In studies for a medication, 14 percent of patients gained weight as a side effect. Suppose 524 patients are randomly selected. Use the normal approximation to the binomial to approximate the probabil

We are given these two numbers:

4*10^(-7) and 1.08*10^(-9).

What is similar is that they are in scientific notation, that is, the base of both is

between 1 and 9.

The difference is in the exponent. 0.0000004 is lesser than 1, so the exponent will be negative, while 1,080,000,000 is greater than 1, so the exponent will be positive.

The volume of the solid is 9 cubic units, which is determined by the base in the first quadrant bounded by the y-axis, the graph of y = x-1, the horizontal line y = 3, and the vertical line x = 1. As the cross sections perpendicular to the x-axis are squares, the volume can be calculated.

The volume of the solid can be calculated by finding the area of the base and then multiplying it by the height of the solid. The base of the solid is in the first quadrant and is bounded by the y-axis, the graph of y = x-1, the horizontal line y = 3, and the vertical line x = 1. This region forms a trapezoid, with an area of 6. As the cross sections perpendicular to the x-axis are squares, the height of the solid is 3 units. Thus, the volume of the solid is 6 multiplied by 3, which gives us a total volume of 9 cubic units. To calculate the volume, it is important to identify the base of the solid and the shape of the cross sections perpendicular to the x-axis. This will allow us to calculate the area of the base, and multiply it by the height of the solid to determine the total volume.

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Answer:

b = 2a

Step-by-step explanation:

The length of DE is equal to length CE since their corresponding angles are equal.

To prove that line DE is equal to line CE, we will take the following steps as shown below.

In the given figure;

line AD = line BC

angle ADC = angle BCD

let the line DB divide angle ADC equally and let line AC divide angle BCD equally.

then our new triangle becomes EDC

so angle EDC = angle ECD, since the angles are divided equally.

If the two angles (m∠EDC = m∠ECD), then their lengths must be equal since the triangle forms an isosceles triangle.

So length DE = length CE, proved.

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To make a volume of 320mL mixture that contains 8% vinegar, use 64mL of the first brand and 256mL of the second brand.

Let F be the volume of the first brand and let S be the volume of the second brand.

Now, we want the total mixture to be 320mL so: F + S = 310

Also, you want the total mixture to contain 12% vinegar so:

0.08F + 0.13S = 0.12(320)

Now, we can solve the system of equations using substitution method.

F + S = 320   -----(1)

0.08F + 0.13S = 0.12(320)   -----(2)

F = 320 - S      [solve 1st equation for F]

0.08(320 - S) + 0.13S = 0.12(320)     [substitute into 2nd equation]

25.6 - 0.08S + 0.13S = 38.4

0.05S = 12.8

S = 256 mL

F + 256 = 320     [substitute answer for S back into original equation]

F = 320 - 256

F = 64 mL

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Since only one box contains gold, then the gold must be in Box 2.

Let's analyze the statements in each box:

Box 1 says, "The gold is not in Box 2." If this statement is true, it means the gold cannot be in Box 2.

Box 2 says, "The gold is in this box." If this statement is true, it means the gold must be in Box 2.

Box 3 says, "The gold is not in this box." If this statement is true, it means the gold cannot be in Box 3.

Now, let's consider the possibilities:

If Box 1 is true, then the gold is not in Box 2 (as stated in Box 1), and it is also not in Box 3 (since Box 3 would be false, and only one box contains the gold).

As per Box's 1 statement, the gold is not in Box 2.

If Box 3 is true, then the gold is not in Box 3 (as stated in Box 3), and it is also not in Box 2 (since Box 2 would be false, and only one box contains the gold).

Therefore, the gold must be in Box 1.

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Answer:

The first one...............

Answer:

$21,616.26.

Step-by-step explanation:

24000 =P(1 + 0.03/4)^14

P = 24000 / (1 + 0.03/4)^14)

21,616.26.

