(b) Work out the value of (2.3 × 10³) × (5.9 × 105)
Give your answer in standard form.

To do the multiplication, we multiply 0.63 by each of the digits & decimal places of 0.24 (and align the products that we get) then add them together.

0.63 x 4 = 2.52, therefore the first missing spot is a 2.

0.63 x 2 = 1.26, therefore the second missing spot is a 2 (the 0 is so that the decimal point can be aligned for the result.)

Answer: Box 1: 2 Box 2: 2

Step-by-step explanation:

So, for box one it would be 2 because 3 x 4 = 12, put the 2 on the bottom and the 1 on the 6, then 6 x 4 + 1 = 25, then put the 5 on the bottom and the 2 on the top, then 4 x 0 + 2 = 2, so the answer would be 2.

For box 2, 252 + 1?60 = 0.1512, so we have to find the missing number. So, 2 + 0 = 2, so put the two on the bottom, then 5 + 6 = 11, so put the 1 on the bottom and the other 1 on the 2 from the first box, so 2 + 1 = 3, plus 2 more would equal 5, so the second box would be 2.

Hope this helps!

Zimbardo did not use a control group. Experiments are performed to reach meaningful conclusions using the appropriate research method. The correct answer is (A).

Experiments whether they are done in natural settings or in a controlled environment need to follow certain ethics. But the Stanford Prison Experiment is an exception. In this experiment, Philip Zimbardo, the Stanford psychologist, took paid participants and asked them to be “guards” in a mock prison at Stanford University.

As soon as the experiment began, the “guards” began mistreating the “prisoners,” in order to provoke evil circumstantially. The conclusion of the study suggested innocent people, thrown into a situation where they have power over others, will begin to misuse that power. And people who are put into a situation where they are powerless will be driven to submission.

The Stanford Prison Experiment has proved to be a Fraud. Philip Zimbardo, the Stanford psychologist who did the experiment, and interviews of the participants, offers convincing evidence that the guards in the experiment were trained to be cruel. This proves that the experiment’s most memorable moment of a prisoner screaming out of rage and proclaiming, “I’m burning up inside!” was the result of the prisoner's acting skills. Many of them think of this study as more of a dramatic demonstration with no real outcomes. The Zimbardo prison experiment is a classic study that has been recently reevaluated and exposed as a fraud.

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1) Radius of the standard tank = 3 feet

2) Existing volume for the tank is 126[tex]\pi[/tex] cubic feet.

3) Sphere volume for the tank is 36[tex]\pi[/tex] cubic feet.

4)Total volume of the tank is  36[tex]\pi[/tex] + 126[tex]\pi[/tex] = 162[tex]\pi[/tex] cubic feet

5) New volume for the tank is 252[tex]\pi[/tex] cubic feet.

6)Trails of values for r is 4 feet.

What do you mean by Volume?

A three-dimensional object's volume, expressed in cubic units (such as inches, quarts, or centimeters): cubic volume. the volume that a material takes up in a given space.

What is radius?

A line segment connecting the circumference or boundary surface of a circle or sphere to its center.

Given that;

Volume of the standard tank [tex]= \pi r^2h + \frac{4}{3} \pir^3[/tex]

                                                [tex]= \pi 3^2h + \frac{4}{3} \pi3^3\\= 90\pi +36\pi\\= 126\pi \ cubic \ feet[/tex]

Volume of new tank = 2 x Volume of standard tank

                                  =  2 x 126π

                                  = 252π

But according to formula, volume of new tank will be;

[tex]V = \pi r^2h + \frac{4}{3}\pir^3[/tex]

where r = radius of new tank

[tex]\pi r^2 \times 10 + \frac{4}{3} \pi r^3 = 252 \pi\\30r^2 +4 r^3 = 756\\2r^3 + 15r^2-378 = 0\\r = 4.04591\\r \approx 4 feet[/tex]

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The probability that the sample mean selling price was more than $210,000 is 0.9772.

The given values are:

The mean selling price(μ) = $215000

Standard deviation(σ) = $25000

The random sample (n) = 100

We have to find the probability that the sample mean selling price was more than $210000.

z-score with z-bar= 210000

z = (x-bar - μ) / (σ/ √n)

 = ( 210000 - 215000) / (25000/ √100)

 = -5000/ 2500

 =-2

Using z-tables, the probability is:

Probability = P[z> -2]

                  = 1 - 0.0228

                  = 0.9772

Therefore the probability is 0.9772.

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A minimum of 71 observations must fall inside the interval (20, 40).

It is true that Chebyshev's Theorem holds true for all conceivable data sets. The minimal percentage of measurements that must fall within one, two, or more standard deviations of the mean is described. The minimum percentage of observations that are within a given range of standard deviations from the mean is calculated using Chebyshev's Theorem. Numerous other probability distributions can be applied with this theorem. Chebyshev's Inequality is another name for Chebyshev's Theorem.

