Writing Exercises
297. Which method do you prefer to use when multiplying a trinomial by a binomial: the Distributive Property or the Vertical Method? Why?

Using the z-distribution, the 90% confidence interval for the difference of proportions is given by: (-0.0534, 0.0434).

For each sample, the mean and the standard error are given as follows:

For the distribution of differences, they are given by:

The interval is given by:

[tex]\overline{p} \pm zs[/tex]

In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.

Hence the bounds of the interval are:

[tex]\overline{p} - zs = -0.005 - 1.645(0.0294) = -0.0534[/tex]

[tex]\overline{p} + zs = -0.005 + 1.645(0.0294) = 0.0434[/tex]

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There are 80 different combinations of 3 cupcakes are there if order does not matter

The given parameters are:

Flavors = 10

Flavors to choose = 3

The number of combination is calculated using:

[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]

This gives

[tex]^{10}C_3 = \frac{10!}{7!3!}[/tex]

Expand

[tex]^{10}C_3 = \frac{10 * 9 * 8 * 7!}{7!3 * 2 * 1}[/tex]

Evaluate quotient

[tex]^{10}C_3 = 80[/tex]

Hence, there are 80 different combinations of 3 cupcakes are there if order does not matter

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Answer:

B. 8

Step-by-step explanation:

Triangle's weight is equal to the sphere's weight.

Total of 16 blocks. Since the triangle's weight is equal to the sphere's, the weight will be half of the blocks.

Divide 2 from 16.

16/2=8

The triangle's weight is equal to 8 blocks.

Hope this helps!

If not, I am sorry.

Answer:

B. 39.59

Step-by-step explanation:

So 43 degrees, you know the length of the opposite side (27) and the angle (43 degrees), the only unknown is the hypotenuse. So you're looking for a trigonometric ratio that uses the angle (all of them do, except technically the inverse don't), the opposite side, and the hypotenuse. Sine is defined as [tex]\frac{opposite}{hypotenuse}[/tex]. So let's plug in known values:

[tex]sin(43) = \frac{27}{x}[/tex]

Multiply both sides by x

[tex]sin(43) * x = 27[/tex]

divide both sides by sin(43)

[tex]x=\frac{27}{sin(43)}[/tex]

Normally I would use a calculator, but in this case I'll use the approximation given in the problem of 0.682

[tex]x=\frac{27}{0.682}[/tex]

simplify the fraction

[tex]x\approx39.59[/tex]

[tex]revenue = selling \: price \times quantity \: sold[/tex]

[tex]m(t) = 3t[/tex]

#1

Because

revenue=sold price×no of items

#2

The restriction is of 75tickets and the tickets can't be negative

so

Domain

Answer:

Answer: x ≤ q - 17/6.

Step-by-step explanation:

Divide both sides of the inequality by the coefficient of variable

11812.5 Jamaican dollars is equivalent to $135

The conversion rate is given as:

$1 = JA 87.50

Multiply both sides of the conversion rate by 135

135 * $1 = JA 87.50 * 135

Evaluate the product

$135  = JA 11812.5

Hence, 11812.5 Jamaican dollars is equivalent to $135

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The correct answer is 5.25%.

These include the optimal muscle fibre length, the length at which the muscle can generate maximum force, and the tendon slack length, the length at which the tendon starts to generate a resistive force to stretch.

Given,

           two figure

To find, slack length (l)

          AB =  √4² + 3² ⇒ 5

                l = [tex]5 + \frac{5}{100} * 5[/tex]

                   l   = 5.25

    Hence slack length is 5.25

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If it were completely straight. You compare ΔABC  to Fiqure DEF where curve DE   is 5%  longer than line segment AB . t Right Triangle without Slack Figure with Slack Brake :cord Enter the length of curve DE  given that the curve is 5% longer than line segment  AB.

Answer:

x=55°

Step-by-step explanation:

x=180°-125°

x=55°

Answer:

Step-by-step explanation:

Equation

3x + 9 + 2x = x - 2x - 3              

Solution

Combine all the like terms.

3x+2x+9 =  x - 2x - 3

5x + 9 = -x - 3                            Add x to both sides of the equation

5x+x +9 = -x+x -3                      Combine

6x + 9 = - 3                                Subtract 9 from both sides of the equation

6x+9-9 = - 3-9                           Combine

6x = -12                                      Divide both sides by 6

6x/6 = -12/6

x = - 2

Answer x = - 2

Answer:

.88

Step-by-step explanation:

[tex] \sqrt{.7775} = .88[/tex]

The standard deviation is the square root of the variance.

