The required number of markers does Gerald has 56 markers.
How to find markers does he have?Let's represent the number of markers that Gerald has with the variable "m", and the number of pens he has with the variable "p". We can set up two equations based on the information given:
According to question:m + p = 78 (equation 1)
(m + 11) + (p + 11) = 78 (equation 2)
In equation 2, we add 11 to both the number of markers and the number of pens, since Gerald has 11 more of each. We can simplify equation 2 by combining like terms:
m + p + 22 = 78
m + p = 56 (equation 3)
Now we have two equations with two variables. We can use either substitution or elimination to solve for one of the variables. Let's use substitution and solve for "m" in terms of "p" using equation 1:
m + p = 78
m = 78 - p
Now we can substitute this expression for "m" into equation 3:
m + p = 56
(78 - p) + p = 56
Simplifying the equation, we get:
78 - p + p = 56
78 = 56 + p
p = 22
Therefore, Gerald has 22 pens. To find the number of markers he has, we can substitute this value of "p" into equation 1:
m + 22 = 78
m = 56
So, Gerald has 56 markers.
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Lars, Rita and Alan regularly go swimming. Lars goes every
2 days, Rita goes every 3 days and Alan goes every 5 days.
They all went swimming together on Friday 1st June.
a) On what date will Lars and Rita next go swimming together?
b) On what date will Rita and Alan next go swimming together?
c) On what day of the week will all 3 next go swimming together?
d) Which of the 3 (if any) will go swimming on 15th June?
Part (a)
Lars goes every 2 daysRita goes every 3 daysThe LCM of 2 and 3 is 2*3 = 6.
Lars and Rita's schedule aligns every 6 days.
These two went swimming together on June 1st.
6 days later would be June 7th, which is when they swim together again. See the chart in part (d) below.
Answer: June 7th======================================================
Part (b)
Rita goes every 3 daysAlan goes every 5 days.LCM = 3*5 = 15
Add 15 days to the first of June to get 1+15 = 16. See the chart in part (d) below.
Answer: June 16th======================================================
Part (c)
The LCM of 2, 3, and 5 is 2*3*5 = 30
The trio will swim together every 30 days.
Since there are 7 days in a week, divide 30 over 7 and find the remainder.
30/7 = 4 remainder 2
We don't care about the quotient. All we focus on is the remainder.
A remainder of 2 means that we move 2 days ahead of Friday to land on Sunday. You can use a calendar to confirm that adding 30 days to the starting Friday will get you to Sunday. It doesn't matter what month you are in, so it could be June or any month really.
Answer: Sunday======================================================
Part (d)
Here's a chart when all three go swimming:
[tex]\begin{array}{|c|c|c|} \cline{1-3}\text{Lars} & \text{Rita} & \text{Alan}\\\cline{1-3}1 & 1 & 1\\\cline{1-3}3 & 4 & 6\\\cline{1-3}5 & 7 & 11\\\cline{1-3}7 & 10 & 16\\\cline{1-3}9 & 13 & 21\\\cline{1-3}11 & 16 & 26\\\cline{1-3}13 & 19 & 31\\\cline{1-3}15 & 22 & 36\\\cline{1-3}\end{array}[/tex]
Each number refers to a day number in June, with exception to the 36 for Alan. Treat that "36" as 36-30 = 6 days beyond the end of June (aka July 6th).
Each person starts at 1. Lars will involve adding 2 to each item. Rita has +3 to each item. Alan has +5 to each item. That chart shows "15" only in the Lars column.
Answer: Lars onlyNayeli is going to an amusement park. The price of admission into the park is $40,
and once she is inside the park, she will have to pay $2 for every ride she rides on.
How much money would Nayeli have to pay in total if she goes on 9 rides? How much
would she have to pay if she goes on r rides?
Answer:
Step-by-step explanation:
The total cost for Nayeli to enter the amusement park is $40. If she goes on 9 rides, the cost for the rides would be 9 * $2 = $18. Therefore, the total cost for Nayeli to enter the park and go on 9 rides would be $40 + $18 = $58.
