To carry out the student's request, you would first raise 'g' to the 7th power to obtain g^7, then subtract 'h' from this result to get the final expression 'g^7 - h'.
Explanation:To solve the expression mentioned by the student, you need to carry out two mathematical operations in sequence. The first operation is raising 'g' to the 7th power, which can be expressed as g^7. The second operation is subtracting 'h' from the result of the first operation. This can be represented mathematically as g^7 - h.
For example, if g equals 2 and h equals 3, then you would first calculate 2^7 which equals 128. Then you would subtract 3 from 128, yielding an answer of 125.
A popular extreme sport is artificial wall climbing. A climber is resting at a height of 42 feet while on a climbing tower. If this is 60% of the tower's total height, find the height of the tower.
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.
The senate in a certain state is comprised of 51 republicans, 48 democrats, and 1 independent. How many committees can be formed if each committee must have 3 republicans and 2 democrats
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]
To learn more about the combination visit:
brainly.com/question/28065038
#SPJ4
6/15=2/c need to solve
A hardware store sells 35% fewer lawnmowers in july than in april. If 39 were sold in july, how many were sold in april/
Answer: 0.65a = 39
Step-by-step explanation:
Select the option for "?" that continues the pattern in each question.
(1.) 3, -6, 12, 4, 20, ?
(2.) 7, 16, 8, 27, 9, ?
(3.) 2, 7, 26, 101, 400, ?
(4.) 7, 21, 8, 72, 9, ?
A bank is offering 2.5% simple interest on a savings account. If you deposit $5000, how much interest will you earn in one year?
Answer:
125.00
Step-by-step explanation:
A bag contains
9
marbles:
2
are green,
2
are red, and
5
are blue. Omar chooses a marble at random, and without putting it back, chooses another one at random. What is the probability that the first marble is green and the second is red? Write your answer as a fraction in simplest form.
A rectangular room is 1.5 times as long as it is wide, and its perimeter is 35 meters. find the dimesions of the room
The width of the room is 7 meters and the length is 10.5 meters.
Explanation: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.
One milliliter of blood contains approximately 5 million red blood cells, and one pint is about 473 milliliters. Create and solve an equation that can be used to find approximately how many red blood cells are in a pint of blood. Use scientific notation for the first box of the equation.
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
Explanation: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
Learn more about equation here:https://brainly.com/question/29657983
#SPJ2
What is 14.7 times 11.361 showing your work ?
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
Heights of men on a baseball team have a Bell shaped distribution with a mean of 172cm and a standard deviation of 8cm. Using the empirical rule, what is the approximate percentage of the men between the following values? a. 156cm and 188cm b. 164cm and 180cm
The sum of nine and two times a number is 35. What is the number?
the Lynch family bought a house for 75,300 .a few years later ,they sold the house for 80,250 how much greater was selling price than the purchase price
the Golden Ratio, is present not just in mathematics, but may also be present within your own brain and body (at the atomic or subatomic level), what do you think it means? Is this number evidence of a grand design, a massive freak coincidence or something else?
a) A box contains 50 diodes of which 10 are known to be bad. A diode is selected at random. What...
a) A box contains 50 diodes of which 10 are known to be bad. A diode is selected at random. What is the probabil ity that it is bad?
b) If the first diode drawn from the box was good, what is the probability that a: second diode drawn wi ll be good?
c) If two diodes are drawn from the box what is the probability that they are both good?
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.
Explanation: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.
a) The probability that a randomly selected diode is bad is the number of bad diodes divided by the total number of diodes. Therefore, it is 10/50 or 1/5 or 0.2.b) If the first diode drawn is good, we have 49 diodes left with 10 bad still among them. The probability that a second diode drawn will be good is the number of remaining good diodes divided by the total remaining diodes, which is 39/49.c) To find the probability that both diodes are good when two are drawn without replacement, we multiply the probability of drawing one good diode by the probability of drawing a second good diode (having already drawn one good). This gives us (40/50) * (39/49), which simplifies to 0.8 * 0.7959 or approximately 0.6367.
