Answer: 55 performances are needed to break even.
Step-by-step explanation:
Let x represent the number of musical performances that are made.
Producing a musical costs $88,000 plus $5900 per performance. This means that the total cost of x musical performances would be
88000 + 5900x
One sold-out performance earns $7500 in revenue. If every performance sells out, it means that the total revenue would be
7500 × x = 7500x
In order to break even, total cost would be equal to total revenue. Therefore,
7500x = 88000 + 5900x
7500x - 5900x = 88000
1600x = 88000
x = 88000/1600 = 55
Sprinklers are being installed to water a lawn. Each sprinkler waters in a circle. Can the lawn be watered completely by 4 installed sprinklers?
(1) The lawn is rectangular and its area is 32 square yards.
(2) Each sprinkler can completely water a circular area of lawn with a maximum radius of 2 yards.
Answer:yes, the lawn can be watered completely by 4 installed sprinklers.
Step-by-step explanation:
The lawn is rectangular and its area is 32 square yards. Sprinklers are to be installed and each sprinkler waters in a circle. The formula for determining the area of a circle is expressed as
Area = πr²
Where
r represents the radius of the circle.
π is a constant whose value is 3.14
If each sprinkler can completely water a circular area of lawn with a maximum radius of 2 yards., the the maximum area that can be watered by each sprinkler would be
Area = 3.14 × 2² = 12.56 yards²
If 4 sprinklers are completely installed, then the total area that they can water would be
12.56 × 4 = 50.24 yards²
Therefore, the lawn can be watered completely by 4 installed sprinklers.
Last week, Ray worked 46 hours. He incorrectly calculated he earned $45 of additional pay. What was Ray's error when he miscalculated his overtime pay? Explain your answer.
Answer: +$45
Step-by-step explanation: if his actual pay for the week was $100 then from the question he incorrectly calculated it as {$100 + $45} = $145 which is $45 above his actual pay.
Error = measured value - actual
value.
= $145 -$100 =$45.
NOTE: since the value he assumed{$145} is greater than his actual pay{$100}, we have to include a positive sign to the error{$45}.
Therefore, Error = +$45.
Ray's error was incorrectly calculating his additional pay as $45 instead of the correct amount of $90. To find the correct overtime pay, we need to determine how many hours Ray worked in excess of his regular hours and the rate at which he receives overtime pay.
Explanation:The error Ray made when calculating his overtime pay was incorrectly calculating the additional pay. To find the correct overtime pay, we need to determine how many hours Ray worked in excess of his regular hours and the rate at which he receives overtime pay. Let's assume that Ray receives time-and-a-half for overtime work.
First, we need to find Ray's regular hours. If we assume his regular hours are 40 hours per week, we can subtract this from the total hours worked to find the overtime hours: 46 hours - 40 hours = 6 hours of overtime. Next, we need to calculate the overtime pay rate. If Ray gets paid $10 per hour for regular work, we'll calculate the overtime rate by multiplying his regular pay rate by 1.5: $10/hour x 1.5 = $15/hour. Finally, we can calculate Ray's actual overtime pay by multiplying the overtime hours by the overtime pay rate: 6 hours x $15/hour = $90.
Therefore, Ray's error was incorrectly calculating his additional pay as $45 instead of the correct amount of $90.
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Trevor stores his baseball cards in a book with nine pages each page holds nine cards seven of his cards won't fit in the book how many cards does he have
Answer:
88
Step-by-step explanation:
9 pages
Each holds 9
He has 7 more
81+7=88
A random sample of 225 measurements is selected from a population, and the sample mean and standard deviation are x =32.5 and s = 30.0, respectively. It is claimed that the population mean exceeds 30. State the null and an appropriate alternative hypothesis, and perform a test at 5% significance level.
Answer:
[tex]t=\frac{32.5-30}{\frac{30}{\sqrt{225}}}=1.25[/tex]
[tex]p_v =P(t_{(224)}>1.25)=0.106[/tex]
If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can't conclude that the true mean is actually its significantly higher than 30.
Step-by-step explanation:
Data given and notation
[tex]\bar X=32.5[/tex] represent the sample mean
[tex]s=30[/tex] represent the sample standard deviation
[tex]n=225[/tex] sample size
[tex]\mu_o =30[/tex] represent the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean exceeds 30, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 30[/tex]
Alternative hypothesis:[tex]\mu > 30[/tex]
If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]t=\frac{32.5-30}{\frac{30}{\sqrt{225}}}=1.25[/tex]
P-value
The first step is calculate the degrees of freedom, on this case:
[tex]df=n-1=225-1=224[/tex]
Since is a one side rigth tailed test the p value would be:
[tex]p_v =P(t_{(224)}>1.25)=0.106[/tex]
Conclusion
If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can't conclude that the true mean is actually its significantly higher than 30.
