Explain the difference:

4 times the sum of x and y and the sum of 4 x and y

Answer:

To find the number of federally insured banks in 1985, we need to substitute t = 1985 into the equation B(t) = -328.2t + 13716:

B(1985) = -328.2 * 1985 + 13716

B(1985) = -648537 + 13716

B(1985) = 7122

So, there were approximately 7122 federally insured banks in 1985.

The slope of the graph of B represents the rate of change. From the equation B(t) = -328.2t + 13716, we can see that the slope is -328.2. Therefore, the interpretation of the slope as a rate of change is: "The number of banks decreased by 328.2 banks per year."

The y-intercept of the graph of B represents the value of B when t = 0, which corresponds to the year 1980. From the equation B(t) = -328.2t + 13716, the y-intercept is 13716. Therefore, the interpretation of the y-intercept is: "The y-intercept is the number of banks in 1980."

The surface area of the sphere is 98 yd².

To find the surface area of a sphere, we can use the formula:

Surface Area = 4πr²

Given that the radius, r, of the sphere is 7/3.14 yd, we can substitute this value into the formula:

Surface Area = 4 x 3.14 x (7/3.14)²

= 4 x 3.14 x 49/9.86

= 4 x 49/2

= 98 yd²

Therefore, the surface area of the sphere is 98 yd².

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Hello !

Answer:

[tex]\Large \boxed{\sf length=13cm}[/tex]

Step-by-step explanation:

The volume of a pyramid is given by [tex]\sf V_{pyramid}=\frac{1}{3} \times B\times h[/tex] where B is the area of the base and h is the height.

This is a rectangular pyramid. We have where [tex]\sf B=l\times w[/tex] l is the length and w is the width (breadth).

So [tex]\sf V_{pyramid}=\frac{1}{3} \times l\times w\times h[/tex]

Given :

Let's replace h, w, l, [tex]\sf V_{pyramid}[/tex] with their values in the previous formula :

[tex]\sf 728=\frac{1}{3} \times x\times 8 \times 21\\728=56x[/tex]

Let's solve for x !

Divide both sides by 56 :

[tex]\sf \frac{56x}{56} =\frac{728}{56}\\ \boxed{\sf x=13cm}[/tex]

Have a nice day ;)

Answer:

$27.01

Step-by-step explanation:

100% + 19.3% = 119.3%.

$32.22 = 119.3%

divide both sides by 119.3:

(32220/1193) = 1

multiply by 100 to get 100% ie the bill before the tip:

$27.01 = 100%

$27.01 is bill to nearest cent

Answer:

Step-by-step explanation:how many grams of active dry yeast must be used for bread recipe

Hello!

Event A:

is a 5 or 6 = 2 numbers on 6 = 2/6 = 1/3

EventB:

is not a 1 = 2,3,4,5,6 = 5/6

P(A and B) = 1/3 x 5/6 = 1x5/3x6 = 5/18 ≈ 0.28

The answer is 0.28.

Answer:

288in³

Step-by-step explanation:

volume for one = 12 X 6 X 2 = 144.

for two books, it is 2 X 144 = 288in³

The angle relationship between DCA and BCA is that they are congruent.

In Mathematics and Geometry, an angle bisector is a type of line, ray, or segment, that typically bisects or divides a line segment exactly into two (2) equal and congruent angles.

Generally speaking, the diagonals of a rhombus are angle bisectors. In this context, we can logically deduce that the two (2) angles that would result from the bisection of angle C by a straight line are congruent.

By applying the angle bisector theorem to the given square sign (rhombus ABCD) below, we would have the following congruent angles;

∠DCA ≅ ∠BCA

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Ki traveled at an average speed of approximately 41.05 miles per hour without any stops.

To calculate the average speed at which Ki traveled from Memphis to Atlanta, we can use the formula:

Average Speed = Total Distance / Total Time

First, let's calculate the total time taken for the journey. Ki started from Memphis at 5:30 am and arrived in Atlanta at 3:00 pm, which is a total of 9.5 hours.

Next, we divide the total distance traveled, which is 391 miles, by the total time taken, which is 9.5 hours:

Average Speed = 391 miles / 9.5 hours

Calculating this, we find that Ki's average speed was approximately:

Average Speed ≈ 41.05 miles per hour

Therefore, Ki traveled at an average speed of approximately 41.05 miles per hour without any stops.

