Answer:
The different card designs possible are:
224
Step-by-step explanation:
It is given that:
There are 2 sizes, 4 colors, 7 phrases, and 4 pictures for her to choose from. (The printing company charges a fee to add extra design elements, so she will choose only one of each.)
As she has to choose one from each given item this means she will use a combination to choose the item.
We know that the combination for r choices out of total n choices is given as:
[tex]n_C_r=\dfrac{n!}{r!\times (n-r)!}[/tex]
Hence, the total combinations made are given as:
[tex]2_C_1\times 4_C_1\times 7_C_1\times 4_C_1\\\\\\=\dfrac{2!}{1!\times (2-1)!}\times \dfrac{4!}{1!\times (4-1)!}\times \dfrac{7!}{1!\times (7-1)!}\times \dfrac{4!}{1!\times (4-1)!}\\\\=2\times 4\times 7\times 4\\\\=224[/tex]
Hence, the different card designs that are possible are:
224
The different card designs that are possible will be 224. The formula for the combination is used to solve the problem.
What are permutation and combination?A permutation is an act of arranging the objects or elements in order.
Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.
The given data in the problem is;
Paula is going to choose 2 sizes, 4 colors, 7 phrases, and 4 pictures . If the one item has to be chosen;
The total combination is;
[tex]= \rm 2C_1 \times 4C_1 \times 7C_1 \times 4 C_1 \\\\ = \frac{2!}{1!\times (2-1)!} \times \frac{4!}{1! \times (4-1)!} \times \frac{7!}{1!\times (7-1)!} \times \frac{4!}{1!\times (4-1)!} \\\\ =2 \times 4 \times 7 \times 4 \\\\ =224[/tex]
Hence different card designs are possible will be 224.
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A box contains 3 red balls, 2 white balls, and 5 black balls. two balls are drawn at random from the box (with replacement of the first before the second is drawn). what is the probability of getting a red ball on the first draw and a white ball on the second?
Karla is mowing her lawn. She knows 2/5 of the lawn before stopping for a snack. She resumes mowing after her snack and mows another 1/3 of her lawn before stopping. What total fraction of the lawn does Karla mow before lunch?
Karla mows a total of 11/15 of her lawn before lunch after adding the fractions 2/5 and 1/3 with a common denominator of 15.
The student's question has two parts where Karla mows her lawn in fractions, first 2/5 and then another 1/3. To find the total fraction of the lawn that she mows before lunch, these two fractions need to be added. However, since they do not have the same denominator, we first need to find a common denominator to combine these fractions properly.
The least common denominator (LCD) for 5 and 3 is 15. We convert the fractions to have this common denominator:
(2/5) becomes (6/15) after multiplying both the numerator and denominator by 3.(1/3) becomes (5/15) after multiplying both the numerator and denominator by 5.Now we add the fractions:
(6/15) + (5/15) = (11/15)
Thus, Karla mows a total of 11/15 of her lawn before lunch.
Omar uses 1/6 of his tickets to ride the water slide. How many tickets does he use he has 24 in total?
What is 5(7h+3m) equal to?
△ABC is reflected to form △A′B′C′ .
The vertices of △ABC are A(−7, 1) , B(−5, −3) , and C(−3, 2) . The vertices of △A′B′C′ are A′(−7, −1) , B′(−5, 3) , and C′(−3, −2) .
Which reflection results in the transformation of △ABC to △A′B′C′ ?
A)reflection across the x-axis
B) reflection across the y-axis
C)reflection across y = x
D)reflection across y=−x
Answer:
The correct option is A.
Step-by-step explanation:
The vertices of △ABC are A(−7, 1) , B(−5, −3) , and C(−3, 2) . The vertices of △A′B′C′ are A′(−7, −1) , B′(−5, 3) , and C′(−3, −2) .
The relation between coordinates of preimage and image is defined as
[tex](x,y)\rightarrow (x,-y)[/tex]
Sign of y-coordinate changes but x-coordinate remains the same. It is possible it the figure is reflection across the x-axis.
Therefore the correct option is A.
An apple juice producer buys all his apples from a conglomerate of apple growers in one northwest state. the amount of juice squeezed from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce.what is the probability that a randomly selected apple will contain between 2.00 and 2.15 ounces?
an athlete is training to run a marathon. she plans to run 2 miles the first week. she increases the distance by 8% each week. whixh function models how far she will run in the nth week
Calculate the effective rate of interest (to the nearest hundredth percent) of the following Treasury bill. Given: $10,000 Treasury bill, 3.85% for 13 weeks.
a leatherback turtle swims at a constant rate of 2.5 kilometers per hour, at its constant rate of speed how long will it take for a leatherback turtle to swim 10 kilometers?
