The test statistic of z= -1.32 is obtained when testing the claim that p = 0.302. This is a two-tailed test. Using a 0.01 significance level, complete parts (a) and (b).
Click here to view the standard normal distribution table for negative z scores. Click here to view the standard normal distribution table for positive z scores,
a. Find the critical value(s).
Select the correct choice below and fill in the answer box(es) within your choice.
(Round to two decimal places as needed.)
A. There are two critical values; the lower critical value is and the upper critical value is blank and the upper critical value is blank

The reduction in reserve requirements led to an increase of $79 billion in both excess reserves and the lending capacity of Chinese banks.

According to the news accounts from March 2020, the reduction in the reserve requirement ratio (RRR) by the People's Bank of China increased the lending capacity of Chinese banks by approximately US$79 billion

(a) The excess reserves in China increased by $79 billion.

(b) As a result of the reduction in the reserve requirement, the lending capacity of Chinese banks increased by $79 billion.

This means that Chinese banks had an additional $79 billion available for lending purposes, which aimed to stimulate economic growth and support the country's economy. By lowering the reserve requirement, commercial banks were able to hold a smaller portion of their deposits as reserves, thus freeing up more funds that could be utilized for lending to businesses and individuals.

In summary, the reduction in reserve requirements led to an increase of $79 billion in both excess reserves and the lending capacity of Chinese banks.

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The measure of the angle S is 54 degrees

Using the Pythagorean theorem, we have that;

r² = t² + s²

Subsitute the values

s² = 24² - 14²

Find the square values

s² = 576 - 196

s² = 380

find the square root value

s = 19. 5

Then, using the law of sines, we have that;

sin R/r = sin S/s

Substitute the values, we get;

sin 98/24 = sin S/19.5

cross multiply the values

sin S = 19.3/24

Divide the values

sin S = 0. 8045

S = 54 degrees

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Alfa receives 70 Naira, and since Aisha gets twice as much, she receives 2 * 70 = 140 Naira.

(1)

(a) The relationship between D, o, and S can be expressed as follows:

DoS (D divided by o multiplied by S) = D / (35 * S)

(b) To find the value of S when D is 176, we can substitute D = 176 into the equation from part (a):

DoS = 176 / (35 * S)

Since the relationship between DoS is not specified further, we cannot determine a specific value of S without additional information. We need more context or a specific equation to solve for the value of S.

Let's denote the amount Alfa gets as x Naira. According to the given information, Aisha gets twice as much as Alfa, so Aisha receives 2x Naira.

The sum of the amounts they receive is 210 Naira, so we can set up the equation:

x + 2x = 210

Combining like terms:

3x = 210

Dividing both sides by 3:

x = 70

Therefore, Alfa receives 70 Naira, and since Aisha gets twice as much, she receives 2 * 70 = 140 Naira.

In summary, Alfa receives 70 Naira, while Aisha receives 140 Naira.

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Explanation:

Let's find the roots aka x intercepts.

Plug in y = 0 and solve for x.

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

(x+3)(x-7) = 0

x+3 = 0 or x-7 = 0

x = -3 or x = 7 are the two roots.

Now find the midpoint of those roots.

Add them up and divide in half.

(-3+7)/2 = 4/2 = 2

The midpoint happens at x = 2, which is the x coordinate of the vertex. This is the axis of symmetry where the vertex is located.

The vertex in this case is the lowest point on the parabola. It's the turning point where it goes from decreasing to increasing.

Plug x = 2 back into the original equation to find its paired y value.

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

y=(2+3)(2-7)

y=(5)(-5)

y=-25

Therefore, the vertex is located at (2, -25) as indicated in the graph below. I used GeoGebra to make the graph. Desmos is another good choice.

The total cost of the fabric that Christine needs for the tablecloths is $90.0.

A rectangle is a figure which has four sides of which opposite sides have equal length.

The area of a rectangle is the amount of space to be covered by the figure in a 2 dimensional plane.

Area of a rectangle = length x width

In the information given, we have;

area of the tablecloth = length x width

                      = 6 x 5/2

                      = 3 x 5

                      = 15

The area of the tablecloth is 15 sq. ft.

But Christine plans to make 1 tablecloth for each 4 seasons of the year.