Given,

The data set has 80 observations and has mean 30 and standard deviation 5.

Chebyshev's theorem states that for each data set, the proportion (or percentage) of values ​​that lie within k standard deviations of the mean (that is, the interval (x -ks , x +ks) is at least 1-1/k² . where k > 1.

x = 30

s = 5

Three standard deviations are added to and subtracted from the mean to get the interval (10, 40).

(30 - 3.5, 30 + 3.5) = (10, 40)

According to Chebyshev's Theorem, this interval contains at least 1 -1/3² = 8/9 of the data. Given that 8/9 of  80 is 71.11, the interval must include at least 71.11 observations. However, one cannot make a fractional observation, so we draw the conclusion that the interval must contain at least 71 observations.

A minimum of 71 observations must fall inside the interval (20, 40).

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The surface area of the triangular prsim is 290.4 in² and the right option is B. 290.4 in².

Surface area is the space occupied by a two-dimensional flat surface is called the area. It is measured in square units.

To calculate the surface area of the triangular prism, we use the formula below.

Fromula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the right option is B. 290.4 in².

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The distance up the house the ladder will reach after pulling it 10 feet further from the base of the house is 43.9 ft.

The ladder is set against the side of the house so that it reaches up 48 feet.  Shaniece grabs the ladder at its base and pulls it 10 feet farther from the house.

The height of the ladder on the house can be computed as follows:

The situation form two right angle triangle.

The initial distance of the base of the ladder from the house can be calculated as follows;

using Pythagoras's theorem,

b² = 50² - 48²

b = √2500 - 2304

b = √196

b = 14 ft.

Therefore, the initial distance of the ladder from the base of the house is 14 feet.

Let's find the height of the ladder on the house after pulling it 10 ft further.

using Pythagoras's theorem,

b² = 50² - 24²

b = √2500 - 576

b = √1924

b = 43.8634243989

b = 43.9 ft

Therefore,

height of the ladder up the house = 43.9 ft

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(a) The nth term of the sequence is given by A(n)=195 + (n - 1)10.

(b) The 12th term of the sequence is A(12) = 305.

One arithmetic progression with a common difference of 2 is the sequence 5, 7, 9, 11, 13, 15,...

The term "finite arithmetic progression" or "arithmetic progression" refers to a limited segment of an arithmetic progression.

A mathematical sequence has the following structure: a, a+d, a+2d, a+3d, etc., up to n terms. The initial term is a, the shared distinction is d, and n is the total number of words. Find the AP, the first term, the number of terms, and the common difference for the computation using the arithmetic sequence formulae. To determine the nth term, sum, or common difference of a given arithmetic sequence, many formulae related to arithmetic series are utilized.

A(n)=195+(n-1)10

The given arithmetic sequence is 195, 205, 215, 225,.....

The first term a =195

The common difference d= 205-195

d =215-205

d =225-215

So, d = 10

(a) The nth term is given by

A(n)=a+(n-1)d

A(n)=195+(n-1)10

(b) For n=12, the 12th term is given by

A(12)=195+11(10)

A(12)=305

Therefore, A(n)=195+(n-1)10

And A(12)=305

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Answer:

Step-by-step explanation:

The rate of the plane in still air is a = 1170 km/hr, and the rate of the wind is w = 210 km/hr.

The distance covered in a unit of time is known as speed.

Given that, the airplane travels 7680 km in 8 hours flying against the wind, and 12420 km in 9 hours.

Therefore, the rate of the airplane against the wind is:

7680/8

= 960 km / hr

The rate of the airplane with the wind is:

12420/9

=1380 km / hr

Let the rate of the airplane in still air be a and the rate of the wind be w.

The net rate while flying against the air is:

a - w = 960       (1)

The net rate while flying with the wind is:

a + w = 1380      (2)

Add equations (1) and (2):

2a = 2340

a = 1170 km/hr

Substitute a = 1170 into equation (1):

1170 - w = 960

1170 - 960 = w

210 = w

Hence, the rate of the plane in still air is a = 1170 km/hr, and the rate of the wind is w = 210 km/hr.

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The absolute value function graphed in this problem is given by the rule presented as follows:

y = |x - 3| + 5.

The first step to obtain the graph of an absolute value function is obtaining the vertex of the function, which is the turning point of the curve in the format of V.

Then, the definition of an absolute value function with vertex (h,k) is defined by the equation presented as follows:

y = |x - h| + k.

For the graphed function, the coordinates of the vertex are given as follows:

(3,5).

The reason for these coordinates are as follows:

Considering the coordinates of the vertex obtained previously on the problem, the absolute value equation graphed is defined by:

y = |x - 3| + 5.

