Final answer:
After three days, starting with 9-2x widgets, producing 2x+1 widgets daily, and destroying 3-x widgets daily, the student is left with 3 + 7x widgets, in terms of x.
Explanation:
Let's find out how many widgets are left after three days, starting with 9-2x widgets, producing 2x+1 widgets daily, and destroying 3-x widgets daily.
To calculate the total number of widgets after one day, we add the produced widgets (2x+1) and subtract the destroyed widgets (3-x) from the initial amount (9-2x):
At end of day 1: (9-2x) + (2x+1) - (3-x) = 9 - 2x + 2x + 1 - 3 + x = 7 + x
Repeat this process for two more days:
At end of day 2: (7+x) + (2x+1) - (3-x) = 7 + x + 2x + 1 - 3 + x = 5 + 4x
At end of day 3: (5+4x) + (2x+1) - (3-x) = 5 + 4x + 2x + 1 - 3 + x = 3 + 7x
Therefore, after three days, you are left with 3 + 7x widgets, in terms of x.
The student initially has 9-2x widgets, and each day there's a net change of 3x-2 widgets. After three days, the student is left with 7x+3 widgets.
Explanation:The student starts with 9-2x widgets. Each day, they produce 2x+1 widgets and destroy 3-x widgets. To find out how many widgets the student is left with after three days, we need to account for the daily production and the daily destruction of widgets and sum them up over the three days.
Let's calculate the daily net change in widgets. The number of widgets produced each day is 2x+1, and the number destroyed is 3-x, so the net change in widgets each day is:
(2x+1) - (3-x) = 2x + 1 - 3 + x = 3x - 2
Now, let's multiply this daily net change by three days:
3 days × (3x - 2) = 9x - 6
Finally, let's add this to the initial number of widgets to find the total:
(9-2x) + (9x - 6) = 9 - 2x + 9x - 6 = 7x + 3
Therefore, after three days, the student is left with 7x + 3 widgets in terms of x.
walt is mixing fruit punch for the party. he combines 1 gallon 2 quarts 3 pints of orange juice , 1 gallon 3 quarts 7 pints of pineapple juice, and 1 gallon 3 quarts 3 pints of ginger ale. what is the total liquid measure of the punch ?
Each second for 20 seconds, an elevator descends 6 feet. Find the total change in elevation.
What is 0.17 as an equivalent fraction
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).
i need help with 1 and 2
Write an equation that defines the exponential function with base a > 0.
a grading machine can grade 48 tests in 1 minute. How
long will it take the machine to grade 300 tests?
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
What is the simplified expression for –3cd – d(2c – 4) – 4d?
A:–5cd
B:cd – 8d
C:5cd – 8d
D:–5cd – 8d
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)=
B. if lucinda has only $18 to spend and the price of kewpie dolls and the price of beanie babies are both $6, how many of each would lucinda buy if she were rational? 0 kewpie dolls and 3 beanie babies 3 kewpie dolls and 0 beanie babies 2 kewpie dolls and 1 beanie baby 1 kewpie doll and 2 beanie babies
Lucinda can rationally choose to buy 0 Kewpie dolls and 3 Beanie Babies, 3 Kewpie dolls and 0 Beanie Babies, 2 Kewpie dolls and 1 Beanie Baby, or 1 Kewpie doll and 2 Beanie Babies, as all combinations fit within her $18 budget. The prices for each are $6.
In order to determine how many Kewpie dolls and Beanie Babies Lucinda can buy, we need to explore her budget constraint. Lucinda has $18 to spend, and the prices of both Kewpie dolls and Beanie Babies are $6 each. We can calculate the maximum possible combinations of each that fit within her budget.
If Lucinda buys 0 Kewpie dolls and 3 Beanie Babies, she spends $0 + $18 = $18.If Lucinda buys 3 Kewpie dolls and 0 Beanie Babies, she spends $18 + $0 = $18.If Lucinda buys 2 Kewpie dolls and 1 Beanie Baby, she spends $12 + $6 = $18.If Lucinda buys 1 Kewpie doll and 2 Beanie Babies, she spends $6 + $12 = $18.All these combinations maximize her budget, so any of these options could be rational depending on her preference. Therefore, Lucinda could rationally choose to buy any of the following combinations: 0 Kewpie dolls and 3 Beanie Babies, 3 Kewpie dolls and 0 Beanie Babies, 2 Kewpie dolls and 1 Beanie Baby, or 1 Kewpie doll and 2 Beanie Babies.
solve th inequality y/-6 > 10
The governor of state a earns $50,935 more than the governor of state b. If the total salaries is $287,225. Find the salaries for both
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)
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
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]
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.
Which set of ordered pairs could be generated by an exponential function?
(0, 0), (1, 1), (2, 8), (3, 27)
(0, 1), (1, 2), (2, 5), (3, 10)
(0, 0), (1, 3), (2, 6), (3, 9)
(0, 1), (1, 3), (2, 9), (3, 27)
Answer:
THE ANSWER IS D
Step-by-step explanation:
THE ANSWER IS D because if you square 3 you get 9, if you cube 3, you get 27
Answer: (0, 1), (1, 3), (2, 9), (3, 27)
Step-by-step explanation:
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]
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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If P = Q squared ⋅ O, express O in terms of P and Q.
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 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
Which statement best describes the function h(t) 210- 15t
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]
Ryan runs 9 miles in 73 minutes. How many minutes does he take per mile?
Is dividing 4/5 the same as multiplying by 5 then dividing by 4?
f(x) = 3x + 10x and g(x) = 4x – 2, find (f – g)(x)
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?
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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