To find the total cost if she goes on r rides, we can use the formula:
Total cost = $40 + r * $2
So, if Nayeli goes on r rides, she would have to pay $40 + r * $2 in total.
To calculate the total cost, multiply the number of rides by the cost per ride and add it to the admission price.
To calculate the total amount Nayeli would have to pay if she goes on 9 rides, we need to first calculate the cost of admission. The admission price is $40. Then, we multiply the number of rides (9) by the cost per ride ($2) and add it to the admission price to get the total cost.
Total cost = Admission price + (Number of rides x Cost per ride) = $40 + (9 x $2) = $40 + $18 = $58.
If Nayeli goes on 'r' rides, we can use the same formula to calculate the total cost. The total cost would be the admission price ($40) plus the product of the number of rides ('r') and the cost per ride ($2). Total cost = $40 + (r x $2) = $40 + $2r.
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justin has a bird feeder which gets visited by an average of 18 birds every 2 hours during daylight hours. what is the probability that the bird feeder will be visited by more than 5 birds in a 40 minute period during daylight hours? (round your answer to three decimal places.)
The probability that the bird feeder will be visited by more than 5 birds in a 40 minute period during daylight hours is 0.835.
In the question Justin has a bird feeder which gets visited by an average of 18 birds every 2 hours during daylight hours and we have to find what is the probability that the bird feeder will be visited by more than 5 birds in a 40 minute period during daylight hours.
This can be calculated using the Poisson distribution formula, P(X > 5) = 1 - P(X ≤ 5).
P(X > 5) = 1 - P(X ≤ 5)
= 1 - (P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5))
= 1 - (0.0022 + 0.0133 + 0.0514 + 0.1245 + 0.2141 + 0.2769)
= 0.8351
Therefore, the probability that the bird feeder will be visited by more than 5 birds in a 40 minute period during daylight hours is 0.835.
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help me plssssssssss
what answer below best addresses the following statistical problem? a new advertisement for ben and jerry's ice cream introduced in late may of last year resulted in a 30% increase in ice cream sales for the following three months. does this mean that the advertisement was effective? a. yes, because an increase in sales means the advertisement worked. b. no, because the increase in sales was all caused by another variable (specifically a change in weather) c. uncertain, because there are other variables at play and correlation does not equal causation d. uncertain, because it's impossible to measure the effectiveness of advertising.
The correct answer to this statistical problem is (c) uncertain, because there are other variables at play and correlation does not equal causation.
In this scenario, we're looking at the sales of Ben and Jerry's ice cream before and after the advertisement was introduced. The sales increased by 30% for the following three months after the advertisement. So, does this mean that the advertisement was effective? The answer is not as straightforward as a simple "yes" or "no."
Option (c) acknowledges that there are other variables at play and that correlation does not equal causation.
This is the most accurate answer because it recognizes that while the increase in sales may be related to the advertisement, it's impossible to say for sure whether the advertisement was the cause of the increase in sales.
There could be other factors, such as the weather or a change in consumer preferences, that also contributed to the increase in sales.
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Find the ratio of 24 min to 1 hour
Work Shown:
24 min : 1 hour
24 min : 60 min
24 : 60
24/12 : 60/12
2 : 5
The ratio of 24 minutes to 1 hour is 2 : 5
What is ratio?
A ratio compares values. A ratio says how much of one thing there is compared to another thing. even though there are more squares. The trick with ratios is to always multiply or divide the numbers by the same value. Example: A Recipe for pancakes uses 3 cups of flour and 2 cups of milk.
Solution:
Find the ratio of 24 to 1 hour = 60 minutes:
[tex]= > Ratio = \frac{24}{60} \\\\\\= > Ratio =\frac{2}{5} \\\\= > \boxed{Ratio =\bold{2:5}}[/tex]
Hence, the ratio of 24 minutes to 1 hour is 2 : 5.
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Find the inverse equations for each of the functions below. Use function notation. Justify that each inverse equation works for its function.