A store sells two kinds of candles, scented and unscented. The scented burns 1/12 inches in 20 minutes and the unscented burns 1/6 inches in 30 minutes. Which type of candle burns in 1 hour and what is its burn rate?
Given :The scented burns [tex] \frac{1}{12} [/tex] inches in 20 minutes
The scented candle will burn [tex] \frac{1}{12} times 3 =\frac{1}{4} [/tex] inches in one hour.
The unscented candle burns [tex] \frac{1}{6} [/tex] inches in 30 minutes
In one hour it will burn [tex] \frac{1}{6} times 2=\frac{1}{3} [/tex] inches .
Burn rate of scented is [tex] \frac{1}{4} [/tex] inches per hour.
Burn rate of unscented is [tex] \frac{1}{3} [/tex] inches per hour.
Trigonometric Identities and Applications?
Trigonometric identities are equations that hold true for all permissible values of the involved variables. They are fundamental to many areas of mathematics and have applications in various fields such as physics and engineering.
Explanation:Trigonometric identities are equations that are true for all values of the variables where both sides of the equation are defined. They are fundamental to the study of mathematics, particularly in geometry, calculus and physics.
Some of the basic trigonometric identities include:
Reciprocal identities:sin = 1/csc θcos = 1/sec θtan = 1/cot θPythagorean identities:sin² θ + cos² θ = 11 + tan² θ = sec² θ1 + cot² θ = csc² θ...Trigonometric identities are widely used in solving trigonometric equations and proving other identities, and in many fields such as engineering, physics and computer science.
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They could mow the lawn in how many hours if they work together
the width of a large, rectangular-shaped tree farm is 1.9 kilometers. The length of the farm is 4.4 kilometers. What is the best estimate of the area of the farm ?
Answer:- The best estimate of the area of the farm is 8 kilometers.
Explanation:-
Given:- Width of the rectangular shaped tree farm= 1.9 kilometers
⇒Estimated width of the farm=2 kilometers [2 is the nearest integer to 1.9]
Length of the rectangular shaped tree farm=4.4 kilometers
⇒Estimated length of the farm=4 kilometers [4 is the nearest integer to 4..4]
To make estimates, we usually round the numbers the nearest integer.
Now, Estimated Area of the Farm= estimated width × estimated length
= 2×4 kilometers = 8 kilometers.
∴the best estimate of the area of the farm =8 kilometers.
your water hose is leaking at a rate of 0.25 cups per hour. how many gallons did you hose leak in a full 24 hour day
Solution:
we are given that
water hose is leaking at a rate of 0.25 cups per hour.
We have been asked to find that
how many gallons did you hose leak in a full 24 hour day.
Since water hose is leaking at a rate of 0.25 cups per hour.
It mean the tank will leak by [tex] 0.25*4=1 \ Cup [/tex] in 4 Hours.
So in 24 Hours the tank will leak by [tex] \frac{24}{4}*1=6*1=6 \ Cups [/tex] .
As we know that 1 Gallon=16 Cups.
It mean in 24 Hours the tank leaked by [tex] \frac{1}{16}*6= 0.375 \ Gallon [/tex]
There are 50 dimes in a roll of dimes, 40 nickels in a roll of nickels, and 40 quarters in a roll of quarters. Rob has 12 rolls of coins with a total value of $70.00. He has 3 more rolls of nickels than dimes. How many rolls of each coin does he have?
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What is the trigonometric ratio for sin S?
Enter your answer, as a simplified fraction, in the boxes.
Answer: [tex]\frac{8}{17}[/tex] or 8:17
Step-by-step explanation:
For any angle x (other than right angle) in a right triangle ,the trigonometric ratio of sin x is given by :-
[tex]\sin x=\frac{\text{side opposite to x}}{\text{Hypotenuse}}[/tex]
Given: A right triangle with hypotenuse = 68 units
The side adjacent to S = 60
Let h be the side opposite to S, then using Pythagoras in the given right triangle, we get
[tex](68)^2=60^2+h^2\\\\\Rightarrow\ h^2=68^2-60^2\\\\\Rightarrow\ h^2=1024\\\\\Rightarrow\ h=\sqrt{1024}=32[/tex]
Thus, the side opposite to S = 32 units
Now, the trigonometric ratio for sin S is given by :-
[tex]\sin S=\frac{\text{side opposite to S}}{\text{Hypotenuse}}\\\\\Rightarrow\sin S=\frac{32}{68}=\frac{8}{17}[/tex]
Hence, the trigonometric ratio for sin S =[tex]\frac{8}{17}[/tex] or 8:17
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One side of a square is 2^3 inches.