Joaquin can send up to 250 to text messages each month so far this month he has sent 141 text messages let t represent the number of text messages Joaquin can send during the rest of the month
Question is Incomplete,Complete Question is given below;
Joaquin can send 250 text each month so far this month he has sent 141 text message let T represent the number of text messages Joaquin can send during the rest of the month. Write an inequality to model the situation. Solve the inequality for t.
Answer:
The Inequality modelling the situation is [tex]141+t\leq 250[/tex].
Joaquin can send at the most 109 messages for the remaining of the month.
Step-by-step explanation:
Given:
Number of messages already sent = 141
Total number of messages he can send = 250
We need to write the inequality to model the situation and solve for the same.
Solution:
Let remaining number of messages he can send be 't'.
Now we know that;
Number of messages already sent plus remaining number of messages he can send should be less than or equal to Total number of messages he can send.
framing in equation form we get;
[tex]141+t\leq 250[/tex]
Hence The Inequality modelling the situation is [tex]141+t\leq 250[/tex].
On Solving the above equality we will find the value of 't'.
Now we will subtract both side by 141 using subtraction property of inequality we get;
[tex]141+t-141\leq 250-141\\\\t\leq 109[/tex]
Hence Joaquin can send at the most 109 messages for the remaining of the month.
In the test of gender selection technique, results consisted of 281 baby girls and 291 baby boys. Based on this result, what is the probability of a girl born to a couple using this technique? Does it appear that the technique is effective in increasing the likelihood that a baby will be a girl?
-The probability that a girl will be born using this technique is approximately______
Does this technique appear effective in improving the likelihood of having a baby girl?
Answer:
The probability for a girl to be born is 0.4913. This technique doesnt appear to improve the likelihood of having a baby girl.
Step-by-step explanation:
Since the number of babies selected for this technique, using the law of big numbers, we conclude that the proportion of babies that are girls in the selection is approximately equal than the probability for a girl to be selected. Thus, the probability that a girl will be born using the technique is 281/(281+291) = 0.4913.
Since in general girls are slightly more likely to be born than boys, then we can conclude that the technique doesnt have an effect in improving the likelihood of having a baby girl, but the opposite.
Let the universe be the set U = {1, 2, 3,..., 10}. Let A = {1, 4, 7, 10}, B = {1, 2, 3, 4, 5}, and C = {2, 4, 6, 8}. List the elements of each set.(a) \overline{A} \cap C =\\
|\overline{A} \cap C| =\\
(b) B - \overline{C} = \\
|B - \overline{C}| \\
(c) B \cup A = \\
|B \cup A| =\\
(d) \overline{B} \cap (A - C) = \\
|\overline{B} \cap (A - C)| =\\
(e) (A - B) \cap (B - C) =\\
|(A - B) \cap (B - C)|
In a universe of numbers 1 to 10, sets A, B, and C hold specific values. We explore intersections, differences, and unions. A's complement intersects C to give {2, 6, 8}, while B minus C's complement reveals {2, 4}. Their union boasts {1, 2, 3, 4, 5, 7, 10}, while B's complement meets A minus C in {7, 10}. Finally, (A minus B) and (B minus C) share no elements, resulting in an empty set.
Explanation:Set Operations in U
Here's the breakdown of each set operation and the resulting sets:
(a) \overline{A} ∩ C:
\overline{A}: The complement of A, which includes all elements in U that are not in A. In this case, U \ A = {2, 3, 5, 6, 8, 9}.
\overline{A} ∩ C: The intersection of U \ A and C. This gives us {2, 6, 8}.
|\overline{A} ∩ C|: The cardinality (number of elements) of the intersection. Therefore, |\overline{A} ∩ C| = 3.
(b) B - \overline{C}:
\overline{C}: The complement of C, which includes all elements in U that are not in C. In this case, U \ C = {1, 3, 5, 7, 9, 10}.
B - \overline{C}: The difference between B and U \ C. This removes elements from B that are also in U \ C. Therefore, B - \overline{C} = {2, 4}.
|B - \overline{C}|: The cardinality of the difference. Hence, |B - \overline{C}| = 2.