The length of the base of a triangle is twice its height. If the area of the triangle is 64 square kilometers, find the height.
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.
Explanation: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 area of a rectangle wall of a barn is 234 square feet. It's length is 8 feet longer than twice its width. Find the length and width of the wall of the barn.
The length of the wall is : 26 ft.
and width of the wall is: 9 ft.
What is area of a rectangle?
The shape/polygon of a rectangle is two dimensional, having four sides, four vertices, and four right angles. The rectangle's two opposing sides are equal and parallel to one another. The space a rectangle occupies is known as its area. The area of a rectangle can also be defined as the region inside its border.
The area of a rectangle is: Area= length × width
Solution:
area = 234
length = ?
width = ?
Given, length is 8 ft greater than twice the width.
Now, l = 2w ₊ 8
l × w = 234 (given)
Substitute for l
(2w ₊ 8)w = 234
multiply
2w² ₊ 8w = 234
2w² ₊ 8w ₋ 234 = 0
Now divide by 2 to eliminate the coefficients of w.
w² ₊ 4w ₋ 117=0
get the factors for the above equation.
We get the factors as: 9 and ₋13,( ₋13 is not applicable as width cannot be negative)
Hence we get the width as 9, now substitute it in:
l = 2w ₊ 8
l = 2(9) ₊ 8
l = 26 ft,
Hence the length and width of the rectangle is 26 ft and 9 ft respectively.
Learn more about "Rectangles" here-
brainly.com/question/1549055
#SPJ2
The digits 2 comma 3 comma 4 comma 5 comma and 2, 3, 4, 5, and 6 are randomly arranged to form a three-digit number. (Digits are not repeated.) Find the probability that the number is even and greater than 600.
Complete the square to put he equation in convenient form for graphing. Then graph the conic section
16x^2+9y^2+96x-18y+9=0
A small business owner made $40,000 the first year he owned his store and made an additional 7% over
the previous year in each subsequent year. Find how much he made during his fourth year of business.
Find his total earnings during the first four years.
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]
solve tan(2θ)+tan(θ)=0 exactly
the production line where you work can assemble 5 amplifiers every 30 minutes at this rate how long should it take the line to assemble 125 amplifiers
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.
Learn more:
https://brainly.com/question/10442853
https://brainly.com/question/3028294
What is 1/6+1/12=what does this equal?
what is the answer of 21 + m = 33
Which problem could be solved with the expression 4*(4+2)
A - Danny ran 4 miles in the morning and 2 miles in the afternoon. He did this for 4 days. How many miles did he run?
B - Bobby sold 4 baseball cards on Monday. He then sold 2 more on Tuesday. He sold the same amount for 2 weeks. How many did he sell?
C - Suzanne makes wooden dolls. She made 2 in the morning and 2 in the afternoon. She did this for 4 days. How many dolls did she make?
A Danny's Problem
B Bobby's Problem
C Suzanne's Problem
if 3 apples cost $1.25 what is the cost of 7 apples?
Your neighbor had to drop the selling price of her home from $180,000 to $165,000. What percent did the price get lowered? Round to nearest tenth
14.4% of 72.5 is what number?
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:
Convert the percentage to a decimal by dividing by 100: 14.4% ÷ 100 = 0.144.Multiply the decimal by the number: 0.144 × 72.5.Perform the multiplication: 0.144 × 72.5 = 10.44.Therefore, 14.4% of 72.5 is 10.44.
The sum of five times a number and 6 more than the number is the same as the difference between -18 and twice the number. What is the number?
The number is given by -3.
What is an Equation?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.
Learn more about Equation here -
https://brainly.com/question/1214333
#SPJ2
s(t)=9t-4, find S(4)
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.
Explanation: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:
Write down the function: S(t) = 9t - 4Substitute t with 4: S(4) = 9(4) - 4Multiply 9 by 4: S(4) = 36 - 4Subtract 4 from 36: S(4) = 32Therefore, S(4) is 32.
Learn more about Evaluation here:https://brainly.com/question/26582052
#SPJ2