Answer:
125.0600 million
[tex]\frac{6253}{50} million[/tex]
125,060,000
125 million 60 thousand
Step-by-step explanation:
It does not matter how many zeroes we add to the right end after the decimal, it does not change the value of the number.
Thus, 125.06, 125.060, 125.0600,.... all have the same values.
Similarly 125.06 can be change into the rational form
Thus, [tex]125.06=\frac{6253}{50} =\frac{12506}{100} \text{all have same values}[/tex]
We can also write the word "million" into the digits.
Thus, 125.06 million = 125,060,000 = 125 million 60 thousand
Draw one card at random from a standard deck of cards. the sample space s is the collection of the 52 cards. assume that the probability set function assigns 1/52 to each of the 52 outcomes. let a = {x: x is a jack, queen, or king}, b = {x: x is a 9, 10, or jack and x is red}, c = {x: x is a club}, d = {x: x is a diamond, a heart, or a spade}.
We have P(A) = 3/13, P(A ∩ B) = 3/52, P(A ∪ B) = 17/52, P(C ∪ D) = 1, and P(C ∩ D) = 0.
(a) To find P(A), we first determine the number of outcomes in A, which consists of 12 cards (4 jacks, 4 queens, and 4 kings).
Since there are 52 cards in total, P(A) = 12/52 = 3/13.
(b) For P(A ∩ B), we look for the cards that are both in A and B.
There are 3 such cards (jack of hearts, jack of diamonds, and jack of hearts).
So, P(A ∩ B) = 3/52.
(c) To find P(A ∪ B), we combine the outcomes in sets A and B, but we avoid double-counting the jacks.
So, A ∪ B consists of 12 cards from A and 5 cards from B, totaling 17 cards.
Hence, P(A ∪ B) = 17/52.
(d) P(C ∪ D) includes all cards that are clubs, diamonds, hearts, or spades.
Since all cards fall into these categories, P(C ∪ D) = 1.
(e) P(C ∩ D) represents the probability of drawing a card that is both a club and either a diamond, heart, or spade.
Since clubs do not intersect with these suits, P(C ∩ D) = 0.
Complete Question:
Draw one card at random from a standard deck of cards. The sample space S is the collection of the 52 cards. Assume that the probability set function assigns 1/52 to each of the 52 outcomes.
Let
A = {x: x is a jack, queen, or king},
B = {x: x is a 9, 10, or jack and x is red},
C = {x: x is a club},
D = {x: x is a diamond, a heart, or a spade}.
Find (a) P(A), (b) P(A ∩ B), (c) P(A ∪ B), (d) P(C ∪ D), and (e) P(C ∩ D).
A multivitamin tablet contains 14.5mg of calcium. How much calcium does a bottle of 50 tablets contain? Write your answer in grams.
Answer:
The correct answer is 725mg of calcium.
Step-by-step explanation:
To solve this problem, you can to use the rule of three.
1 tablet → 14.5 mg.50 tablets → x mg.Now, you have to multiply 50 tablets by 14.5 mg, then divide by 1 tablet:
[tex]x = \frac{50 tb * 14.5mg}{1 tb} = 725 mg[/tex] // tb divided by tb is 1
[tex]x = 725 mg[/tex]
solve th inequality y/-6 > 10
is a whole number with 4 digits always greater than or less than a whole number with 3 digits explain
A whole number with 4 digits is always greater than a whole number with 3 digits because each position to the left in a decimal number is ten times greater than the one to the right, making the smallest 4-digit number, 1000, larger than the largest 3-digit number, 999.
A whole number with 4 digits is always greater than a whole number with 3 digits. This is because the value of a digit in a number is determined by its position or place value. In our decimal number system, each digit to the left is ten times greater than the one to its immediate right.
For example, the smallest 4-digit number is 1000. The largest 3-digit number is 999. Clearly, 1000 (which has the smallest possible value for a 4-digit number) is greater than 999 (which has the largest possible value for a 3-digit number), hence a 4-digit number is always greater than a 3-digit number.
When considering significant figures, such as those that arise in measurements, certain digits are known exactly, while others may be more uncertain due to rounding or measurement limitations. However, this does not affect the overall rule that more digits in a whole number represent a greater value.
An item is regularly priced at $91 . It is now priced at a discount of 15% off the regular price. What is the price now?
3(a + b + c)2 for a = 2, b = 3, and c = 4.
3(a+b+b)^2 =
3(2+3+4)^2 =
3(9)^2=
3*81 =243
How long will it take you to ski a distance of 36 miles at a speed of 3 miles per 30 minutes?
what is the value of each of these digits in 654321
Write an equation for a linear function whose graph has the given characteristics.
Passes through (42,0), perpendicular to the graph of g(x)=6x+2
f(x)=
If four times a certain number, increased by 6 is equal to 94, what is the number?