(c) B ∪ A:
B ∪ A: The union of B and A, which includes all elements that are in either B or A or both. In this case, B ∪ A = {1, 2, 3, 4, 5, 7, 10}.
|B ∪ A|: The cardinality of the union. Therefore, |B ∪ A| = 7.
(d) \overline{B} ∩ (A - C):
\overline{B}: The complement of B, which includes all elements in U that are not in B. In this case, U \ B = {6, 7, 8, 9, 10}.
A - C: The difference between A and C. This removes elements from A that are also in C. Therefore, A - C = {1, 7, 10}.
\overline{B} ∩ (A - C): The intersection of U \ B and A - C. This gives us {7, 10}.
|\overline{B} ∩ (A - C)|: The cardinality of the intersection. Hence, |\overline{B} ∩ (A - C)| = 2.
(e) (A - B) ∩ (B - C):
A - B: The difference between A and B. This removes elements from A that are also in B. Therefore, A - B = {7, 10}.
B - C: The difference between B and C. As mentioned earlier, B - C = {2, 4}.
(A - B) ∩ (B - C)**: The intersection of A - B and B - C. Since no elements are shared between these sets, the intersection is empty.
|(A - B) ∩ (B - C)|**: The cardinality of the empty set is 0. Therefore, |(A - B) ∩ (B - C)| = 0.
Chris types at an average speed of 35 words per minute. He has already typed 1,500 words of his final paper. The paper has to be more than 3,250 words. Which of the following inequalities could be used to solve for x, the number of minutes it will take Chris to type his paper?
Answer:
1750 + 35x ≥ 3250
Step-by-step explanation:
Average speed = 35 words
He has already typed 1500 words on his final paper
The paper must be more than 3250 words.
To find at least how many more words he has to type, we will subtract 1500 from 3250
3250 - 1500 = 1750 words
The equation will be 35x ≥ 1750
x is the number of minutes
The equation could be
1750 + 35x ≥ 3250
If 9\geq4x+19≥4x+19, is greater than or equal to, 4, x, plus, 1, which inequality represents the possible range of values of 12x+312x+312, x, plus, 3?
Answer:
[tex]12x+3\leq 27[/tex]
Step-by-step explanation:
It is given that
[tex]9\geq4x+1[/tex]
We need to find the possible range of values of 12x+3.
Subtract -1 from both sides.
[tex]9-1\geq 4x[/tex]
[tex]8\geq 4x[/tex]
Multiply both sides by 3.
[tex]24\geq 12x[/tex]
Add 3 on both sides.
[tex]24+3\geq 12x+3[/tex]
[tex]27\geq 12x+3[/tex]
It can be rewritten as
[tex]12x+3\leq 27[/tex]
Therefore, 12x+3 must be less than or equal to 27.
An isosceles triangle has two sides of equal length, a, and a base, b. The perimeter of the triangle is 15.7 inches, so the equation to solve is 2a + b = 15.7. If we recall that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, which lengths make sense for possible values of b? Select two options
Final answer:
To find the possible values of b in the equation 2a + b = 15.7 in an isosceles triangle, we can assume different values for a and solve for b. Two lengths that make sense for possible values of b are 5.7 and 3.7.
Explanation:
To determine which lengths make sense for possible values of b in the equation 2a + b = 15.7, we need to consider the fact that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Since the triangle is isosceles, two sides have the same length, which is represented by a. Let's assume that a = 5 (one possible value) and substitute it into the equation: 2(5) + b = 15.7. Solving for b, we get b = 5.7. This means that a possible value for b is 5.7. Another option is when a = 6, which gives us b = 3.7. Therefore, the two lengths that make sense for possible values of b are 5.7 and 3.7.
Mrs. King gets a 15% discount on merchandise bought in the store where she works. Last week she bought several items that totaled $57.25 before the discount. How much did she have to pay using her discount? Round off the amount to the nearest cent.
Answer:
48.6625 before rounding, I'm sure the instruction told you where it preferred you to round.
Step-by-step explanation:
1. Convert percent value to a decimal.
The way to do this is by moving the period at 15.00 two places to the left.
2. Now that you have the decimal .15, multiply it by Mrs. King's subtotal (57.25).
you should get 8.5875.
3. Subtract the discount amnt. (8.5875) from the subtotal (57.25).
You should get 48.6625.