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Answer:

30/.06 =500

Step-by-step explanation:

30÷6/100

==>

30*100/6

=500

For the expression  [tex]x^2^/^4x^3^/^6[/tex] the value of exponent of x is 1.

8ab²√5a is the simplified form of the expression 4√20a³b⁴ .

The given expression is [tex]x^2^/^4x^3^/^6[/tex]

x is the variable in the expression.

We know that when bases are same in the product then the powers will be added.

[tex]x^1^/^2^+^1^/^2[/tex]

When 1/2 and 1/2 are added we get 1.

So the value of r is 1.

Now 4√20a³b⁴ is the expression.

4√4×5a².a.b².b²

4.2.ab²√5a

8ab²√5a is the simplified form of the expression.

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The solution to the system of equations is x = 2 and y = -1.

To solve the system of equations:

2x - 5y = 9 ...(1)

3x + 4y = 2 ...(2)

Multiplying equation (1) by 4 and equation (2) by 5, we can eliminate the variable 'y':

8x - 20y = 36 ...(3)

15x + 20y = 10 ...(4)

Adding equation (3) and equation (4), the 'y' terms cancel out:

(8x - 20y) + (15x + 20y) = 36 + 10

23x = 46

Dividing both sides of the equation by 23, we find:

x = 2

Plugging the value of 'x'

2(2) - 5y = 9

4 - 5y = 9

Subtracting 4 from both sides of the equation:

-5y = 9 - 4

-5y = 5

y = -1

Therefore, the solution to the system of equations is x = 2 and y = -1.

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Answer:

The area bounded by the two functions f(x) and g(x) on the interval [0, 2π] is 6π.

Step-by-step explanation:

The range of y = sin(2x) is [-1, 1].

As function f(x) = sin(2x) + 1 has been translated 1 unit up, the range of f(x) is [0, 2].

The range of y = cos(x) is [-1, 1].

As function g(x) = cos(x) - 2 has been translated 2 units down, the range of g(x) is [-3, -1].

As ranges of the functions do not overlap, the two functions do not intersect.

As the curve of f(x) is above the x-axis, and the curve of g(x) is below the x-axis, we can integrate to find the area between the curve and the x-axis for each function in the given interval, then add them together.

Note: As g(x) is below the x-axis, the evaluation of the integral will return a negative area. Therefore, we need to negate the integral so we have a positive area (since area cannot be negative).

[tex]\begin{aligned}A_1=\displaystyle \int^{2\pi}_{0} (\sin(2x)+1)\; \text{d}x&=\left[-\dfrac{1}{2}\cos(2x)+x \right]^{2\pi}_{0}\\\\&=\left(-\dfrac{1}{2}\cos(2(2\pi))+2\pi\right)-\left(-\dfrac{1}{2}\cos(2(0))+0\right)\\\\&=\left(-\dfrac{1}{2}+2\pi\right)-\left(-\dfrac{1}{2}\right)\\\\&=2\pi\end{aligned}[/tex]

As the curve is below the x-axis, remember that we need to negate the integral to find the area.

[tex]\begin{aligned}A_2=-\displaystyle \int^{2\pi}_{0} (\cos(x)-2)\; \text{d}x&=-\left[\vphantom{\dfrac12}\sin(x)-2x \right]^{2\pi}_{0}\\\\&=-\left[(\sin(2\pi)-2(2\pi))-(\sin(0)-2(0))\right]\\\\&=-\left[(0-4\pi)-(0-0)\right]\\\\&=-\left[-4\pi\right]\\\\&=4\pi\end{aligned}[/tex]

[tex]\begin{aligned}A_1+A_2&=2\pi+4\pi\\&=6\pi\end{aligned}[/tex]

Therefore, the area bounded by the two functions f(x) and g(x) on the interval [0, 2π] is 6π.

Answer:

Step-by-step explanation:

9 is dependent 6 is independent

Answer:

$81.18

Step-by-step explanation:

Sale Price = Original Price - (Original Price * Discount Percentage)

Given:

Original Price = $82

Discount Percentage = 10%

Let's calculate the sale price:

Sale Price = $82 - ($82 * 10%)

Sale Price = $82 - ($82 * 0.1)

To simplify the calculation, we can convert 10% to its decimal form by dividing by 100:

Sale Price = $82 - ($82 * 0.1)

Sale Price = $82 - ($82 * 0.01)

Sale Price = $82 - $0.82

Using a calculator, we can find the value:

Sale Price = $81.18

Therefore, the sale price after a 10% discount would be $81.18.