What would be the area of the square?
*Solve the equation of 2^3 first*
Marlena is making fruit salad she will choose from 6 of the 11 different fruits offered at a fruit stand. How many different fruit salads can she make
The Correct answer is 462
During a two week period, Norm worked 85.6 hours. His hourly wage is $6.92. How much did he earn? (Round the answer to the nearest cent)
which number is least to greatest 42%,0.43,17/40
find the height of each pyramid square pyramid: volume 297 ft cubed area of the base 81 ft squared
I don't know if this is right but I got 0.14
Katie filled a measuring cup with 9/10 of a cup of vegetable oil. Then she poured 1/4 of a cup of the oil into a frying pan. How much oil is left in the measuring cup? Simplify your answer.
which of the following statements are true? check all that apply
Answer with explanation:
Mean of this data set
[tex]=\frac{\text{sum of all the observation}}{\text{Total number of observation}}\\\\=\frac{30+37+37+41+22+69+45+64+51+22+63+31+64+65+25+51+26+48+28+49}{20}\\\\=43.4[/tex]
Arranging the data set in ascending order
22, 22,25, 26, 28,30,31,37,37,41,45,48,49,51,51,63,64,64,65,69
Median =Middle observation ,if number of terms is odd
and if number of terms is even, divide number of terms by ,2 and then follow the procedure
[tex]=\frac{10^{th term}+11^{th term}}{2}\\\\=\frac{41+45}{2}\\\\=43[/tex]
To find the Outlier
[tex]Q_{1}=\frac{28+30}{2}=29,Q_{3}=\frac{51+63}{2}=57[/tex]
Interquartile range = 57 - 29=28
Data values are approximately equally distributed on both sides of median.
That is, 43-22=21, and ,69 -43=26
So,we can say that there will be no outliers.
Graph will be positively skewed.
Mean > Median
So,mean will be better measure of central tendency because, 43.4-22=21.4, and 69-43.4=25.6
Option A: There are no outliers.
And, Option C: The Mean is good measure of central tendency.
The stopping distance s of a car varies directly as the square of its speed v. If a car traveling at 20 mph requires 28 ft to stop, find the stopping distance for a car traveling at 55 mph
Akira Chang's uncle dies without a will, leaving an estate of $945,000. His heirs consist of a wife and two adult children. His state requires that, in the absence of a will, each child is to receive two-thirds as much as a spouse. How much will his wife receive?
Write a mixed number for p so that 3 1/4 x p is more than 3 1/4
solve equations using addition x+y=5 and x-y=3
Mark’s father drove the family car 32,143 miles last year. He drove the car 29,675 miles this year.
How many fewer miles did Mark’s father drive the car this year?
A. 2,468 mi
B. 2,578 mi
C. 3,468 mi
D. 3,478 mi
True Or False
The term software refers to everything from the machine’s operating system (OS) to the individual programs and applications you use to write, listen, speak, sing, or learn.
Question 10 an urn contains two white marbles and one black marble. a marble is drawn from the urn without replacement and put aside without my seeing it. then a second marble is drawn, and it is white. what is the probability that the unknown removed marble is white, and what is the probability that it is black?
Final answer:
The probability that the unknown removed marble is white is 1/2, and the probability that it is black is also 1/2. This is calculated by considering the outcomes of the draws, their probabilities, and the fact that drawing a white marble after another without replacement affects the outcomes.
Explanation:
The question involves calculating conditional probabilities in a scenario where marbles are drawn from an urn without replacement. Initially, the urn contains two white marbles and one black marble. A marble is drawn and set aside (its color unknown), and then a second marble is drawn, which is observed to be white. We are asked to find the probability that the first marble drawn was white, and the probability it was black.
To solve this, we consider the two possible scenarios for the first draw: drawing a white marble or drawing a black marble, and then drawing a white marble in the second draw. The probability of drawing white then another white (WW) equals, the probability of drawing a white marble first (2/3) multiplied by the probability of drawing the second white marble given the first was white (1/2). This gives (2/3)*(1/2) = 1/3. Alternatively, the probability of drawing a black then a white marble (BW) equals the probability of drawing a black marble first (1/3) multiplied by the probability of drawing a white marble given the first was black (2/2) = 1/3, simplifying to (1/3)*(1) = 1/3
To find the probability that the unknown marble is white, we see that both scenarios WW and BW result in drawing a white marble second, so we only need to calculate the probability of the WW scenario over the total probability of drawing a white marble in the second draw. This gives us 1/3 / (1/3 + 1/3) = 1/2. Therefore, the probability that the unknown marble is white is 1/2, and by complement, the probability it is black is also 1/2