A. g(x)= x³ - 5
B. p(x) = 2(x+3)³
C. t(x) = 10(x-4)/3
The inverse of the functions g(x), p(x), and t(x) are expressed as; g⁻¹(x) = 3√(x + 5), p⁻¹(x) = 3√(x/2) - 3, and t⁻¹(x) = (3x/10) - 3. respectively.
What is Inverse of a functionA function is said to have an inverse if it is both one-to-one and onto
we replace the functions g(x), p(x), and t(x) with y and make x the subject to arrive at the inverse g⁻¹(x), p⁻¹(x), and t⁻¹(x) as follows;
For g(x)= x³ - 5:
y = x³ - 5
y + 5 = x³ {add 5 both sides}
x = 3√(y + 5) {take cube root}
g⁻¹(x) = 3√(x + 5).
For p(x) = 2(x+3)³:
y = 2(x+3)³
y/2 = (x+3)³ {divide through by 2}
3√(y/2) = x + 3 {take cube root}
x = 3√(y/2) - 3 {subtract 3 from both sides}
p⁻¹(x) = 3√(x/2) - 3.
For t(x) = 10(x-4)/3:
y = 10(x-4)/3
3y = 10(x-4) {cross multiplication}
3y/10 = x + 3 {divide through by 10}
(3y/10) - 3 = x {subtract 3 from both sides}
t⁻¹(x) = (3x/10) - 3.
Therefore, the inverse of the functions g(x), p(x), and t(x) are derived by interchanging the value of x for y and expressed respectively as; g⁻¹(x) = 3√(x + 5), p⁻¹(x) = 3√(x/2) - 3, and t⁻¹(x) = (3x/10) - 3.
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3 of 93 of 9 questions question terry has won 18 of 35 chess games. sandra has won 24 of 36 chess games. terry wants to know how many of the remaining games she would have to win for her winning percentage to be greater than sandra's, given that sandra doesn't win any more games. let x represent the number of games remaining, and let y represent the number of games terry needs to win. which inequality represents this situation? responses 18 y35 x>2436 x 18 y35 x>2436 x 35 y18 x>2436 x 35 y18 x>2436 x 18 y35 x>36 x24 18 y35 x>36 x24 18 x35 x>2436 x
The inequality that represents this situation is y - 2x > 16.
Let's start by finding Terry's current winning percentage:
Terry's current winning percentage = 18/35 = 0.5143 (rounded to 4 decimal places)
We want to find out how many of the remaining games Terry needs to win for her winning percentage to be greater than Sandra's winning percentage, given that Sandra doesn't win any more games. Sandra's current winning percentage is:
Sandra's current winning percentage = 24/36 = 0.6667 (rounded to 4 decimal places)
Let x be the number of remaining games and y be the number of games Terry needs to win. Since there are a total of x remaining games and Terry wins y of them, she will have won a total of 18 + y games out of 35 + x games. Therefore, her winning percentage after winning y of the remaining games would be:
(18 + y) / (35 + x)
We want this winning percentage to be greater than Sandra's winning percentage:
(18 + y) / (35 + x) > 24/36
Multiplying both sides by 36(35 + x), we get:
36(18 + y) > 24(35 + x)
Simplifying the left-hand side:
36(18 + y) = 648 + 36y
Simplifying the right-hand side:
24(35 + x) = 840 + 24x
Substituting these simplifications back into the inequality, we get:
648 + 36y > 840 + 24x
Simplifying:
12y - 24x > 192
Dividing both sides by 12:
y - 2x > 16
Therefore, the inequality that represents this situation is:
y - 2x > 16
So Terry needs to win more than twice as many remaining games as the number of games Sandra has won more than her in order to have a winning percentage greater than Sandra's winning percentage.
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6x +16 += 2x+28
How do you do this??
From the given question above we can conclude that when 6x +16 += 2x+28 , then the value of x is 3.
What is Linear Equation?
A linear equation is a mathematical expression in which the highest power of the variable is 1. It can be written in the form of:
y = mx + b
where y and x are variables, m is the slope of the line, and b is the y-intercept of the line. This form is called the slope-intercept form of a linear equation.
