Which of the following statements concerning the standard normal curve is/are true (if any)?

a) The area under the standard normal curve to the left of -3 is zero.

b) The area under the standard normal curve between any two z-scores is greater than zero.

c) The area under the standard normal curve between two z-scores will be negative if both z-scores are negative.

d) The area under the standard normal curve to the left of any z-score is less than 1.

A. a, b
B. b, d
C. a, c
D. a

There are 23,490,600 committees that can be formed if each committee must have 3 Republicans and 2 Democrats

Used the concept of combination which states that,

A combination is a technique to determine the number of possible arrangements in a collection of items where the order of the selection does not matter.

Given that,

The Senate in a certain state is comprised of 51 Republicans, 48 Democrats, and 1 independent.

Since we have 51 Republicans,

So we can choose 3 Republicans out of 51 in [tex]^{51} C_3[/tex] ways.

Similarly, we have 48 Democrats, so we can choose 2 Democrats out of 48 in [tex]^{48} C_2[/tex] ways.

Hence, the number of committees:

[tex]^{51} C_3 \times ^{48} C_2[/tex]

Using the formula for combinations,

[tex]^{n} C_r = \dfrac{n!}{r! (n - r)!}[/tex]

[tex]= \dfrac{51!}{3!(51 - 3)!} \times \dfrac{48!}{2!(48 - 2)!}[/tex]

[tex]= \dfrac{51!}{3!(48)!} \times \dfrac{48!}{2!(46)!}[/tex]

[tex]= \dfrac{51 \times 50 \times 49 \times 48!}{3!(48)!} \times \dfrac{48\times 47 \times 46!}{2!(46)!}[/tex]

[tex]= \dfrac{51 \times 50 \times 49 }{3!} \times \dfrac{48\times 47 }{2!}[/tex]

[tex]= 20,825 \times 1,128[/tex]

So, the number of committees is,

[tex]= 23,490,600[/tex]

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Final answer:

a) The probability of selecting a bad diode is 0.2 (20%). b) If the first diode is good, the probability of the second diode being good is 0.816 (81.6%). c) The probability that both diodes are good is 0.6326 (63.26%).

Explanation:

a) Probability that the diode is bad:

There are 50 diodes in total, with 10 known to be bad. The probability of selecting a bad diode is calculated by dividing the number of bad diodes by the total number of diodes: 10/50 = 1/5 = 0.2 or 20%.

b) Probability of second diode being good:

If the first diode drawn is good, there will be 49 diodes left, with 9 being bad. The probability of selecting a good diode as the second one is 40/49 = 0.816 or 81.6%.

c) Probability that both diodes are good:

If two diodes are drawn, there will be 48 diodes left, with 9 being bad. The probability of selecting a good diode for the first draw is 40/50 and for the second draw is 39/49. Therefore, the probability of both diodes being good is (40/50) * (39/49) = 0.6326 or 63.26%.

The probability of selecting a bad diode from the box of 50 is 0.2. If a good diode is selected first, the probability of selecting another good diode is 39/49. The probability of selecting two good diodes consecutively is approximately 0.6367.

The question deals with the concept of probability within a discrete random variable scenario. Specifically, it requires calculating the probabilities of selecting good and bad diodes from a batch with a known distribution of working and defective parts.

Final answer:

To find 14.4% of 72.5, convert the percentage to a decimal and multiply it by the number, resulting in 10.44.

Explanation:

To calculate 14.4% of 72.5, you can use the following steps:

Therefore, 14.4% of 72.5 is 10.44.

Answer:

125.00

Step-by-step explanation:

The crescent wrench is a type of lever, a simple machine that amplifies force to provide greater torque on fasteners with less input effort.

The crescent wrench is a type of simple machine, specifically it is a form of a lever. When you use a crescent wrench, you apply force to the handle, which then applies force to the object you are turning. The pivot point, or fulcrum, is the adjustable jaw which grips the nut or bolt. This allows the user to exert a greater torque on the fastener with less force than would be needed if just using one's hands.

Like other levers, the crescent wrench allows for a mechanical advantage, which is the ratio of output to input forces for any simple machine. By lengthening the handle of the wrench (the effort arm), we achieve a greater mechanical advantage, and thus, can apply more torque to the bolt or nut we are trying to turn.

The time taken to assemble 125 amplifiers is required.

Time taken to assemble 125 amplifiers is 750 minutes or 12 hours and 30 minutes.

Time taken to assemble 5 amplifiers is 30 minutes

[tex]5\ \text{amplifiers}=30\ \text{minutes}[/tex]

So,

[tex]1\ \text{amplifier}=\dfrac{30}{5}=6\ \text{minutes}[/tex]

[tex]125\ \text{amplifiers}=125\times 6=750\ \text{minutes}=\dfrac{750}{60}=12.5\ \text{hours}[/tex]

So, time taken to assemble 125 amplifiers is 750 minutes or 12 hours and 30 minutes.