If x represents the number, then which of the following equations could be used to solve the problem?
4x + 6 = 94
4(x + 6) = 94
x + 6 = 4(94)
Is dividing 4/5 the same as multiplying by 5 then dividing by 4?
Each second for 20 seconds, an elevator descends 6 feet. Find the total change in elevation.
a rectangle has a length of 2 1/5 yards and a width of 4 9/20 what is the perimeter of the rectangle? express your answer in mixed number form and reduce if possible
A principal of $2,000 was invested in a savings account for 4 years. If the interest earned for the period was $240, what was the interest rate?
To find the interest rate, you can use the formula R = I / (PT). In this case, the principal is $2000, the time is 4 years and the interest is $240, resulting in an interest rate of about 3%.
Explanation:The subject of this question falls under Mathematics, specifically, financial mathematics, which deals with concepts like interest. The principle here is the initial amount of money that was deposited or borrowed. In this case, the principal is $2000. The time, in this scenario, is 4 years and the interest earned over this period is $240.
To answer the question, we'll use a formula for simple interest, expressed as I = PRT (where 'I' stands for the interest, 'P' is the principal, 'R' is the rate of interest and 'T' is the time in years). To calculate the interest rate, we rearrange the formula to R = I / (PT). Here, R would equal $240 / ($2000 x 4).
So, the interest rate (R) would be approximately 3%.
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Enter a formula in cell d5 to calculate b5/b4 rounded to 4 decimal places.
Excel formulas are expressions used to perform computation.
The Excel formula to enter in cell D5 is = ROUND(B5/B4, 4)
From the question, we have:
The formula in cell D5 is the quotient of cells B5 and B4The result is to be approximated to 4 decimal placesThe quotient of cells B5 and B4 is represented as:
B5/B4
To round the quotient, we make use of the ROUND function
So, we have:
ROUND(B5/B4, 4)
Excel formulas begin with the "=" sign
This gives
= ROUND(B5/B4, 4)
Hence, the Excel formula to enter in cell D5 is = ROUND(B5/B4, 4)
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a grading machine can grade 48 tests in 1 minute. How
long will it take the machine to grade 300 tests?
Write an equation that defines the exponential function with base a > 0.
Ryan runs 9 miles in 73 minutes. How many minutes does he take per mile?
Ritz can eat 8 apples in 15 minutes. How long does it take to eat 16 apples at same rate?
Final answer:
To determine how long it takes to eat 16 apples at the same rate as 8 apples in 15 minutes, set up a proportion and solve for the time.
Explanation:
This question demands basic understanding of ratio and proportion in general.
To find out how long it takes to eat 16 apples at the same rate Ritz eats 8 apples in 15 minutes, you can set up a proportion:
8 apples / 15 minutes = 16 apples / x minutes
8/15 × 1/16 = 1/x
1/15 × 1/2 = 1/x
1/x = 1/30
X = 30
A 30-gallon tank initially contains 15 gallons of salt water containing 6 pounds of salt. suppose salt water containing 1 pound of salt per gallon is pumped into the top of the tank at the rate of 2 gallons per minute, while a well-mixed solution leaves the bottom of the tank at a rate of 1 gallon per minute. how much salt is in the tank when the tank is full
Final answer:
Calculate the amount of salt in a tank given rates of inflow and outflow, and determine the final salt quantity when the tank is full.
Explanation:
A 30-gallon tank initially contains 15 gallons of salt water containing 6 pounds of salt.
Find the initial amount of salt per gallon in the tank: 6 pounds / 15 gallons = 0.4 pounds per gallon.
Calculate the rate of salt being added and leaving the tank: In: 1 pound per gallon × 2 gallons per minute = 2 pounds per minute; Out: 0.4 pounds per gallon × 1 gallon per minute = 0.4 pounds per minute.
Subtract the rate of salt leaving from the rate of salt coming in to find the net rate of salt accumulation: 2 pounds per minute - 0.4 pounds per minute = 1.6 pounds per minute.
How much salt is in the tank when it is full?
Using the net rate of salt accumulation, calculate the time needed to fill the tank: 30 gallons / 2 gallons per minute = 15 minutes.
Finally, calculate the total amount of salt in the tank when full: 15 minutes × 1.6 pounds per minute = 24 pounds of salt.
What is the simplified expression for –3cd – d(2c – 4) – 4d?
A:–5cd
B:cd – 8d
C:5cd – 8d
D:–5cd – 8d
Which statement best describes the function h(t) 210- 15t
pls help 7th grade math
48.24 total
divide this by 12 to get the monthly average
48.24 / 12 = 4.02 inches per month
What is 0.17 as an equivalent fraction
y+y+2=18 please help me 8 th grade 45POINTS
If P = Q squared ⋅ O, express O in terms of P and Q.