To solve the equation 6x + 16 = 2x + 28:
Simplify both sides of the equation by combining like terms:
6x + 16 = 2x + 28
Subtract 2x from both sides:
4x + 16 = 28
Subtract 16 from both sides:
4x = 12
Solve for x by dividing both sides by 4:
4x = 12
x = 3
Therefore, the solution to the equation 6x + 16 = 2x + 28 is x = 3.
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please help idek how to slove this give a step by step too please
Answer:
x = 3/85
Step-by-step explanation:
log2 (6) - log2 (5x) = log2 ( 34)
We can use the properties of logs.
First subtract log2 (6) from each side.
log2 (6) - log2 (5x) - log2 (6) = log2 ( 34)-log2 (6)
- log2 (5x) = log2 ( 34)-log2 (6)
Now we know that log a - log b = log a/b
- log2 (5x) = log2 ( 34/6)
- log2 (5x) = log2 ( 17/3)
Multiply each side by -1
log2 (5x) = -log2 ( 17/3)
We know that -log (a/b) = log ( b/a)
log2 (5x) = log2 ( 3/17)
The terms inside the logs must be the same
5x = 3/17
Divide each side by 5
5x/5 = 3/17 * 1/5
x = 3/85
PLS HELP ANSWER QUICK PLEASE SHOW WORK
Answer: NIKES
Step-by-step explanation:
BEFAUSE 5/2 IS THE WHG0LE D[IWJAEOIDHNC;SHCOWIADHJA[OISHWNIOD
Answer: the answer is nike
Step-by-step explanation: Because the shipping fee on callaway is more than the order.
21. Given h(x) = -x-14, if h(x) = -2, find x.
Answer:
Step-by-step explanation:
stop searching answers poopers use ur mind
Answer:
-12
Step-by-step explanation:
Substitute x with -2
-(-2)-14
2-14 = -12
You need to score at least 1500 points on your new video game to abstain the high score. You get 300 points after completing each level. Write a solve an inequality to find the number of levels you must bet to obtain the high score.
Answer:
the answer is 4
Step-by-step explanation:
hope this helps
a scratch off lottery ticket can be purchased for $2. there are multiple prize options, shown along with the probability, in the table below. what is the expected win (or loss) for this lottery ticket? round your answer to the nearest cent. do not round until your final answer.
a result of -$2.00, indicating that, on average, you will lose $2.00 when buying this lottery ticket.
Lose (-$2.00)
The expected win (or loss) for this lottery ticket is -$2.00.
The expected win (or loss) for this lottery ticket is calculated by multiplying the prize amount by the probability of winning and then subtracting the cost of the ticket.
($50 x 0.1%) - $2 = -$2.00
The expected win (or loss) for this lottery ticket is calculated by multiplying the prize amount of $50 by the probability of 0.1% (or 0.001) of winning and then subtracting the cost of the ticket, which is $2. This gives us a result of -$2.00, indicating that, on average, you will lose $2.00 when buying this lottery ticket.
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This shows a triangle.
7ft
8ft
What is the area of the triangle?
The area of the given triangle is 28 squared feet
What is the area of a triangleThe area of a triangle is a measure of the amount of space enclosed by the triangle. It is a scalar quantity, meaning that it is a single numerical value with no direction.
The area of a triangle can be calculated using various formulas, depending on the information available about the triangle.
In this problem, we have the value of base and the height of the triangle.
The formula is given as;
A = 1/2 b * h
Substituting the values into the formula;
A = 0.5 * 7 * 8
A = 28 squared feet
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a. Starting with the number 10, build a sequence of 5 numbers.
Answer:
Step-by-step explanation:
10, 20, 30, 40, 50
Determine algebraically whether the function is even, odd, or neither?
f(x)=3 x 3+5
The function f(x) = 3x³ + 5 is neither even nor odd. To determine whether a function is even or odd, you need to check how the function behaves when x is replaced with -x.