So that;

total area of tablecloth needed for the year = 15 x 4

                            = 60 sq. ft

Then the fabric costs $1.50 per square foot,

total cost of fabric needed = 60 x $1.5

                                             = $90.0

The total cost of the fabric that Christine needed for the tablecloth is $90.0

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The new budget for each category would be:

Housing: $19,680

Food: $8,856

Transportation: $8,856

Other goods and services: $11,808

After the government mandate, the average individual's salary would be reduced by 40%:

New annual salary = $82,000 - (40% x $82,000) = $49,200

Similarly, the prices of all goods and services would be reduced by 40%. Therefore, the new amounts spent on each category would be:

Housing: $32,800 - (40% x $32,800) = $19,680

Food: $14,760 - (40% x $14,760) = $8,856

Transportation: $14,760 - (40% x $14,760) = $8,856

Other goods and services: $19,680 - (40% x $19,680) = $11,808

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Answer:

[tex]39ft^{2}[/tex]

Step-by-step explanation:

Area of a Trapezoid - 1/2 x (base1+base2) x h

1/2(2+5)4

1/2(7)4

1/2(28)

28/2=14

So, the Trapezoid area is 14

Are of a Square - base x height

5(5)=25

14+25=39

So, the total area is [tex]39ft^{2}[/tex]

We can first start off by getting from 5 cups of water to 1 cup of water. We can do this by dividing 5 by 5 to get 1. Since we did this to the water, we need to do the same thing with the sugar. 1 cup of sugar divided by 5 is equivalent to 0.2 cups of sugar.

The answer is 0.2 cups of sugar.

The distance between the points (7,-2) and (3, 1) is √(13).

Since, the distance between two points (x₁, y₁) and (x₂, y₂) is calculated using the distance formula,

d = √((x₂ - x₁)² + (y₂ - y₁)²),

where, d is the distance between the points (x₁, y₁) and (x₂, y₂).

To find the distance between the points (7,-2) and (3, 1) .

Thus the distance between two points (x₁, y₁) and (x₂, y₂) is calculated using the distance formula,

d = √((x₂ - x₁)² + (y₂ - y₁)²),

d = √((1 - (-2))² + (3 - 1)²),

or, d = √((3)² + 2²),

or, d = √((9+ 4),

or, d = √(13),

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The journal entries for to record the issuance of the convertible bond on 1st July 2008 are Cash 475,000,000, Discount on Bonds Payable 25,000,000, Bonds Payable 500,000,000.

To record the issuance of the convertible bond on 1st July 2008

Cash (0.95*500,000,000) 475,000,000

Discount on Bonds Payable 25,000,000

Bonds Payable 500,000,000

(Note: The discount on bonds payable is calculated as the difference between the cash proceeds and the face value of the bond, and it represents the portion of the bond discount that is attributable to the conversion feature.)

To record the interest expense and coupon payment on 30th June 2009

Interest Expense 30,000,000

Discount on Bonds Payable 15,000,000

Cash 45,000,000

(Note: The interest expense is calculated as 6% of the face value of the bond, and the discount on bonds payable is amortized over the life of the bond using the effective interest rate method.)

To record the interest expense and coupon payment on 30th June 2010

Interest Expense 30,000,000

Discount on Bonds Payable 12,750,000

Cash 42,750,000

To record the interest expense and coupon payment on 30th June 2011

Interest Expense 30,000,000

Discount on Bonds Payable 10,088,750

Cash 40,088,750

To record the redemption of the bond on 30th June 2012

Bonds Payable 500,000,000

Premium on Bonds Payable 25,000,000

Cash 525,000,000

(Note: The premium on bonds payable is calculated as the difference between the redemption price and the face value of the bond, and it represents the portion of the bond premium that is attributable to the conversion feature.)

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The volume of the Canada post mailbox is given as follows:

1,152,115.5 cm³.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

Hence the volume of the rectangular bottom is given as follows:

V = 180 x 70 x 85.5

V = 1,077,300 cm³.

The triangular top has a height of 25 cm, hence the volume is obtained as follows:

V = 0.5 x 25 x 70 x 85.5 (multiply by 0.5 as it is a triangle).

V = 74812.5.

Hence the volume is given as follows:

1077300 + 74812.5 = 1,152,115.5 cm³.

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Answer:

Let's assume that the length of the rectangle is "x" units.

According to the problem, the width of the rectangle is 1 unit less than the length. Therefore, the width can be represented as (x-1) units.

We know that the area of a rectangle is equal to its length multiplied by its width. So, the area of this rectangle is given as 56 square units.

Using the formula for the area of a rectangle, we can write:

Length x Width = Area

x(x-1) = 56

Expanding the left side of the equation, we get:

x^2 - x = 56

Rearranging the terms, we get a quadratic equation:

x^2 - x - 56 = 0

Now we can solve for x by factoring the quadratic equation:

(x-8)(x+7) = 0

This gives us two possible values for x: x=8 and x=-7.

Since length cannot be negative, we reject x=-7 and conclude that the length of the rectangle is 8 units.

Therefore, the length of the rectangle is 8 units and the width is (8-1) = 7 units.