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We have coordinates (-2, -3) and (1, 1)

To find: Slope of a line that passes through these two coordinates

Let (-2, -3) be (x₁ , y₁) and (1, 1) be (x₂, y₂)

We will use the formula of Slope :

m = y₂ - y₁ / x₂ - x₁

Where 'm' stands for slope

m = 1 - (-3) / 1 - (-2)

m = 1 + 3 /  1 + 2

m = 4 / 3

The slope of the line is  4/3

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Answer:

6666667

Step-by-step explanation:

Answer: The answer is C: No solution

Step-by-step explanation:

By squaring the other side (to therefor remove the square off X) you get [tex]x-3=x+6\sqrt{x} +9[/tex]

You then cancel out the equal terms, in this case x, to reach the equation:

[tex]-3=6\sqrt{x} +9[/tex]

This equation, has no solution, as the left side is always negative, and the right side will always be positive, making any statement for x false.

The value of the expression when a=2 and b=7 is 41.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

From the information, the expression given is 3a + 5b and we want to find the value of the expression when a=2 and b=7.

This will be illustrated thus:

= 3a + 5b

= 3(2) + 5(7)

= 6 + 35

= 41

The value is 41.

The complete question is given below.

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Complete question

The expression given is 3a + 5b. Find the value of the expression when a=2 and b=7

Step-by-step explanation:

4(2x-17) = 4x+(-5)

Open the bracket

8x - 68 = 4x - 5

Collect like terms

8x - 4x = -5 + 68

2x = 63

x = 63/2

x = 31.5

Using the concepts of probability, we got 0.5 is the probability of drawing the sum $20 or more when  two bills are drawn randomly without replacement.

We have an envelope contains 8 bills;

Two of $1 bills, Two of $5 bills, Two of $10 bills, Two of $20 bills.

When two bills are drawn randomly without replacement, we have to find the probability that their sum is $20 or more.

Total  outcomes = 2 x 2 x 2 x 2 = 16

Total possible outcomes, more than 20;

(1, 20), (20, 1), (5, 20), (20, 5), (10, 10), (20, 10), (10, 20), (20, 20) = 8 cases

That is,

The total possible outcomes is 8.

Now,

The probability of bill to be $20 or more = Possible outcome / Total outcome

Probability = 8/16 = 1/2=0.5

Hence, When two bills are drawn randomly without replacement,  the probability that their sum is $20 or more is 0.5.

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(Complete question)

an envelope contains eight bills: 2 ones, 2 fives, 2 tens, and 2 twenties. two bills are drawn at random without replacement. what is  the probability that their sum is $20 or more?

Answer: positive

Step-by-step explanation:

123 1/23 + (-123 1/23)

123 1/23 - 123 1/23 = 0

0 is a positive number and not negative so the answer is negative

The solution for u in the expression given as 7/u = 3/11 is u = 25.7

From the question, the algebraic expression is given as

7/u = 3/11

There is no constant to add to or subtract from the expression

So, the equation remains the same

7/u = 3/11

Multiply both sides of the equation by u

This gives

u * 7/u = 3/11  * u

Evaluate the products

So, we have the following equation

7 = 3/11u

Multiply both sides of the equation by 11/3

This gives

11/3 * 7 = 3/11u * 11/3

Evaluate the products in the above expression

77/3 = u

So, we have

25.6667 = u

Approximate

25.7 = u

Rewrite as

u = 25.7

Hence, the solution is u = 25.7

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The length of the x is 4.8 units

In the given figure

There is one circle and 2 chords

The chord of the circle is defined as the line segment joining any two points one the circumference of the circle

There are two chords in the figure, those are BD and AC

We know that

DE × EB = AE × EC

This is the rule of chords in the circle

The length of DE = 10 units

The length of EB = x units

The length of AE = 6 units

The length of EC = 8 units

Substitute the values in the equation

10 × x = 6 × 8

10x = 48

x = 48/10

x = 4.8 units

Hence, the length of the x is 4.8 units

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The equation D show the multiplication property of inequality if n+4 =11

What is inequality?

inequality, In mathematics if a statement of an order relationship—greater or greater than or equal to, less than, or less than or equal between two number or algebraic expressions.

An inequality show the relationship between two values in an algebraic equations that are not equal.

Sol-

If n+4 =11

Then by applying the product rule -

(n+4)×2 =11×2

So the correct option is D.

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No , Sydney does not have enough beads to make 15 rings .

beads required for one ring = 60

total rings she have to make is = 15

total beads she has to make rings = 852 beads

now,

60 beads make ring = 1

852 beads make rings = 1/60 x 852

                                     =    14.2 rings

                             OR

                          14 total rings

So , Sydney does not have enough beads to make 15 rings . she can only make 14 beads from the given amount of beads.

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The rectangle's area is growing at a rate of 170 cm per second.

Given that,

Area of Rectangle given by.