To determine whether the given function is even, odd, or neither, we need to check the following conditions:
Even function: If f(-x) = f(x) for all x in the domain of f, then the function is even.
Odd function: If f(-x) = -f(x) for all x in the domain of f, then the function is odd.
Let's check these conditions for the given function:
f(x) = 3x³ + 5
f(-x) = 3(-x)³ + 5 = -3x³ + 5
f(x) = 3x³ + 5
Since f(-x) is not equal to f(x), the function is not even.
f(-x) = 3(-x)^3 + 5 = -3x^3 + 5
-f(x) = -(3x^3 + 5) = -3x^3 - 5
Since f(-x) is not equal to -f(x), the function is not odd.
Therefore, the given function is neither even nor odd.
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Subtract and simplify. (9^2 − 4 − 4) − (−2^3 − + 12)
Answer:
93
Step-by-step explanation:
Answer:
27
28
Step-by-step explanation:
If student 1 had 147 likes and student 2 had 42 did student 2 have a higher or lower percentage of likes than student 1 ?
Student 2 has lower percentage of likes as compare to student 1 ,it is equal to 71.5%.
Number of likes of student 1 is equal to 147
Number of likes of student 2 is equal to 42
147 > 42
⇒Number of likes of student 1 is greater than student 2
Difference between number of likes
= 147 - 42
= 105
Percentage difference = ( 105 / 147 ) × 100
= 71.5%
Student 2 has 71.5% lower percentage of likes than student 1
Therefore, student 2 has lower percentage of likes than student 1 which is equal to 71.5%.
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Need Help Find EI And ST
Answer:
Step-by-step explanation:
So first what you got to do is add and mulytplie
Find the area of the polygon in square units.
The area of the polygon is 7.5 square units
How to determine the area of the polygonNote that the polygon given in the diagram takes the shape of a kite.
The properties of a kite are given as;
It two pairs of adjacent equal sidesIt has one pair of opposite angles that are equalThe diagonals are equalThe shorter diagonal forms two isosceles trianglesThe longer diagonal forms two equal trianglesThe diagonals are perpendicular to each otherThe formula for area of a kite is;
Area = pq/2
Area = 3(5)/2
Area = 15/2
Divide the values
Area = 7.5 square units.
Thus, the value is 7.5 square units
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-3x+8=5x-72 solve for x please
Answer:
x = 10
Step-by-step explanation:
[tex]-3x+8=5x-72[/tex]
Subtract 5x from both sides:
[tex]-3x+8-5x=5x-72-5x[/tex]
[tex]-8x+8=-72[/tex]
Subtract 8 from both sides:
[tex]-8x+8-8=-72-8[/tex]
[tex]-8x=-80[/tex]
Divide both sides by -8:
[tex]\dfrac{-8x}{-8} =\dfrac{-80}{-8}[/tex]
[tex]\boxed{x=10}[/tex]
See had some cherries. Every day he ate 10 cherries and gave 5 away. After he gave that last 5 cherries away he had eaten 40 cherries altogether. How many cherries did Seb have at the start?
50 must have been his starting number of cherries.
Seb had 50 cherries at the start. This can be determined by solving the equation 10x + 5 = 40, where x is the number of days he ate 10 cherries and gave 5 away. When you solve the equation, you get x = 5, meaning he did this 5 times. Since 10x is 50, and 5 is added to that, the total is 50. Therefore, Seb had 50 cherries at the start.
To solve the equation, you first need to subtract 5 from both sides to get 10x = 35. Then, divide both sides by 10 to get x = 3.5. Since Seb could not have eaten 3.5 days worth of cherries, it means that he did the 10 and 5 activity 4 times, giving him 40 cherries before giving away the last 5. So 40 + 5 = 45 and 10x = 50, so 50 must have been his starting number of cherries.
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Lineshasaslopeof
–8
9. Line
tisparalleltoline
s. What
istheslopeofline
t ?
Answer: 4
Step-by-step explanation:
which expression is equivalent to log12x^4√ x^3-2/(x+1)^5?