Step-by-step explanation:

The unit vector that has the same direction as v is u = v/|v| = (2i - 5j)/√(29)

To find the unit vector that has the same direction as the vector v, we need to divide the vector v by its magnitude. The magnitude of a vector is the square root of the sum of the squares of its components. In other words, if v = (a,b), then the magnitude of v is given by:

|v| = √(a² + b²)

Using this formula, we can find the magnitude of the vector v as:

|v| = √(2² + (-5)²) = √(29)

Now, to find the unit vector that has the same direction as v, we divide v by its magnitude:

u = v/|v| = (2i - 5j)/√(29)

This is the unit vector in the same direction as v. It has a magnitude of 1, which means that it is a vector of length 1. By dividing v by its magnitude, we have scaled v so that its length is 1, but its direction is still the same as the original vector v.

In summary, to find the unit vector that has the same direction as the vector v, we divide v by its magnitude. This gives us a vector of length 1 in the same direction as v.

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Answer:

16.03% increase.

Step-by-step explanation:

4.264+25%+6.396 = 16.03% increase.

The value of cosβ is 4/5.

The value of sinβ is 3/5.

The value of tanβ is 3/4

The value of angle α is 53.1⁰.

The basic trigonometric ratios for β is calculated as follows;

The length of AC is calculated as follows;

AC² = AB² - BC²

AC² = 15² - 12²

AC² = 81

AC = √ (81)

AC = 9

The value of cosβ is calculated as;

cosβ = 12/15 = 4/5

The value of sinβ is calculated as;

sinβ = 9/15 = 3/5

The value of tanβ is calculated as;

tanβ = 9/12 = 3/4

The value of angle α is calculated as follows;

sinα = 12/15 = 4/5

sinα = 0.8

α = arc sin (0.8)

α = 53.1⁰

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The dimension of section 1 is

15 ft by 3 ft

The dimension of section 2 is

3 ft by 3 ft

The dimension of section 3 is

10 ft by 3 ft

Option A is the correct answer.

From the figure given below,

We have,

Section 1: 15 ft by 3 ft

Section 2: 3 ft by 3 ft

Section 3: 10 ft by 3 ft

The perimeter of all these sections.

= 15 + 3 + 15 + 3 + 3 + 10 + 3 + 10

= 62 feet

Thus,

The dimensions of each section are:

Section 1: 15 ft by 3 ft

Section 2: 3 ft by 3 ft

Section 3: 10 ft by 3 ft

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The sum of the terms is x^7+10x^4+4x^3-5x^11-10x^6

To determine the value, we need to know that algebraic expressions are described as expressions that are composed of factors, constants, variables, terms and coefficients.

These algebraic expressions are also identified with the presence of arithmetic operations,

These operations are;

From the information given, we have that;

7x^7+10x^4+4x^3-5x^11-10x^6-6x^7

collect the like terms

7x^7 - 6x^7+10x^4+4x^3-5x^11-10x^6

add the like terms

x^7+10x^4+4x^3-5x^11-10x^6

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A statistical question that can result in numerical data is How many times did you go swimming this year? So, the correct option is A).

The statistical question that can result in numerical data is "How many hours this week did you spend on homework?" and "How many times did you go swimming this year?".

These questions involve counting or measuring quantities, which can be represented using numerical data. The other two questions do not involve numerical data and therefore cannot be considered statistical questions that result in numerical data. So, the correct answer is B).

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Answer:

How many pink erasers do the students in your class have?

The distance between the two points plotted is 10 units.

In geometry, the distance between two points is the length of the shortest path connecting them. It is the measure of the length of a straight line segment connecting two points in space.

To find the distance between two points, we can use the distance formula, which is based on the Pythagorean theorem. The formula states that the distance between two points (x₁, y₁) and (x₂, y₂) is given by:

D = √ [ ( y₂ - y₁ )² + ( x₂ - x₁ )² ]

In this problem, the two points plotted are (-6, 4) and (-6, -6). Using the distance formula, we can calculate the distance between these two points as:

D = √((-6 - (-6))² + (-6 - 4)²)

D = √(0² + (-10)²)

D= √(100)

D= 10

Therefore, the distance between the two points plotted is 10 units.

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Answer:

10 units

Step-by-step explanation:

i did in class

The possible values lx + 5| = 6 of x in the equation are x = -11 or x = 1

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

lx + 5= 6

Express properly

So, we have

lx + 5| = 6

The above equation is an absolute value equation

When the above equation is expanded, we abe

x + 5 = -6 or x + 5 = 6

Solving for x in the equations. we have

x = -11 or x = 1

This means that the values of x in the equation are x = -11 or x = 1

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There are 33,800 different four-letter passcodes that can be formed if the first letter must be an S or a T, and the last letter must not be a Z.

The English alphabet consists of 26 letters. Because the initial letter must be a S or a T, there are only two options.