Answer:

see attached graphs

Step-by-step explanation:

Transformations

For a > 0

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]

[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]

[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]

[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]

Parent function:  [tex]f(x) = x[/tex]

Each transformation is a transformation of the parent function only:

Translation of 4 units down

[tex]\implies f(x)-4=x-4[/tex]

[tex]\implies y=x-4[/tex]

A stretch by a factor of 3

[tex]\implies 3f(x)=3x[/tex]

[tex]\implies y=3x[/tex]

A reflection and a translation 1 unit up

[tex]\implies f(-x)+1=-x+1[/tex]

[tex]\implies y=-x+1[/tex]

Answer:

4:3

Step-by-step explanation:

If you divide both 12 and 9 by 3 (the smallest number they can both be divided by), you get 4 and 3. the ratio is for every 4 apples, 3 would be green. So 4:3

The statement is true, it is a polynomial of degree 5 with 3 terms.

A polynomial is of the form:

[tex]p(x) = a_n*x^n + ... + a_0[/tex]

Where the degree is the maximum exponent of the polynomial, in this case, is n.

The given polynomial is:

[tex]p(x) = 6x^5 + 3x^4 + x^3[/tex]

So, the maximum exponent is 5, which means that the degree of the polynomial is 5.

And it has 3 terms, so the statement is true.

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So, 40 Customers are waiting at 10 A.M.

According to statement

Number of customers arrives at coffee shop per hour = 100

Capacity of shop for per minute per customer = 0.8 minute

Capacity of shop for customers per hour = 80

Find number of customers are by

Queue growth rate = Demand - Capacity

Put the values in the formula and find the growth rate

So,

Queue growth rate= 100 - 80 = 20.

Length of queue at 10 a.m. = 2 × 20 = 40.

So, 40 Customers are waiting at 10 A.M.

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The linear function h(x) = 2x + 3, with the domain {-2, -1, 0, 1, 2}, has the range {-1, 1, 3, 5, 7}.

To find the range, we substitute each value of the domain for x, in the linear function h(x) = 2x + 3, as follows:

For the domain value, x = -2:

h(-2) = 2(-2) + 3,

or, h(-2) = -4 + 3,

or, h(-2) = -1.

Therefore, for the domain value, x = -2, the range value h(-2) is -1.

For the domain value, x = -1:

h(-1) = 2(-1) + 3,

or, h(-1) = -2 + 3,

or, h(-1) = 1.

Therefore, for the domain value, x = -1, the range value h(-1) is 1.

For the domain value, x = 0:

h(0) = 2(0) + 3,

or, h(0) = 0 + 3,

or, h(0) = 3.

Therefore, for the domain value, x = 0, the range value h(0) is 3.

For the domain value, x = 1:

h(1) = 2(1) + 3,

or, h(1) = 2 + 3,

or, h(1) = 5.

Therefore, for the domain value, x = 1, the range value h(1) is 5.

For the domain value, x = 2:

h(2) = 2(2) + 3,

or, h(2) = 4 + 3,

or, h(2) = 7.

Therefore, for the domain value, x = 2, the range value h(2) is 7.

Therefore, the linear function h(x) = 2x + 3, with the domain {-2, -1, 0, 1, 2}, has the range {-1, 1, 3, 5, 7}.

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Answer:

x = 8

Step-by-step explanation:

An Equilateral triangle is a triangle in which all three sides and angles are equal. The value of each angle of an equilateral triangle is 60 degrees therefore we get the equation 9x - 12 = 60

Add 12 from both sides to isolate the 9x leaving us with:

9x = 72

Divide both sides by 9 to give us x, which is

x = 8

Number of pink T-shirts was 342

Given: 24% of the T-shirts were white

Let, total number of T-shirts be x

According to question,

Total number of white T-shirts = 24x/100

Total number of pink T-shirt =  24x/100+ 198

Total number of red T-shirts = 114

According to the question:

24x/100+24x/100+ 198 + 114 = x

312 = x - 48x/100

312 = 52x/100

x = (312*100)/52

x = 600

so Number of pink T-shirts :

=(24*600)/100+198

= 144 + 198

= 342

Hence total Number of pink T-shirts was 342.

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The 2 different angles you can name are <UVT and <VST. Hope this helps and please mark brainlist

The statements that are true are AD = BD  , m∠ACD = m∠BCD , m∠CDA = m∠CDB , Option A , C and D

A triangle is a polygon with three sides , angles and vertices.

It is given a Δ ACB

CD is the angle bisector of ∠ACB

AC ≅ CB

To determine which statement are true

First it has to be proved that Δ DCB is congruent to Δ ACD

In the triangles

AC = CB (Given )

∠ACD =  ∠DCB (CD is the angle bisector of ∠ACB)

DC = DC ( Common side )

thus Δ DCB is congruent to Δ ACD

Therefore the following statements are true

AD = BD (CPCTC)

m∠ACD = m∠BCD (CPCTC)

m∠CDA = m∠CDB (CPCTC)

Therefore Option A , C and D are the statements that are true .