Answer: $73.80 is sale price

Step-by-step explanation:

Original: $82

10% of 82

=.1(82)

=8.2       >this is your discount

Subtract

82-8.2

$73.80 is sale price

The revised Doubtful Debts Provision should be, $4,555.

Now, Using a net debtors value of $91,100 and a provision rate of 5%, use the calculation to get the adjusted Provision for Doubtful Debts (PDD):

Net Debts x Provision Rate equals Adjusted PDD.

The computation would then be:

= $91,100 x 0.05

= $4,555 is the adjusted PDD.

Because of the additional $550 in bad debt and the revised net debtors value of $91,100, the Provision for Doubtful Debts must be raised by ,

= $4,555 - $3,500

= $1,055

Hence, The revised Doubtful Debts Provision should be $4,555.

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Option B has the highest overall cost by $64.50.

To determine the option that would result in the highest overall cost for the employee

we need to compare the costs of both options based on the estimated prescription drug expenses.

Option A:

Monthly premium: $94

Prescription coverage: 80%

Option B:

Monthly premium: $42

Prescription coverage: 75% for the first $500, 85% for costs over $500

Let's calculate the costs for each option:

Option A:

Total prescription drug cost: $1,250

Employee's share (20%): 20% × $1,250 = $250

Monthly premium: $94

Total cost for Option A: $250 + $94 = $344

Option B:

Total prescription drug cost: $1,250

Employee's share for the first $500 (25%): 25% × $500 = $125

Employee's share for costs over $500 (15%): 15% × ($1,250 - $500) = $112.50

Monthly premium: $42

Total cost for Option B: $125 + $112.50 + $42 = $279.50

Comparing the total costs for each option, we see that Option B has a lower overall cost for the employee.

Hence, Option B has the highest overall cost by $64.50.

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The sale price of a pillow originally priced at 12 dollars is given as follows:

$9.

The sale price of a pillow originally priced at 12 dollars is obtained applying the proportions in the context of the problem.

The original price is given as follows:

$12.

The markdown rate for this problem is given as follows:

25%.

Hence the sale price of a pillow originally priced at 12 dollars is given as follows:

0.75 x 12 = $9.

(markdown of 25% means that 75% of the price is paid).

The complete problem is:

"A pillow was marked down at 25%. What is the sale price of a pillow originally priced at 12 dollars?"

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To calculate the volume of a cylinder, we use the formula:

Volume = π * radius^2 * height

Given:

Radius = cm

Height = 4 cm

π (pi) = 3.14

Let's substitute these values into the formula and calculate the volume:

Volume = 3.14 * (cm)^2 * 4 cm

= 3.14 * (cm^2) * 4 cm

= 12.56 * cm^3

Rounding the answer to the nearest tenth, we get:

Volume ≈ 12.6 cm^3

Among the answer choices provided, the closest option to 12.6 cm^3 is:

B. 28.3 cm^3

Therefore, the correct answer is B. 28.3 cm^3.

Answer:

7) No

8) Yes

9) Yes

Step-by-step explanation:

Plug each possible solution into the inequality and see if it holds true:

If x=1 (Not a solution)

[tex]\displaystyle 3(1)-2\stackrel{?}{ < }2-2(1)\\3-2\stackrel{?}{ < }2-2\\1\nless0[/tex]

If x=1/2 (Is a solution)

[tex]\displaystyle 3\biggr(\frac{1}{2}\biggr)-2\stackrel{?}{ < }2-2\biggr(\frac{1}{2}\biggr)\\\frac{3}{2}-2\stackrel{?}{ < }2-1\\\\\frac{1}{2} < 1[/tex]

If x=1/3 (Is a solution)

[tex]\displaystyle 3\biggr(\frac{1}{3}\biggr)-2\stackrel{?}{ < }2-2\biggr(\frac{1}{3}\biggr)\\1-2\stackrel{?}{ < }2-\frac{2}{3}\\\\-1 < \frac{4}{3}[/tex]

Answer:

When you cut the sample size in half while making a statistical inference about the mean of a normally distributed population, the effect on the margin of error depends on the relationship between the sample size and the margin of error. Generally, the margin of error is inversely proportional to the square root of the sample size.

So, if you reduce the sample size by half, it means you are taking a smaller sample, which will result in a larger margin of error. In other words, the margin of error is multiplied by a factor greater than 1.

Among the given options, the correct answer is:

D. The margin of error is multiplied by 2.

This option correctly reflects the relationship between reducing the sample size by half and the resulting increase in the margin of error.