The amounts below represent the last twelve transactions made to Juan's checking account.Positive numbers represent deposits and negative numbers represent debits from his account. $28 -$20 $67 -$22 -$15 $17 -$38 $41 $53 -$13 $30 $75A) $75B) $113C) $37D) -$113
Answer:
Option B. Range of the given sample data is 113.
Step-by-step explanation:
The given question is incomplete; here is the complete question.
Find the range for the given sample data.
The amounts below represent the last twelve transactions made to Juan's checking account. Positive numbers represent deposits and negative numbers represent debits from his account.
$28 -$20 $67 -$22 -$15 $17 -$38 $41 $53 -$13 $30 $75
Option A. $75
Option B. $113
Option C. $37
Option D. -$113
Transaction done by Juan can be arrange from lowest to highest
-38 -22 -20 - 15 -13 17 28 30 41 53 67 75
Now we know rage of the sample data = Highest value - Lowest value
= 75 - (-38)
= 113
Therefore, range of the given sample data is 113.
Option B is the answer.
In Missy's sports card collection,3/4 of the cards are baseball cards. In franks collection 8/12 are baseball cards. Frank says they have the same fraction of baseball cards. Is he correct?
Frank is incorrect because both fractions are not same.
Step-by-step explanation:
We have to compare both fractions in their simplest forms to compare them
Given
Baseball cards in Missy's Collection: [tex]\frac{3}{4}[/tex]
Baseball cards in Frank's Collection: [tex]\frac{8}{12}[/tex]
Converting the fraction in simplest form will give us:
[tex]\frac{2}{3}[/tex]
Both the fractions are not same as one is 3/4 and one is 2/3.
Hence,
Frank is incorrect
Keywords: Fractions, decimals
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I like math because I get it done fast. And I get A's. And I made myself and my parents do it. I make my parents do it and myself. Thats why I love math
Answer:
proud of you keep ya head up
Step-by-step explanation:
Simplify the expression.
(9x + 1/2)+(4x − 8 1/2)
PLZ RESPOND QUICK THIS IS FOR A MIDTERM AND THEY ARE SO ANNOYING!!!
Answer:
The simplified expression is:
⇒ [tex]13x-8[/tex]
Step-by-step explanation:
Given expression:
[tex](9x + \frac{1}{2})+(4x-8\frac{1}{2})[/tex]
To simplify the given expression.
Solution:
In order to simplify, we will combine the like terms by removing the parenthesis.
We have:
⇒ [tex]9x + \frac{1}{2}+4x-8\frac{1}{2}[/tex]
Combining like terms.
⇒ [tex]9x+4x+\frac{1}{2}-8\frac{1}{2}[/tex]
⇒ [tex]13x+\frac{1}{2}-8\frac{1}{2}[/tex]
In order to combine fractions, we will combine the whole number and the fraction separately.
⇒ [tex]13x-8+(\frac{1}{2}-\frac{1}{2})[/tex]
⇒ [tex]13x-8+0[/tex]
Thus, the simplified expression is:
⇒ [tex]13x-8[/tex]
(sum of interior angles = 180 (n-2) where n is the number of sides of the polygon)
1. if the sum of the interior angles of a polygon equals 1980, how many sides does the polygon have ?
2. how many degrees are there in the sum of the interior angles of a nine sides polygon ?
3. how many sides does a polygon have if the sum of its interior angles is 1620 ?
4. how many degrees are there in the sum of the interior angles of an eighteen sides polygon ?
5. how many degrees are there in the sum of the interior angles of a seventeen sides polygon ?
6. what is the sum of the interior angles of a quadrilateral ?
(i don't need an explanation, just the answers)
Answer:
Step-by-step explanation:
The sum of the interior angles = 180 (n-2)
where n is the number of sides of the polygon.
1) if the sum of the interior angles of a polygon equals 1980,
180(n - 2) = 1980
180n - 360 = 1980
180n = 1980 + 360 = 2340
n = 2340/180 = 13
2) if n = 9, the number of degrees would be
180(n - 2) = 180(9 - 2)
= 180 × 7 = 1260 degrees
3) 180(n - 2) = 1620
n - 2 = 1620/180 = 9
n = 9 + 2 = 11
4) n = 18
The number of degrees would be
180(n - 2) = 180(18 - 2) = 2880 degrees.
5) n = 17
The number of degrees would be
180(n - 2) = 180(17 - 2) = 2700 degrees.
6) the sum of the interior angles of a quadrilateral is 360 degrees.
If z varies jointly with x and y, x = 2 and y = 2, z = 7. Find z when x = 4 and y = 8.