Gretchen lives in Florida, for the current temperature 69°F and rising at a rate of 2°F per hour. She's talking on the phone to her friend in Indiana where the temperature is now 84°F and falling at a rate of 3°F per hour.
A.) If the temperature continue changing at the same rates, how many hours would Gretchen and her friend have to talk before the temperature become equal?
B.) What will the temperature be?
Answer:
A) Gretchen and her friend have to talk 3 hours before the temperature become equal.
B) The temperature after 3 hours will be 75°F.
Step-by-step explanation:
Current temperature in Florida = 69°F
Rate at which temperature is rising = 2°F per hour
Current temperature in Indiana = 84°F
Rate at which temperature is falling= 3°F per hour
A) Suppose in x hours both places have same temperature:
[tex] 69^oF +2F^o\times x=84^oF-3^oF\times x[/tex]
[tex]5x=84^oF-69^oF[/tex]
x = 3 hours
Gretchen and her friend have to talk 3 hours before the temperature become equal.
B) The temperature after 3 hours:
x = 75°F
[tex]69^oF +2F^o\times x=69^oF +2F^o\times 3=75^oF[/tex]
write the quadratic equation whose roots are -1 and 3 and whose leading coefficient is 1
The quadratic equation with roots -1 and 3 and a leading coefficient of 1 is: [tex]f(x) = x^2 - 2x - 3[/tex]
To write a quadratic equation with roots -1 and 3, we can use the factored form of a quadratic equation:
A quadratic equation in factored form looks like this:
[tex]f(x) = a(x - r1)(x - r2)[/tex]
where:
f(x) is the quadratic function,
a is the leading coefficient,
r1 and r2 are the roots of the quadratic equation.
Given the roots -1 and 3, the factored form of the quadratic equation is:
[tex]f(x) = a(x - (-1))(x - 3)[/tex]
Now, you mentioned that the leading coefficient (a) is 1. So we can rewrite the equation as:
[tex]f(x) = 1(x + 1)(x - 3)[/tex]
Now, we can expand the equation to its standard form:
[tex]f(x) = (x + 1)(x - 3)[/tex]
Using the FOIL method (First, Outer, Inner, Last):
[tex]f(x) = x^2 - 3x + x - 3[/tex]
Simplify:
[tex]f(x) = x^2 - 2x - 3[/tex]
So, the quadratic equation with roots -1 and 3 and a leading coefficient of 1 is: [tex]f(x) = x^2 - 2x - 3[/tex]
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Solve the inequalities for x, and match each solution to its number line graph.Two less than 3/2 of a number (x) is no more than 5 1/2 . The sum of two times a number (x) and -2 is at least 8. Seven subtracted from 4 times a number (x) is more than 13. Four added to 3 times a number (x) is less than 19. Pairs Number Line Graph Inequality
Answer:
(i) [tex]x\leq 5[/tex]
(ii) [tex]x\geq 5[/tex]
(iii) [tex]x>5[/tex]
(iv) [tex]x<5[/tex]
Step-by-step explanation:
(i) Two less than [tex]\frac{3}{2}[/tex] of a number (x) is no more than [tex]5\frac{1}{2}[/tex],
⇒ Two less than [tex]\frac{3}{2}[/tex] of x is less than equal to [tex]5\frac{1}{2}[/tex],
[tex]\implies \frac{3}{2}x-2\leq 5\frac{1}{2}[/tex]
[tex]\frac{3x-4}{2}\leq \frac{11}{2}[/tex]
[tex]3x-4\leq 11[/tex]
[tex]3x\leq 15[/tex]
[tex]\implies x\leq 5[/tex]
(ii) The sum of two times a number (x) and -2 is at least 8,
[tex]\implies 2x+(-2) \geq 8[/tex]
[tex]2x-2\geq 8[/tex]
[tex]2x\geq 10[/tex]
[tex]x\geq 5[/tex]
(iii) Seven subtracted from 4 times a number (x) is more than 13,
[tex]\implies 4x-7>13[/tex]
[tex]4x>20[/tex]
[tex]\implies x>5[/tex]
(iv) Four added to 3 times a number (x) is less than 19.
[tex]3x+4<19[/tex]
[tex]3x<15[/tex]
[tex]\implies x<5[/tex]
What are the input variable and the output variable?
number of rowers in a rowboat and the speed of the rowboat
input: number of rowers in the rowboat; output: speed of the rowboat
input: speed of the rowboat; output: number of rowers in the rowboat
input: number of rowboats; output: speed of the rowboat
input: number of rowers in the rowboat; output: the number of rowboats
Answer:
input: number of rowers in the rowboat; output: speed of the rowboat
Step-by-step explanation:
took the test and this was correct