There are 26 options for each letter in the second and third letters because there are no constraints. As a result, the second and third letters have a total of 26 26 = 676 potential combinations.

We have 25 options for the fourth letter (which cannot be a Z).

As a result, the total number of possible four-letter passcode combinations is:

2 × 676 × 25 = 33,800

So, if the first letter is a S or a T and the last letter is not a Z, there are 33,800 possible four-letter passcodes that may be constructed.

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The equation in each case will be 5(x - 2) = x + 7, 2x - 4 > 10, and 2x - 2 = x + 5 and their solution will be 4.25, more than 7, and 7, respectively.

1. Let the number be x. Then the equation can be written as,

5(x - 2) = x + 7

5x - 10 = x + 7

4x = 17

x = 4.25

2. Let the number be x. Then the equation can be written as,

2x - 4 > 10

2x > 14

x > 7

3. Let the number be x. Then the equation can be written as,

2x - 2 = x + 5

x = 7

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The resultant force acting on the block is 47.6N.

The acceleration of the block will be 23.8 m/s².

The speed of the block after 5 seconds of movement is 119 m/s.

In this question, we need to make use of Newton's second law, hence:

resultant force = mass × acceleration

So, for question a. The value of the resultant force  will be obtained by adding the two forces together:

resultant force = F₁ + F₂

                       = 25N + 22.6N

                        = 47.6N

b.  Its acceleration will be:

acceleration = resultant force / mass

                  = 47.6N / 2kg

                  = 23.8 m/s²

c. The speed of the block after 5 seconds of movement will be:

Velocity  (v) = u + at

velocity = initial velocity + acceleration x time

Based on the block was initially at rest, the initial velocity is 0.

Hence:

V = acceleration x time

    = 23.8 m/s² x 5s

     = 119 m/s

Hence the speed of the block after 5 seconds of movement will be: 119 m/s.

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See full text below

The block in the figure is at rest when the forces begin to act.

F₁ = 25N

F, = 22.6 N

m = 2kg

to. Find the value of the resultant force.

b. Determine its acceleration.

C. Calculate the speed of the block after 5 seconds of movement.

Answer:

14:09 (5 hours and 9 minutes later)

Step-by-step explanation:

To determine the time the truck will arrive in Kimberley if it left Johannesburg at 09:00, we can use the formula:

time = distance/speed

where the distance is 505.5 km and the speed is 98 km/h.

Substituting these values into the formula gives:

time = 505.5 / 98 = 5.15 hours

Therefore, if the truck left Johannesburg at 09:00, it will arrive in Kimberley at approximately 14:09 (5 hours and 9 minutes later) to the nearest minute.

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The area of a sector TOP is 89.019 square meter.

Given that, radius of the sector is r=9 m and measure of arc TP = 126°.

Here, ∠TOP =measure of arc TP = 126°.

We know that, area of a sector = θ/360° ×πr²

= 126°/360° ×3.14×9²

= 0.35×3.14×81

= 89.019 square meter

Therefore, the area of a sector TOP is 89.019 square meter.

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The cash discount is $38.40

The rate of cash discount is 4%.

The invoice price is $960, and the cash price is $921.60. The cash discount is the difference between these two price :

Cash discount = Invoice price - Cash price

Cash discount = $960 - $921.60

Cash discount = $38.40

The cash discount is $38.40.

The proportion of the cash discount in relation to the invoice price is necessary to calculate the cash discount rate. By dividing the cash discount by the invoice price, then multiplying the result by 100, we can determine this:

Rate of cash discount = (Cash discount / Invoice price) x 100%

Rate of cash discount = ($38.40 / $960) x 100%

Rate of cash discount = 0.04 x 100%

Rate of cash discount = 4%

Therefore, the rate of cash discount is 4%.

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The equation of the circle in the form (x - h)² + (y - k)² = r² is (x + 7)² + 7(y - 33/7)² = 49.

The equation of a circle is given by the standard form:

(x - h)² + (y - k)² = r²

where

h = center of the circle

r = radius of the circle.

To find the center and radius of the circle in the given equation:

x² + 14x + y - 8y = -16

we need to rewrite the equation in standard form

(x - h)² + (y - k)² = r²

First, let's group the x-terms and y-terms separately:

x² + 14x + y - 8y = -16

Decompose the equation on the left

x² + 14x = (x + 7)² - 49

y - 8y = -7y

Substituting the above expressions back into the original equation, we get:

(x + 7) - 49 - 7y = -16

Simplifying the equation:

(x + 7)^2 + 7y = 33

Now, we can rewrite the equation in standard form by completing the square again, this time for y:

(x + 7)² + 7(y - 33/7)² = 49

Comparing this with the standard form (x - h)² + (y - k)² = r², we have:

centre of the circle = (-7, 33/7)

radius = 7.

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