=

The present value that will grow to ​$24000 if interest is 3​% compounded quarterly for 14 quarters is $21,482.40

To find the present value that will grow to $24,000 at 3% interest compounded quarterly for 14 quarters, we use the formula for compound interest:

\(PV = FV / (1 + r/n)^{(n*t)}\)

Where:

PV = Present Value

FV = Future Value ($24,000)

r = Annual interest rate (3% or 0.03 as a decimal)

n = Number of compounding periods per year (quarterly, so n = 4)

t = Number of years (14 quarters = 14/4 = 3.5 years)

Substitute the values into the formula:

PV = \($24,000 / (1 + 0.03/4)^{(4*3.5)}\)

PV = \($24,000 / (1 + 0.0075)^{(14)}\)

PV = \($24,000 / (1.0075)^{14}\)

PV ≈ $21,482.40 (rounded to the nearest cent)

Therefore, the present value required for it to grow to $24,000 in 14 quarters at 3% interest compounded quarterly is approximately $21,482.40.

In this explanation, we used the formula for compound interest to calculate the present value (PV). The formula accounts for the future value (FV), the annual interest rate (r), the number of compounding periods per year (n), and the time in years (t). By plugging in the given values and performing the calculations, we arrived at the present value of approximately $21,482.40.

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Answer:

\(842\ \text{ft}\)

\(y(t)=906-16t^2\)

Step-by-step explanation:

Let \(y\) be the height the object from the ground.

\(s\) be the initial height of the object = 906 ft

\(u\) = Initial velocity = 0

\(g\) = Acceleration due to gravity = \(32\ \text{ft/s}^2\)

\(t\) = Time

The expression would be

\(y(t)=s-ut-\dfrac{1}{2}gt^2\\\Rightarrow y(t)=906-16t^2\)

The required expression is \(y(t)=906-16t^2\)

At \(t=2\ \text{s}\)

\(y(2)=906-16\times 2^2\\\Rightarrow y(2)=842\ \text{ft}\)

The height of the object after 2 seconds of falling is \(842\ \text{ft}\).

Answer:

No, the litter box will overflow.

Step-by-step explanation:

first you need to find the volume of the litter box.

FORMULA:

cat litter box: V=lxWxH

V= 1 x 2 x 1/3

V= 2/3

Since the bag of cat litter has more cat litter than the litter box can hold, the answer is no. 1 ft 3 is more than 2/3 ft.

IM SORRY IF THIS DOESN'T MAKE SENSE I WAS CONFUSED BY THE 1 ft 3.

One bagel costs 155 cents.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question.

Let x = cost of one bagel

y = cost of one toast

z = cost of one muffin

If two pieces of toast and a bagel costs $3.15, then 2y + x = 3.15.

2y + x = 3.15   ⇒   x = 3.15 - 2y     (equation 1)

If a bagel and a muffin costs $3.30, then x + z = 3.30.

x + z = 3.30     (equation 2)

Substitute equation 1 to equation 2.

x + z = 3.30     (equation 2)

3.15 - 2y + z = 3.30   ⇒   z = 0.15 + 2y      (equation 3)

If a piece of toast, two bagels, and three muffins costs $9.15, then

y + 2x + 3z = 9.15     (equation 4)

Substitute equations 1 and 3 to equation 4.

y + 2x + 3z = 9.15     (equation 4)

y + 2(3.15 - 2y) + 3(0.15 + 2y) = 9.15

y + 6.30 - 4y + 0.45 + 6y = 9.15

3y = 2.4

y = 0.8

Substitute the value of y to equation 1.

x = 3.15 - 2y     (equation 1)

x = 3.15 - 2(0.8)

x = 1.55

Hence, the cost of one bagel is $1.55 or 155 cents.

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Answer:

non linear because a line goes straight this drops back down

Answer:

C

Step-by-step explanation:

There is a difference of 16 between consecutive terms, that is

259 - 243 = 275 - 259 = 291 - 275 = 16

This indicates the sequence is arithmetic with nth term

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 243 and d = 16 , then

\(a_{n}\) = 243 + 16(n - 1) = 243 + 16n - 16 = 227 + 16n → C

Answer: Let's assume the cost of 1 kilogram of bananas is represented by 'x'.

