below.

2, 5, [tex]\dfrac{25}{2}[/tex],

The first term is 2. And the common difference is given as,

[tex]r = \dfrac{5}{2}[/tex]

r = 2.5

Then the 9th term is given as,

a₉ = 2 x  (2.5)⁹⁻¹

a₉ = 2 x (2.5)⁸

a₉ = 2 x 1525.8789

a₉ = 3,051.7578

The 9th term of the geometric sequence will be 3,051.7578.

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The surface area of the roof is the amount of space on it

The surface area of the roof is 600 square meters,

From the complete question, we have the parameters for the roof:

The surface area of the roof is calculated using:

[tex]A = b^2 + 2b \sqrt{\frac{b^2}4 + h^2}[/tex]

So, we have:

[tex]A = 15^2 + 2 * 15 \sqrt{\frac{15^2}4 + 10^2}[/tex]

Evaluate the exponents

[tex]A = 225 + 30 * \sqrt{\frac{225}4 + 100[/tex]

The equation becomes

[tex]A = 225 + 30 * 12.5[/tex]

Evaluate the sum

[tex]A = 600[/tex]

Hence, the area of the roof is 600 square meters

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Answer:

3,628 sq ft

Step-by-step explanation:

Answer:

14130 cubic inches

Step-by-step explanation:

A = 4/3 n x rxrxr

A = 3.14 x 15x15x15

A = 3.14 x 3375

A = 10597.5

A = 4/3 10597.5

A = 14130

Answer: [tex]z=91.6[/tex]

Step-by-step explanation:

A pentagon has 5 sides and 5 angles and equals up to 540 degrees

So we need to make the equation of

[tex]145+120.1+112.3+71+z=540[/tex]

[tex]448.4+z=540[/tex]

[tex]448.4+z=540\\-448.4 = -448.4[/tex]

[tex]z=91.6[/tex]c

To check work just plug in 91.6 for z in the equation that was created [tex]145+120.1+112.3+71+91.6=540[/tex]

Answer:

C

Step-by-step explanation:

let x be number of adults and y the number of underage , then

x + y = 350 → (1)

6x + 4y = 1600 → (2)

multiplying (1) by - 4 and adding to (2) will eliminate y

- 4x - 4y = - 1400 → (3)

add (2) and (3) term by term to eliminate y

(6x - 4x) + (4y - 4y) = 1600 - 1400

2x + 0 = 200

2x = 200 ( divide both sides by 2 )

x = 100

the number of adults who attended is 100

Answer:

(-3,1)

Step-by-step explanation:

As their are two lines so these are simultaneous linear equations

Hence this is (-3,1)

Note: The solution of a graph is the intersection of 2 lines.

Plotting the solution on the graph:

To plot the solution on the graph,

Identifying a solution on the graph:

To identify the solution, you willl need to determine it's coordinates.

     1. Determine the x and y coordinate by drawing a line going                                 downwards and rightwards. Keep in mind that the                                               intersection of the lines on the x and y axis are the x and y                               coordinates repectively.

    2. The x and y coordinate obtained should be put in (x,y) form.

Determining the solution on the graph:

⇒ Intersection point: (x, y) = (x = -3; y = 1) = (-3, 1)                [Refer to image]

Hi There! Hope you are having a great day! As you know, you need to find the unit rate of the problem. In order to do that you must divide how much ounces there is, (52.8) and divide that integer by how much money she made (26.4) leaving you with a unit rate of 2. Hope this helps! :)

Answer:

Step-by-step explanation:

The length of b, the base of the triangle, is

The area of the triangle is

The area of the rectangle is

The area of the irregular figure is

Answer:

[tex]b=2\frac23\:\sf ft[/tex]

Area of triangle = 4 ft²

Area of rectangle = [tex]6\frac23\: \sf ft^2[/tex]

Area of irregular figure = [tex]10\frac23\: \sf ft^2[/tex]

Step-by-step explanation:

[tex]\begin{aligned}\sf Base\:of\:triangle\:(b) & = 5-2\frac13\\\\& = \dfrac{15}{3}-\dfrac73\\\\ & = \dfrac83\\\\ & = 2\frac23\:\sf ft \end{aligned}[/tex]

[tex]\begin{aligned}\sf Area\:of\:a\:triangle & =\dfrac12 \sf \times base \times height\\\\& = \dfrac12 \times b \times 3\\\\ & = \dfrac12 \times \dfrac83 \times \dfrac31\\\\ & = \dfrac{24}{6}\\\\ & = 4\: \sf ft^2\end{aligned}[/tex]

[tex]\begin{aligned}\sf Area\:of\:rectangle& =\sf length \times width\\\\& = 5 \times 1\frac13\\\\ & = \dfrac51\times \dfrac43\\\\& = \dfrac{20}{3}\\\\ & = 6\frac23\: \sf ft^2\end{aligned}[/tex]

[tex]\begin{aligned} \sf Area\:of\:irregular\:figure & = \sf area\:of\:triangle+area\:of\:rectangle\\\\ & = 4 + 6\frac23\\\\ & = 10\frac23\: \sf ft^2\end{aligned}[/tex]

Answer:

The area of a trapezoid = 1/2 (altitude)(base 1 + base 2)

Step-by-step explanation:

Answer:

322ft2

Step-by-step explanation:

I promise this is correct