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Answer:

Step-by-step explanation:

a,c,d

From the information given about  the triangle, the transformation that can map Triangle PQR onto Triangle STU is D. reflection, then translation.

Congruent triangles are known as triangles that have the same size, shape and angles.

It is also important to note that the transformation that can map Triangle PQR onto Triangle STU is reflection, then translation. This is so because it is a vital to form of congruent triangles.

There, the transformation that can map triangle PQR onto triangle STU is reflection, then translation. Option D

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Answer:

reflection, then translation

Step-by-step explanation:

The answer above is correct.

Answer:

90 degree and the angle sides

Population dynamics must consider the number of individuals that are lost per unit of time, also called the mortality rate.

Mortality, or mortality, is a measure of the number of deaths (generally or due to a particular cause) in a particular population, scaled to the size of that population per unit of time.

The relative incidence of deaths in a particular population over a particular time period. Often expressed as the rate of human deaths or wildlife deaths from environmental hazards during a public health crisis. The highest mortality rate for patients over the age of 80 was during the last flu season.

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Option 1. The equation that represents the direct variation that exists between a and b is b = –a.

The direct variation is of this form y ∝ x

This gives the equation

y = kx

The constant is k

From our question we have

b ∝ a so b = ka

b = [tex]2\frac{3}{4}[/tex]

a = [tex]-2\frac{3}{4}[/tex]

Remember that b = ka

[tex]2\frac{3}{4} = -2\frac{3}{4} k[/tex]

This would cancel out to

1 = -k

or k = -1

Hence the equation would be written as

b = -a

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A triangle is a three-edged polygon with three vertices. The measure of arc AB is 72°. Thus, the correct option is C.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

Since in the ΔAOB, the length of the side OA and OB are,

OA = OB = radius

Therefore, the triangle is an isosceles triangle. Thus, we can write,

∠OAB = ∠OBA = 54°

Now, the sum of all the angles of ΔAOB is,

∠AOB + ∠OAB + ∠OBA = 180°

∠AOB + 54° + 54° = 180°

∠AOB = 72°

Hence, the measure of arc AB is 72°. Thus, the correct option is C.

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Answer:

at 5 mins Holly traveled 2 miles. At 10 mins Holly traveled 4 miles. from there on she stayed there for 10 mins then went on her way. At 30 mins she traveled 5 1/2 miles. when she hit 35 mins she hit her destination then went back home.

Step-by-step explanation:

pretty simple

Answer:

D

Step-by-step explanation:

First let's list down the formulas we will be using.

Area of Quadrant = 1/4 x Area of Circle

= [tex]\frac{1}{4} \pi r^{2}[/tex]

Area of Part of a circle = (θ/360)[tex]\pi r^{2}[/tex]

First, we will find Angle QOT.

Angle QOT = 360 - 231 = 129

Area of ORST = [tex]\frac{129}{360} \pi (21)^{2} \\=\frac{6321}{40} \pi cm^{2}[/tex]

Next we know that, Q is midpoint of OR, therefore OQ = QR

and OQ = 0.5 * OR

OQ = 0.5 * 21 = 10.5cm = radius of Quadrant QOP

Area of Quadrant QOP = [tex]\frac{1}{4} \pi (10.5)^{2} \\=\frac{441}{16} \pi cm^{2}[/tex]

Lastly,

Area of Shaded Region = Area of ORST - Area of Quadrant QOP

= [tex]\frac{6321}{40} \pi -\frac{441}{16} \pi \\= 409.86cm^{2}[/tex]

Similar to the other question you asked, choose the closes answer as there might be some rounding differences. I kept it in fractions as it will ensure maximum precision.

Answer:

13/8

Step-by-step explanation:

let the number be x

5/8 - x = -1

-x = -1 - 5/8

-x = - 13/8

x = 13/8

5/8- 13/8 = -1

Answer:

13/8

Step-by-step explanation:

5/8 - x = -1   where x is the number to be found.

- x = -1 - 5/8

x = 5/8 + 1

   = 13/8.

Answer:

x = 3

y = 2

Step-by-step explanation:

Equations

7x - 7y = 7                            

-4x - 7y = - 26                          Multiply both sides of the equation by - 1

-1(-4x - 7y = - 26)

4x + 7y = 26

Solution

Add the two equations together

7x - 7y = 7      

4x + 7y = 26

11x = 33                                  Divide by 11

11x/11 = 33/11

x = 3

4x + 7y= 26                           Use this equation to solve for y. Use x = 3

4*3 + 7y = 26                        Combine the left

12 + 7y = 26                          Subtract 12 from both sides

12 - 12 + 7y = 26 - 12            Combine

7y = 14                                  Divide by 7

7y/7 = 14/7

y = 2