Answer:
56
Step-by-step explanation:
z varies jointly with x and y:
z = kxy
When x = 2 and y = 2, z = 7.
7 = k(2)(2)
k = 7/4
z = 7/4 xy
When x = 4 and y = 8:
z = 7/4 (4)(8)
z = 56
A trains leaves Cincinnati at 2:00 pm.A second train leaves the same station in the same direction at 4:00 pm.The second train travels 24 mph faster than the first.If the second train overtakes the first at 7:00 pm, what is the speed of each train?
Answer:
Speed of first train = 36 mph
Speed of second train = 60 mph
Step-by-step explanation:
Given:
First train leaves Cincinnati at 2:00 PM
Second train leaves same station at 4:00 PM
Speed of second train is 24 mph faster than first train.
The second train overtakes the first at 7:00 PM
To find the speeds of each train.
Solution:
First train:
Let speed of first train be = [tex]x\ mph[/tex]
Time of travel between 2:00 PM to 7:00 PM = [tex]7-2=5\ h[/tex]
Distance traveled by 1st train in 5 hours in miles = [tex]Speed\times time = x\times 5 = 5x[/tex]
Second train:
Then, speed of second train will be = [tex](x+24)\ mph[/tex]
Time of travel between 4:00 PM to 7:00 PM =[tex]7-4 = 3\ h[/tex]
Distance traveled by second train in 3 hours in miles = [tex]Speed\times time = (x+24)\times 3=3x+72[/tex]
At 7:00 PM both trains meet as the second train overtakes the first. This means the distance traveled by both the trains is same at 7:00 PM as they both leave from same stations.
Thus, we have:
[tex]5x=3x+72[/tex]
Solving for [tex]x[/tex]
Subtracting both sides by [tex]3x[/tex]
[tex]5x-3x=3x-3x+72[/tex]
[tex]2x=72[/tex]
Dividing both sides by 2.
[tex]\frac{2x}{2}=\frac{72}{2}[/tex]
∴ [tex]x=36[/tex]
Speed of first train = 36 mph
Speed of second train = [tex]36+24=[/tex] 60 mph
Final answer:
The speed of the first train is 36 mph and the speed of the second train, which is 24 mph faster, is 60 mph. This was determined by setting up an equation based on the equal distances covered by both trains when the second overtakes the first.
Explanation:
The question involves solving a rate, time, and distance problem typically found in algebra or kinematics. To find the speeds of the two trains, we can set up an equation based on the fact that the distance covered by both trains is the same at the point where the second train overtakes the first. Let's define the speed of the first train as s (in mph). Therefore, the speed of the second train will be s + 24 mph. Since the first train leaves at 2:00 pm and is overtaken at 7:00 pm, it travels for 5 hours. The second train, leaving two hours later at 4:00 pm, travels for 3 hours.
The distance covered by each train can be expressed as their speed multiplied by the time traveled. For the first train, it's s 5 hours, and for the second train, it's (s + 24) 3 hours. Setting these two distances equal gives us:
s 5 = (s + 24) imes 3
Solving for s gives:
s imes 5 = 3s + 72
5s - 3s = 72
2s = 72
s = 36
So, the speed of the first train is 36 mph, and the speed of the second train is 60 mph (36 + 24).
Matt wants to build a rectangular enclosure for this animal. One wide of the pen will be against the barn, so he needs no fence on that side. The other three sides will be enclosed with wire fencing. If Matt has 1000 feet of fencing. You can find the dimensions that maximize the area of the enclosed.
Answer:
500 feet by 250 feet.
Step-by-step explanation:
Let the length be x and the width y feet.
As we have 1000 feet of wire:
x + 2y = 1000
2y = 1000 - x
y = 500 - 0.5x
So the area = x(500 - 0.5x)
A = 500x - 0.5x^2
For a maximum area the derivative
A' = 500 -x = 0
x = 500 feet.
2y = 1000 - 500
y = 250 feet.
Consider the two functions. Which statement is true? A) Function 1 has a greater rate of change by 2 B) Function 2 has a greater rate of change by 2 C) Function 1 has a greater rate of change by 3 2 D) Function 2 has a greater rate of change by 3 2
Answer:
D. Function 2 has a greater rate of change by
3
2
Step-by-step explanation:
Function 2 has a greater rate of change by
3
2
m =
y2 − y1
x2 − x1
Function 1 has a slope of
1
2
.
x-int = (−4, 0)
y-int = (0, 2)
m =
2 − 0
0 − (−4)
=
2
4
=
1
2
Function 2 has a slope of 2.
m =
5 − 3
3 − 2
=
2
1
= 2
thus,
2 −
1
2
=
4
2
−
1
2
=
3
2
What is the value of x
Help is needed.