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The number is given by -3.

Equation is a mathematical relation between more than one variable, number or mathematical quantities involving mathematical operations using equal sign in between them.

Let the number be x

Five times the number is = 5x

6 more than the number is = x+6

Sum of five times a number and 6 more than the number is = 5x+(x+6) = 5x+x+6 = 6x+6

The difference between -18 and twice the number = -18-2x

According to condition,

6x+6 = -18-2x

6x+2x = -18-6

8x = -24

x = -24/8 = -3

Hence the number is -3.

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The width of the room is 7 meters and the length is 10.5 meters.

To find the dimensions of the rectangular room, let's assume the width of the room is x meters. According to the given information, the length of the room is 1.5 times the width, so the length would be 1.5x meters.

The perimeter of a rectangle is calculated by adding twice the length to twice the width. So, we have the equation:

2x + 2(1.5x) = 35

Simplifying the equation, we get:

2x + 3x = 35

Combining like terms, we have:

5x = 35

Dividing both sides of the equation by 5, we find that x = 7.

Therefore, the width of the room is 7 meters and the length is 1.5 times the width, which is 1.5 * 7 = 10.5 meters.

To find the height of the triangle with an area of 64 square kilometers and a base twice its height, we use the area formula: A = (1/2) × base × height, which leads us to determine that the height is 8 kilometers.

The question given involves finding the height of a triangle when the area is known and the relation between the base and height is given. Since the base is twice the height (b = 2h), and we know the formula for the area of a triangle is A = (1/2) × base × height, we can substitute the known area and the base-height relationship into this formula to solve for the height.

The area (A) is given as 64 square kilometers, which leads to the equation:

A = (1/2) × b × h = (1/2) × (2h) × h = h²,

Therefore, with A = 64 km², we obtain:

64 = h².

Taking the square root of both sides gives us the height (h):

h = √64 km = 8 km.

So the height of the triangle is 8 kilometers.

The small business owner made $44,486 during his fourth year of business. His total earnings during the first four years equal $173,168.

The small business owner made $44,486 during his fourth year of business.

To calculate this, we find that he made $40,000 in the first year, then 7% more each year.

So, in the fourth year:

[tex]$40,000 + ( 0.07 * 40,000) + (0.07^2 * 40,000) + (0.07^3 * 40,000) = 44,486[/tex]

His total earnings during the first four years equal $173,168.

This total is found by summing his earnings from each year:

[tex]$40,000 + 42,800 + 45,796 + 44,486 = 173,168.[/tex]

Answer: Hello mate!

this multiplication can be hard because of the numbers after the decimal point. You could use the next trick.

14.7*10 = 147 and 11.361*1000 = 11361

now you could do the multiplication without concerning about the decimals, and afther that divide it back by 10*1000.

and [tex]14.7*11.361 = \frac{147}{10}*\frac{11361}{1000} = \frac{147*11361}{10*1000}  = \frac{147*11361}{10000} = \frac{1670067}{10000}[/tex]

now you need to divide by 10000, that is equivalent to move the decimal point by 4 ) places to the left.

1670067/10000 = 167.0067

To find the approximate number of red blood cells in a pint of blood, multiply 5 million by 473.We get approximately 2.365 billion red blood cells

To find the approximate number of red blood cells in a pint of blood, we can use the given information. One milliliter of blood contains approximately 5 million red blood cells. And one pint is about 473 milliliters. So, we can set up the equation:

Number of red blood cells in a pint = 5 million x 473

Using scientific notation for the first box of the equation:

Number of red blood cells in a pint = 5 x 106 x 473

Simplifying the equation, we get:

Number of red blood cells in a pint = 2.365 x 109 or approximately 2.365 billion red blood cells

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Answer: 0.65a = 39

Step-by-step explanation:

The total height of the climbing tower is found by dividing 42 feet by 0.60, as 42 feet represents 60% of the total height. The calculation gives us 70 feet, which is the height of the tower.

The student has asked a question related to artificial wall climbing and its connection to mathematics, specifically regarding percentages and solving for an unknown total given a part and its percentage of the whole. The question asks to find out the total height of a climbing tower given that 42 feet is 60% of its total height.

To solve this, we would set up a proportion where 42 feet equals 60% of the total height. Using the formula part = percent × whole, we can represent the total height of the tower by the variable x. Therefore, the equation is:

42 = 0.60x

To find x, we divide both sides of the equation by 0.60:

x = 42 / 0.60
x = 70 feet

Thus, the height of the tower is 70 feet.

To calculate S(4), substitute the value of t with 4 into the function S(t), which results in S(4) = 9(4) - 4, giving the final answer of 32.

To find S(4), we need to substitute the value of t with 4 in the function S(t) = 9t - 4. This is a simple evaluation of a function for a given input.

Step-by-step calculation:

Therefore, S(4) is 32.

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