A = length x width

A = LW

L =length of Rectangle

W =width of Rectangle

Now, dA/dt = W dl/dt + l dw/dt

dA/dt is the rate of change of area of the rectangle

dl/dt is the rate of change of length of the rectangle

dw/dt is the rate of change of width of the rectangle

at  L = 40cm, W= 15 cm

dw = 2 cm/s,

dl = 6 cm/s,

dA = ?

dA/dt = W dl/dt + l dw/dt

         = 15x6 + 40x2

         = 90 +80

          =170 cm /sec

Thus, the area of the rectangle increasing at 170 cm /sec

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The compound interest calculated for 10 years annually, semi-annually, quarterly, monthly, and daily are (a) $2195.05,  (b) $2206.18  (c) $2211.88 (d) $2215.75, and, (e) $2217.63

The formula for Compound Interest is

Amount = Principal X (1 + r/n100)ⁿˣ

where,

Principal = original mount

n = no. of times the interest is applied

t = time period

Here,

Principal = $1400

x = 10

r = 4.6

a)

Since it is compounded annually, the interest will be given 10 times in 10 years. therefore, once a year

Hence,

n = 1

Amount = 1400 X (1 + 4.6/100)¹⁰

= 1400 X (104.6/100)¹⁰

= 1400 X (1.046)¹⁰

= $2195.05

b)

Since the interest is compounded semi-annually here, it will be calculated twice a year.

Hence, n = 2

Therefore we get

Amount = 1400 X (1 + 4.6/200)²⁰

= 1400 X (204.6/200)²⁰

= 1400 X (1.023)²⁰

= $2206.18

c)

Since it is compounded 4 times a year now,

n = 4

Hence we get

Amount = 1400 X (1 + 4.6/400)⁴⁰

= 1400 X (1.0115)⁴⁰

= $2211.88

d)

Here, the interest is calculated 12 times a year

Hence we get

Amount = 1400 X (1 + 4.6/1200)¹²⁰

= 1400 X (10038)¹²⁰

= $2215.75

e)

Here we are told to ignore leap years, hence we are only going to consider a year to have 365 days.

Hence,

n = 365

Therefore, we get

Amount = 1400 X (1 + 4.6/36500)³⁶⁵⁰

= 1400 X (1 + 4.6/36500)³⁶⁵⁰

= 1400 X (1.00012)³⁶⁵⁰

= $2217.63

Correct Question

If 1400 dollars is invested in an account for 10 years. find the value of the investment at the end of 10 years if the interest is:

(a) 4.6% compounded annually

(b) 4.6% compounded semiannually

(c) 4.6% compounded quarterly

(d) 4.6% compounded monthly

(e) 4.6% compounded daily (ignore leap years)

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Answer:

Step-by-step explanation:

Let's break down the problem:

Quotient =  result obtained by dividing one quantity by another

So its division of x (a number implying variable) by 6

Then it says equal to 2 so we can piece together an equation like this

x/6 = 2

Then we use algebra to solve it

6(x/6)= (2)6

x = 12

So 12 is the unknown number

The total number of cupcakes ordered, using proportions, is of:

5.

A proportion is a fraction of an amount, and this fraction is combined with the unit rates in the context of a problem to find the desired amounts in the same context of the problem.

These amounts are found using basic arithmetic operations, especially multiplication and division, with the unit rates in the context of the problem.

In this problem, the amounts are given as follows:

The total number of cupcakes that will be ordered is the sum of the amounts that will be needed for the family and for the friends, hence:

3.5 cupcakes + 1.5 cupcakes = 5 cupcakes.

The problem is:

I'd like to order 7 halves of cupcakes for my family plus an amount for six friends, considering that each of them wants a quarter. What is the total amount?

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The value of k for the expression, 3 (2− k) = −3k + 2, does not exist.

According to the question,

We have the following expression:

3 (2− k) = −3k + 2

Now, we will multiply 3 into the bracket:

6-3k = -3k+2

Now, moving -3k from the left hand side to the right hand side will result in the change of the sign from minus to plus:

6-3k+3k = 2

Now, 3k will get subtracted from 3k. So, we do not have any variable left for this equation.

Hence, the value of k  for the expression, 3 (2− k) = −3k + 2, does not exist.

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Answer:9x>6=76

Step-by-step explanation:9x>6=76

Answer:

x=10

Step-by-step explanation:

4x+5x+angle g should equal 180 degrees total.

with this in mind, we can subtract angle g from 180, as it is know,. (180-90)

so 4x+5x=90. 9x=90, x=10.

hope this helps.

Check the picture below.

As sample size grows, sample variance (variation among observations) grows, while sample mean variance (standard error) decreases, and therefore precision grows.

The normal curve approximates the sample distribution of averages as well as proportions from just a large number of distinct experiments.

Thus, the better the normal approximation here to sampling distribution for sample mean, the greater the sample size.

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