The conical base of the silo provides stability and structural integrity, enabling the company to offer reliable storage solutions for grains. It optimizes space utilization and supports easy handling and retrieval of stored grains.

The silo manufactured by the company features a conical base, as depicted in the drawing. The given dimensions are as follows: the height is 8.5 feet, the length measures 4 feet, and the width is 13 feet.

The height of 8.5 feet refers to the vertical distance from the base of the silo to the top of the conical base. It represents the overall height of the silo structure.

The length of 4 feet represents the measurement from one side of the conical base to the other. This dimension determines the diameter of the circular base of the silo.

The width of 13 feet signifies the measurement from the front to the back of the conical base. It determines the circumference of the circular base of the silo.

With these dimensions, the silo exhibits a conical shape, where the circular base gradually tapers towards the top. This design is well-suited for storing grains, as it allows for efficient distribution of pressure and facilitates the flow of grains during loading and unloading processes.

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Evaluating the piecewise function we will get:

g(-1) = -2

g(2) = 0

g(3) = 1/2

To evaluate the piecewise function we need to use the correct part depending on the domains.

g(-1), here x = -1, then we need to use the second part of the function:

g(-1) = -(-1 - 1)² + 2 = -4 + 2 = -2

For the second one x = 2, we use the last part:

g(2) = (1/2)*2 - 1 = 0

For the last one, we have x = 3, again we need to use the last part:

g(3) = (1/2)*3 - 1 = 3/2 - 2/2 = 1/2

These are the 3 values.

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Answer: [tex]=\frac{2x}{x-3}[/tex]  

Step-by-step explanation:

 [tex]\frac{2x^{2} +10x}{x^{2} + 2x-15}[/tex]                        >Take out GCF(greatest common factor) on top

                                       >factor the bottom,  find 2 numbers that mulitply to

                                         "c" term, -15 and adds to the "b" term, +2

                                        >+5 and -3 mulitpy to -15 and add to +2

                                        > put +5 and -3 into factored form on bottom

[tex]=\frac{2x(x+5)}{(x-3)(x+5)}[/tex]                      >reduce the x+5 on top and bottom

[tex]=\frac{2x}{x-3}[/tex]                                >This is simplified

Answer: The radius of the circle rounded to the nearest integer is 11 cm

Step-by-step explanation:

To resolve this issue we can utilize the properties inherent to circles along with Pythagoras' theorem while denoting our circle's radius as "r".

Given that we know of a chord of length equaling up to 18 cm placed at a distance measuring exactly 6.3 cm away from the center of our circle sketching out a diagram would make it easier for us to visualize such a situation. Once visualizing this problem statement through our aforementioned diagram we may approach it using Pythagoras' theorem and examine the components regarding the right-angled triangle formed by half-length chord radius "r" and distance between center and chord respectively.

Our calculations factor in measurements representing half of our chords length (which is equal to precisely 9cm) alongside distances measuring up to exactly 6.3cm while possessing "r" on one end as shown below:

r^2 = (6.3cm)^2 + (9cm)^2

Simplifying said equation leads us to have:

r^2 =39.69cm^2+81cm^2

r²=120.69cm²

Calculating square roots on both sides leads us towards the approximation of r equaling around:

r ≈ √120.69cm²

r ≈10.99cm

Therefore rounding off R towards its nearest whole number would give us R=11cm in this case scenario.

Answer:

x = 6 , y = 4

Step-by-step explanation:

for the figure to be a parallelogram , the opposite sides must be congruent, that is

5y = 20 ( divide both sides by 5 )

y = 4

and

2(x + y - 1) = x + 3y ← distribute parenthesis on left side by 2

2x + 2y - 2 = x + 3y ← substitute y = 4

2x + 2(4) - 2 = x + 3(4)

2x + 8 - 2 = x + 12

2x + 6 = x + 12 ( subtract x from both sides )

x + 6 = 12 ( subtract 6 from both sides )

x = 6

Answer will be 27.

Given,

3√81

Now, to solve the expression the squares of whole numbers and square roots for some numbers must be known.

For example, squares of

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81
10² = 100

Square roots,

√100 = 10

√81 = 9

√64 = 8

√49 = 7

√36 = 6

√25 = 5

√16 = 4

√9 = 3

√4 = 2

√1 = 1

Now ,

3√81 = 3× 9

= 27.

Thus the value is 27.

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