According to the given information, 4.5 kg of bananas and 3.5 kg of apples together cost £6.75. We also know that the cost of 1 kg of apples is £5.40.

Using this information, we can set up the following equation:

4.5x + 3.5(£5.40) = £6.75

Now let's solve for 'x':

4.5x + 3.5(£5.40) = £6.75

4.5x + £18.90 = £6.75

4.5x = £6.75 - £18.90

4.5x = -£12.15

x = (-£12.15) / 4.5

x ≈ -£2.70

The cost of 1 kilogram of bananas, based on this calculation, is approximately -£2.70. However, it's important to note that a negative cost doesn't make sense in this context. It's possible there may be an error in the given information or the setup of the equation.

Answer:

graph 1  

Step-by-step explanation:

Graph using table of values

x           y

2       -2/3

1         -4/3

0          -2

they are all on that graph

The graph represents a line with a slope of -2/3 and a y-intercept equal to that of the line y = 2/3x – 2 is A coordinate plane with a line passing through (negative 3, 0) and (0, negative 2).

The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx.

Using the common convention that the horizontal axis represents a variable x and the vertical axis represents a variable y, a y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system. As such, these points satisfy x = 0.

According to the question

Represents a line with a slope of -2/3  

i.e ,

m = -2/3  

y-intercept equal to that of the line

y = \(\frac{2}{3}x-2\)

i.e ,

at y-intercept , x = 0

y = -2

Now, Putting value in standard form of line

y = mx + c

-2 = 0 + c  

c = -2

now , substituting the values of m and c in standard form of line

y = mx + c  

y =  \(\frac{-2}{3}x-2\) --------- (equation of graph )

Now ,

x             y

0            -2

3/2         1

3             0

Only option 4 have these points

Hence, The graph represents a line with a slope of -2/3 and a y-intercept equal to that of the line y = 2/3x – 2 is A coordinate plane with a line passing through (negative 3, 0) and (0, negative 2).

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Answer:

it would take them 4 days to build the house

Answer:

Step-by-step explanation:

Well, the midpoint formula is M=((x↓1 +x↓2)/2,(y↓1 +y↓2)/2 ). (not exponents, they tell you which x or y value).

If you plug in your 2 points, it becomes m=((2+0)/2,(6+2)/2).

When you add, it is m=(2/2, 8/2)

When simplified, it is m=(1,4)

Answer:

224

Step-by-step explanation:

im pretty sure its right

Answer:

173.2 cm²

Step-by-step explanation:

Use the equilateral triangle area formula, A = \(\frac{\sqrt{3}}{4}\)a²

Plug in the side length and solve:

A = \(\frac{\sqrt{3}}{4}\)a²

A = \(\frac{\sqrt{3}}{4}\)(20)²

A = \(\frac{\sqrt{3}}{4}\)(400)

A = 173.2

So, the area of the triangle is approximately 173.2 cm²

The first integral to evaluate the volume of the tetrahedron is \(\int\limits\int\limits \int\limits R dV\). The integral that represents the volume in the order dx dy dz is \(\int\limits\int\limits \int\limits R dz dy dx\).

(a) Evaluating the integral ∫∫∫ R dV:

The limits of integration for z will be determined by the intersection of the plane and the coordinate axes. When x = 0 and y = 0, we have 12(0) + 4(0) + 3z = 12, which gives z = 4. When z = 0, we have 12x + 4y + 3(0) = 12, which gives 12x + 4y = 12. Dividing by 4, we get 3x + y = 3, which represents the line in the xy-plane.

To find the limits of integration for y, we need to consider the bounds of this line. When x = 0, we have y = 3; when x = 1, we have y = 0.

Finally, the limits of integration for x will be 0 to 1, as we are in the first octant.

So, the first integral to evaluate the volume is \(\int\limits^1_0 \int\limits^0_3 \, \int\limits^{({12-3x-4y} )}_4 \, dz dy dx.\)

(b) Writing the integral in the order dx dy dz:

The limits of integration for x will be determined by the intersection of the plane and the coordinate axes.