Answer:
D
Step-by-step explanation:
Tell me if u need explain
(03.03 LC)
How does the graph of g(x) = (x - 2)3 + 7 compare to the parent function f(x) = x³?
The graph of g(x) = (x - 2)^3 + 7 is a transformation of the parent function f(x) = x^3.
The parent function f(x) = x^3 has a shape that is symmetrical about the origin and increases as x moves away from the origin. The graph of g(x) = (x - 2)^3 + 7 is also symmetrical about the origin, but it has been translated 2 units to the right and 7 units up from the parent function.
So, the graph of g(x) = (x - 2)^3 + 7 is similar in shape to the parent function f(x) = x^3, but it is shifted to the right and up on the coordinate plane.
Factor 26r³s
O 13(2r³s + 475-37²54)
037²s(27+ 47³-38³)
O 13r²(2rs + 4r3 – 384)
O 13r²(26r³s + 527-5-39²4)
+5275-39724. What is the resulting expression?
The factor of the algebraic expression is 13r²(2rs + 4r³ - 3s⁴).
option C is the correct answer
What is the factor of the algebraic expression?
The factor of the algebraic expression given as
26r³s + 52r^(5) - 39r²s⁴
can be determined by finding the highest common factor and factorize it out.
The highest common factor of the letters is r²
Factors of 26 = 1, 2, 13, 26
Factors of 39 = 1, 3, 13, 39
Factors of 52 = 1, 2, 4, 13, 26, 52
The highest common factor for the 3 numbers is 13.
Thus, in total, the highest common factor for the algebraic expression is 13r².
Finally, we have;
13r²(2rs + 4r³ - 3s⁴)
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The complete question is below:
Factor 26r³s + 52r^(5) - 39r²s⁴
A. 13(2r³s + 475-37²s⁴)
B. 37²s(27+ 47³-38³)
C. 13r²(2rs + 4r³ – 3s⁴)
D. 13r²(26r³s + 527-5-39²4)
Write an equation in point-slope form for the given point and slope:
Point: (4, -6)
Slope: 2
Answer:
y = 2x -14
Step-by-step explanation:
The point-slope form is y = mx + b
m = 2
y-intercept is located at (0, -14)
So, the equation is
y = 2x - 14
Answer:
y-6=2(x-4)
Step-by-step explanation:
point-slope form y-y1=m(x-x1)
Which situation can be represented by y = 4x?
Responses
There are y cats and x dogs in a shelter. The cats and dogs each have 4 legs.
There are , y, cats and , x, dogs in a shelter. The cats and dogs each have 4 legs.
A recipe uses y cups of flour and x cups of sugar. The amount of flour is 4 times the amount of sugar.
A recipe uses , y, cups of flour and , x, cups of sugar. The amount of flour is 4 times the amount of sugar.
Tricia is y years old. This is 4 years older than her younger brother, Max, who is x years old.
Tricia is , y, years old. This is 4 years older than her younger brother, Max, who is , x, years old.
Sebastian buys y sacks of groceries. Each sack weighs 4 pounds. He carries x pounds of groceries home from the store.
Sebastian buys , y, sacks of groceries. Each sack weighs 4 pounds. He carries , x, pounds of groceries home from the store.
Answer:
a recipe uses y cups of flour and x cups of sugar the amount of flour is 4 times the amount of sugar
my proof I took the quiz
Ok I know it’s late but I really need help with these problems and no one can help me so can someone please help and explain. I know it’s a lot but I’m really confused, thank you so much.
Answer:
1. x = 0.75
2. p = 4
3. L = 11
4. t = 42
Step-by-step explanation:
1. The price of pen is x, then
=> 6x + 24 = 28.5
=> 6x = 4.5
x = 4.5/6 = 0.75
2. p is the number of lbs
=> 2p + 50 = 58
2p = 8
p = 4
3. Perimeter = 2(L + W)
2(L + 4) = 30
=> 2L + 8 = 30
2L = 22
L = 11
4. t is the number of tickets
3t + 24 = 150
3t = 126
t = 126/3 = 42