Answer:
x = 27.2.
Step-by-step explanation:
As BD || CE the triangles ABD and ACE are similar.
AB = 25 - 8 = 17.
AB / AC = AD / AE ( similar triangles)
17 / 25 = x / 40
x = 17*40 / 25
= 27.2.
Keisha bought cups of coffee and bagels for the people in her office. Each bagel cost $2 and each cup of coffee cost $1.50. Keisha spent a total of $40 to buy 23 items. Let x represent the number of bagels and y represent the number of cups of coffee.
Answer:
The number of bagels is 11 and the cups of coffee is 12.
Step-by-step explanation:
Given:
Keisha bought cups of coffee and bagels for the people in her office. Each bagel cost $2 and each cup of coffee cost $1.50.
Keisha spent a total of $40 to buy 23 items.
Now, to find the number of cups of bagels and coffee.
As given in question:
Let [tex]x[/tex] represent the number of bagels.
And [tex]y[/tex] represent the number of cups of coffee.
So, the total number of items:
[tex]x+y=23[/tex]
[tex]x=23-y[/tex] ......(1)
Now, the total money spent on items:
[tex]2x+1.50y=40[/tex]
Substituting the value of [tex]x[/tex] from equation (1):
[tex]2(23-y)+1.50y=40[/tex]
[tex]46-2y+1.50y=40[/tex]
[tex]46-0.50y=40[/tex]
Subtracting both sides by 46 we get:
[tex]-0.50y=-6[/tex]
Dividing both sides by -0.50 we get:
[tex]y=12.[/tex]
The number of cups of coffee = 12.
Now, to get the number of bagel we substitute the value of [tex]y[/tex] in equation (1):
[tex]x=23-y[/tex]
[tex]x=23-12[/tex]
[tex]x=11.[/tex]
The number of bagels = 11.
Therefore, the number of bagels is 11 and the cups of coffee is 12.
The number of lacrosse sticks sold at a sporting goods store in November decreases by 35% from the number sold in October. In October, 80 sticks were sold. How many lacrosse sticks were sold in November?
Answer:the number of lacrosse sticks that were sold in November is 52
Step-by-step explanation:
The number of lacrosse sticks sold at a sporting goods store in November decreases by 35% from the number sold in October. If the number of lacrosse sticks sold in October is 80, then the amount by which it decreased would be
35/100 × 80 = 0.35 × 80 = 28
Therefore, the number of lacrosse sticks that were sold in November would be
80 - 28 = 52
(1) 4m+5=3m-5/2 (2) -2+7(x+2)=5(2x-2)+4 Show work for every step.
Answer:
m = -3x = 6Step-by-step explanation:
1)
[tex]4m+5=\dfrac{3m-5}{2} \quad\text{given}\\\\2(4m+5)=\dfrac{2(3m-5)}{2} \quad\text{multiply by 2}\\\\8m+10=3m-5 \quad\text{use the distributive property}\\\\(8m+10)-(3m+10)=(3m-5)-(3m+10) \quad\text{subtract $3m+10$}\\\\5m=-15 \quad\text{collect terms}\\\\\dfrac{5m}{5}=\dfrac{-15}{5} \quad\text{divide by 5}\\\\m=-3 \quad\text{simplify}[/tex]
____
2)
[tex]-2+7(x+2)=5(2x-2)+4 \quad\text{given}\\\\-2+7x+14=10x-10+4 \quad\text{use the distributive property}\\\\7x+12=10x-6 \quad\text{collect terms}\\\\(7x+12)-(7x-6)=(10x-6)-(7x-6) \quad\text{subtract $7x-6$}\\\\18=3x \quad\text{collect terms}\\\\\dfrac{18}{3}=\dfrac{3x}{3} \quad\text{divide by 3}\\\\6=x \quad\text{simplify}[/tex]
A binomial event has n = 50 trials. The probability of success for each trial is 0.60. Let x be the number of successes of the event during the 50 trials. What are μx and σx?
30 and 3.4641
30 and 5.4772
20 and 3.4641
20 and 5.4772
50 and 3.4641
Answer:
A. 30 and 3.4641
Step-by-step explanation:
The solution is Option A.
