To find the rate of the faster car, set the speed of the slower car as 'x' km/h and the speed of the faster car as 'x + 16' km/h. Since they meet in 2 hours, and the total distance is 300 km, the equation is 2x + 2(x + 16) = 300. The faster car's speed is found to be 83 km/h.
Explanation:The question involves solving for the rate of the faster car when two cars travel towards each other from a distance of 300 kilometers apart and meet after 2 hours. We'll designate the speed of the slower car as 'x' km/h, which implies the speed of the faster car is 'x + 16' km/h. Since they meet in 2 hours, the total distance covered by both cars together is 300 kilometers.
Using the formula for distance (distance = rate × time), we can set up an equation:
2x + 2(x + 16) = 300
Simplifying this equation:
2x + 2x + 32 = 300
4x = 268
x = 67
The speed of the slower car is 67 km/h, and therefore, the rate of the faster car must be 67 + 16, which is 83 km/h.
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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 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.
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 sum of nine and two times a number is 35. What is the number?
if 3 apples cost $1.25 what is the cost of 7 apples?
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
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6/15=2/c need to solve
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.
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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, ?
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
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]
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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.
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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.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
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.
What is 1/6+1/12=what does this equal?
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:
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.
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Together, Louisa and Jill scored more than 30 points in the basketball game. If Jill scored 12 points, how many points P did Louisa score? A. P > 18
Answer:
Option A) P > 18 is the correct option.
Step-by-step explanation:
Louisa and Jill scored jointly in basketball = Score of Louisa + score of Jill
Joint score is greater than 30 points
So Score of Louisa P + score of Jill > 30
If Jill scored 12 points then inequality becomes as
score of Louisa P + 12 > 30
Now by subtracting 12 from both side
score of Louisa P + 12 - 12 > 30 - 12
score of Louisa P > 18
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]
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.
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.
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
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:
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
solve tan(2θ)+tan(θ)=0 exactly
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.
what is the answer of 21 + m = 33