When y = 0 and z = 0, we have 12x + 4(0) + 3(0) = 12, which gives x = 1.

When x = 0, we have 12(0) + 4y + 3z = 12, which gives 4y + 3z = 12.

Dividing by 4, we get \(y + (\frac{3}{4})z = 3\), which represents the line in the yz-plane.

To find the limits of integration for y, we need to consider the bounds of this line. When z = 0, we have y = 3; when z = 4, we have y = 0.

Finally, the limits of integration for z will be 0 to 4, as we are in the first octant. Therefore, the integral that represents the volume in the order dx dy dz is:

\(\int\limits^1_0\int\limits^{4(1-(3/4)z}_{3}\int\limits^{12-4y-(3/4)z}_0 \, dx dy dz\).

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Answer:

(0,1)

Step-by-step explanation: going down 4 times would make it (0,7). Then going right 6 times would make it (0,1) hope I was right :>

you divide by 3 each time

With a critical value of 1.96 and a margin of error of 0.022, the standard error is 0.011.

To find the standard error, we can use the formula for the margin of error, which is:
Margin of Error = Z* × Standard Error
Given that the margin of error is 0.022 and the critical value (Z*) is 1.96, we can rearrange the formula to find the standard error:
Standard Error = Margin of Error / Z*
Standard Error = 0.022 / 1.96
Standard Error = 0.011224
Rounded to three decimal points, the standard error is 0.011.

Given a confidence interval with a critical value of 1.96 and a margin of error of 0.022, the standard error is approximately 0.011.

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Answer:

13. After 25 days

14. 68-77 degress

Step-by-step explanation:

13.

100*3= 300

300-100= 200

200/8= 25

Answer:

The answer to the first question is 25 days. The range of temperatures is 68 - 77. Hope this is helpful! =)

Step-by-step explanation:

In linear equation, 57 cents per cubic foot  should clint charge for a cubic foot .

What are a definition and an example of a linear equation?

cubic meter =  [3.28 ft ]^3  ≈ 35.29 cubic feet

So,

 price [ in cents] / 35.29  cubic feet  = 2000 / 35.29  ≈  57 cents per cubic foot

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Answer:

Step-by-step explanation:

25% = 1/4 of 100

100 represents 200 people here, that means that if 25 = 1/4 to 100, then it is 1/8 to 200. 25x8=200

If 25% = 50, since 50x4=200 and 1/4 = 25% of 100%.

50... ok......

50 = 25%

Now, because there are 5 parts in 25, let's divide 5 by 50, that is 10. That means that 5 = 10 in that 50. 5% = 10 people

So, if 25-15=10

and then 5% = 10 people

5%+5%=10

10+10=20

That means, that 20 people more liked the movie than disliked it.

Answer: angle 5 and angle 10

angle 8 and angle 11

hope this helps!

Answer:

\( \boxed{ \tt{j} = \boxed{\tt 13.5}}\)

Step-by-step explanation:

Given equation:

\( \sf \cfrac{j}{ \tt3} = \tt 4.5\)

To find:

Value of x

Solution:

\( \implies\sf \cfrac{j}{ \tt3} = \tt 4.5\)

Multiply both sides by 3:

\(\sf \implies \cfrac{j}{3} \times 3 = 4.5 \times3\)

Use cancellation method to cancel LHS :

\( \sf \implies \cfrac{j}{ \cancel3 \: {}^{1} } \times \cancel3 \: {}^{1} = 4.5 \times 3 \: \: \)

\(\sf \implies{j} \times 1 = 4.5 \times 3\)

\(\sf \implies{j} = 4.5 \times 3\)

Now Multiply the RHS(4.5 and 3):

\( \sf \implies{j} = \boxed{13.5}\)

We're done!

Hence , the value of j would be 13.5 .

\( \rule{225pt}{2pt}\)

I hope this helps!

Let me know if you have any questions.