The value of the standard deviation is given by μx = 30 and σx = 3.4641
What is Standard Error?The standard deviation of a statistic's sample distribution, or an approximation of that standard deviation, is the statistic's standard error. The standard error of the mean is used when referring to a statistic that is the sample mean. The standard error of the mean, or simply standard error, indicates how different the population mean is likely to be from a sample mean.
The standard error S = √ [ ( 1 - p ) p / n ]
where p = population proportion
n = sample size
Given data ,
Let the number of trials n = 50
Let the probability of success be represented as p = 0.60
Now , let the standard deviation be σ
S = √ [ ( 1 - p ) p / n ]
Substituting the values in the equation , we get
S = √ ( 0.60 ) ( 0.40 ) / 50
S = √ 0.24/50
S = √0.0048
S = 0.0692820
So , the value of σ = 0.0692820
Therefore , the value of σx = 0.0692820 x 50 = 3.4641
Now , the value of μx = 0.60 x 50 = 30
Hence , the value of μx and σx are 30 and 3.4641 respectively
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Megan spent two out of five of her money on a doll and half of the remainder on a musical box she spent eight dollars more on the doll than on a musical box how much money did she have left
Answer:
Megan has left with $24.
Step-by-step explanation:
Let the total money she has be 'y'.
Given:
Megan spent two out of five of her money on a doll.
So we can say that;
Money spent on doll = [tex]\frac{2}{5}y[/tex]
Also Given:
half of the remainder on a musical box.
Money spent on musical box = [tex](y-\frac{2}{5}y)\frac{1}2[/tex]
Now we will make the denominator common using LCM we get;
Money spent on musical box =[tex](\frac{5y}{5}-\frac{2y}{5})\times\frac{1}2}=(\frac{5y-2y}{5})\times \frac{1}{2}=\frac{3y}{10}[/tex]
Now Given:
she spent eight dollars more on the doll than on a musical box.
[tex]\frac{2y}{5} = \frac{3y}{10}+8[/tex]
Combining like terms we get;
[tex]\frac{2y}{5}-\frac{3y}{10}=8[/tex]
Now we will make the denominator common using LCM we get;
[tex]\frac{2y\times2}{5\times2}-\frac{3y}{10}=8\\\\\frac{4y}{10}-\frac{3y}{10}=8\\\\\frac{4y-3y}{10}=8\\\\y=8\times10\\\\y=\$80[/tex]
Money spent on doll = [tex]\frac{2}{5}y=\frac{2}{5}\times 80 = \$32[/tex]
she spent eight dollars more on the doll than on a musical box.
So we can say that;
Money spent on musical box = Money spent on doll -8 = [tex]32-8 = \$24[/tex]
Now to find the remaining money left we will subtract Money spent on doll and Money spent on musical box from total money she had.
framing in equation form we get;
remaining money left = [tex]80-32-24= \$24[/tex]
Hence Megan has left with $24.
For his phone service, Ivan pays a monthly fee of $14, and he pays an additional $0.05 per minute of use. The least he has been charged in a month is $74.75.What are the possible numbers of minutes he has used his phone in a month?
Answer:
1215 minutes are the possible numbers he has used his phone in a month.
Step-by-step explanation:
He has a monthly fee of 14$ then to the least that he has been charged we need to substract the monthly fee as follows:
Monthly charged = 74,75-14
Monthly charged= 60,75$
Then he pays an additional 0,05 $/minute of use, to know the consume:
Minutes= [tex]\frac{60,75}{0,05}[/tex]
Minutes= 1215 possible numbers of minutes he has used his phone.
Fred’s company is planning a new logo. The diagrams show two similar versions of the planned logo.
A) calculate the lengths of the sides marked a and b.
B) the smaller of the two versions of the logo costs £4.48 to paint with gold paint. Calculate the cost of the logo with the same gold paint.
Answer:
a=7.2*1.5=10.8 cm
b=6.3/1.5=4.2 cm
[tex]\pounds 4.48*2.25=\pounds 10.08[/tex]
Step-by-step explanation:
Proportional Geometric Shapes
A) We are given two similar shapes of a logo. They are to be proportional. We only need to find the proportion ratio of two of them to find the rest of the lengths.
The upper sides have 7.5 cm and 5 cm respectively. This gives us the ratio
[tex]\displaystyle r=\frac{7.5}{5}=1.5[/tex]
Which means all the measures of the smaller logo are 1.5 smaller than those of the larger. This means
b=6.3/1.5=4.2 cm
a=7.2*1.5=10.8 cm
B) To paint the logos, we need to cover its surface, so the ratio of the surface is 1.5*1.5=2.25
This means the cost to paint the larger logo is
[tex]\pounds 4.48*2.25=\pounds 10.08[/tex]
Answer:
A) a = 10.8, b = 4.2
B) £10.08
Step-by-step explanation:
A) 7.5/5 = 1.5
a = 7.2 x 1.5 = 10.8
5/7.5 = 2/3
b = 6.3 x 2/3 = 4.2
B) 1.5 x 1.5 = 2.25
£4.48 x 2.25 = £10.08
Javon, Sam, and Antoine are baking cookies. Javon has 3/2 cup of flour, Sam has 4 1/3 cups of flour, and Antoine has 3 4/6 cups of flour. How many cups of flour do they have altogether?
Answer:
They have [tex]9\frac{3}{6}\ cups[/tex] of flour altogether.
Step-by-step explanation:
Given:
Amount of flour Javon has = [tex]\frac{3}{2}\ cup[/tex]
Amount of flour Sam has = [tex]4\frac{1}{3}\ cups[/tex]
[tex]4\frac{1}{3}\ cups[/tex] can be Rewritten as [tex]\frac{13}{3}\ cups[/tex]
Amount of flour Sam has = [tex]\frac{13}{3}\ cups[/tex]
Amount of flour Antoine has = [tex]3\frac{4}{6}\ cups[/tex]
[tex]3\frac{4}{6}\ cups[/tex] can Rewritten as [tex]\frac{22}{6}\ cups[/tex]
Amount of flour Antoine has = [tex]\frac{22}{6}\ cups[/tex]
We need to find the amount of cups of flour they have altogether.
Solution:
Now we can say that;
the amount of cups of flour they have altogether can be calculated by sum of Amount of flour Javon has and Amount of flour Sam has and Amount of flour Antoine has.
framing in equation form we get;
amount of cups of flour they have altogether = [tex]\frac{3}{2}+\frac{13}{3}+\frac{22}{6}[/tex]
Now to solve we need to make the denominator common by using L.C.M we get;
amount of cups of flour they have altogether = [tex]\frac{3\times3}{2\times3}+\frac{13\times2}{3\times2}+\frac{22\times1}{6\times1}=\frac{9}{6}+\frac{26}{6}+\frac{22}{6}[/tex]
Now Denominators are common so we will add the numerators we get;
amount of cups of flour they have altogether = [tex]\frac{9+26+22}{6}= \frac{57}{6}\ cups\ \ OR \ \ 9\frac{3}{6}\ cups[/tex]
Hence They have [tex]9\frac{3}{6}\ cups[/tex] of flour altogether.
There are 25 white cars, 15 blue cars, 21 red cars, and 30 black cars on a dealership lot. What is the probability of selecting a red car off the lot? Round to three decimals.
Answer:
The probability of selecting a red car off the lot is 0.231.
Step-by-step explanation:
Given:
Number of white cars = 25
Number of blue cars = 15
Number of red cars = 21
Number of black cars = 30
We need to find the probability of selecting a red car off the lot.
Solution:
First we will find the Total number of cars in the lot.
Now we can say that;
Total number of cars in the lot is equal to sum of Number of white cars and Number of blue cars and Number of red cars and Number of black cars.
framing in equation form we get;
Total number of cars in the lot = [tex]25+15+21+30 = 91[/tex]
Now to find the probability of selecting a red car off the lot we will divide Number of red cars by Total number of cars in the lot.
framing in equation form we get;
P(red) = [tex]\frac{21}{91}=0.2307[/tex]
Rounding to three decimals we get;
P(red) = 0.231
Hence The probability of selecting a red car off the lot is 0.231.
The probability of selecting a red car off the lot, rounded to three decimals, is 0.231.
First, we need to find the total number of cars on the lot by adding up the number of cars of each color:
Total number of cars = Number of white cars + Number of blue cars + Number of red cars + Number of black cars
Total number of cars = 25 + 15 + 21 + 30
Total number of cars = 91
Next, we find the probability of selecting a red car by dividing the number of red cars by the total number of cars:
Probability of selecting a red car = Number of red cars / Total number of cars
Probability of selecting a red car = 21 / 91
To round to three decimals, we perform the division:
Probability of selecting a red car = 0.2308
Rounded to three decimals, the probability is 0.231.