The probability of an event is given by dividing the favorable outcomes by total number of outcomes. The sum of all the probabilities of events is always 1.
The probability that 2 red cards and 11 black cards are dealt is .
What is probability ?The probability of an event is given by dividing the favorable outcomes by total number of outcomes. The sum of all the probabilities of events is always 1. If for finding probability we have to select r out of n. Combination is used to select r items out of n, the formula is as follows,
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Finding the probability that 2 red cards and 11 black cards are dealt,
Number of favorable outcomes will be [tex]^{26}C_2\times^{26}C_{11}[/tex].
Total number of outcomes will be [tex]^{52}C_{13}[/tex]
Now, the probability will be,
[tex]P()=\frac{^{26}C_2\times^{26}C_{11}}{^{52}C_{13}} \\\\=\frac{325\times7726160}{635013559600} \\\\=0.00395[/tex]
Therefore, the probability that 2 red cards and 11 black cards are dealt is 0.00395.
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The fastest cheetah on record is Sarah who lives at the Cincinnati Zoo in Ohio. The fastest human on record is Usain Bolt. Sarah can
run 161 meters in the same time that Usain can run 100 meters. If Sarah's speed is 6.4 meters per second faster than Usain's, how
fast do Sarah and Usain run? Round values to one decimal place.
sarah’s speed:
usains speed:
Sarah can run = 100 metres.
Speed of usain bolt.It takes several steps to convert between the two rates of meters per second and miles per hour in this task.Since the units in this case are measured in meters per second, we do not know what this translates to in miles per hour. Since the speedometers in our cars utilize these numbers, the majority of us are accustomed to thinking of speeds in terms of miles per hour; therefore, it is advantageous for students to be able to convert between miles per hour and other units of speed that naturally arise.The first approach displays all units used in the calculations but waits until the very end to perform any calculations. The second option takes a step-by-step approach and offers anacc to our question=
Usain Bolt traveled 100 meters in 9.63 seconds. 1 meter is 3.28 feet, so 100 meters is.Usain Bolt traveled 1 foot in 0.02936 seconds. 1 mile is 5280 feet, so at this speed, he would travel 1 mile in 5280×0.02936=155 seconds.learn more about speed,distance,time click here:
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Line ℓ has equation y=
–
x+5. Find the distance between ℓ and the point G(6,4).
Answer:
2.5√2 units
Step-by-step explanation:
The shortest distance between a point and a line is the length of the line segment perpendicular to the line and passes through the given point.
~~~~~~~~~~~~~~~~~~~~~
y = - x + 5 , slope m = - 1
Slope of perpendicular line is opposite reciprocal. In our case is 1 .
G ( 6 , 4 )
y - 4 = 1 × ( x - 6 )
y = x - 2
x - 2 = - x + 5 , x = 3.5
y = 1.5
Perpendicular line intersect the given line at the point O ( 3.5 , 1.5 )
OG = [tex]\sqrt{(6-3.5)^2 +(4-1.5)^2 }[/tex] = 2.5√2 units
A scientist is observing two ant colonies. The colonies each have 800 ants when he begins observing them. The population of Colony A increases by 25% each week. The population of Colony B decreases by 25% each week. In each equation, y represents the ant population with respect to a number of weeks, x. Drag each equation to show whether it can be used to represent the ant population of Colony A, Colony B, or neither of these.
In writing the equations that describe each of the colonies A ad B we have;
y = 800e^0.25x (Colony A)y = 800e^-0.25x (colony B )What are the equations?We know that the increase or decrease of population are exponential problems. We such, we must be able to look at the problem form the exponential perspective. This is how we would be able to know how to write the appropriate equation that would be able to be used in each of the cases that have been shown in the problem.
We are told that; a scientist is observing two ant colonies. The colonies each have 800 ants when he begins observing them. The population of Colony A increases by 25% each week. The population of Colony B decreases by 25% each week. In each equation, y represents the ant population with respect to a number of weeks, x.
Thus;
For colony A we can write;
y = 800e^0.25x
For colony B we can write;
y = 800e^-0.25x
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A pediatrician prescribes 5 milliliters (ml) of a pain reliever for every 25 pounds of a child's weight. How many milliliters of
medicine will the doctor prescribe for a child who weighs 60 pounds?
If the child's weight is 60 pounds , then the doctor will prescribe 12 milliliter of medicine .
In the question, '
it is given that
the for every 25 pounds of weight 5 milliliter of pain reliever is required .
we need to find the amount of medicine for the child weighing 60 pounds
So , for 25 pounds = 5 milliliter is needed
for 1 pound = 5/25 ml is needed
hence for 60 pound = 60*(5/25) ml will be prescribed .
on simplifying further ,
we get
= 60*(5/25)
= 60*(1/5)
= 12 ml
Therefore , the doctor will prescribe 12 ml of medicines .
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1. in an experiment in which a six-sided dice is rolled twice, what is the probability that 4-dots side appears in at least one roll?
Answer:
11/36 = 0,305556 = 30,5556%
Step-by-step explanation:
5/6 * 5/6 = 25/36
36/36 - 25/36 = 11/36
For this problem, write the numbers in scientific notation. 2,156 A. 21.56 × 102 B. 2.156 × 103 C. 2.156 × 102
Answer:
2,156 A. 21.56
Step-by-step explanation:
Write an equation in slope-intercept form of the line that passes through $\left(-5,\ 19\right)$ and $\left(5,\ 13\right)$ .
Answer:
hmmm say 5)13
Step-by-step explanation:
i can't explain it
The equation of the line is y = (-3/5)x + 16
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The equation of a line is given by:
y = mx + c
The line passes through:
(-5, 19) and (5, 13)
So,
m = (13 - 19) / (5 + 5)
m = -6/10
m = -3/5
Now,
(5, 13) = (x, y)
13 = (-3/5) x 5 + c
13= -3 + c
13 + 3 = c
c = 16
Now,
y = mx + c
y = (-3/5)x + 16
Thus,
The equation of the line is y = (-3/5)x + 16
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what is the scale factor of a figure with a shape with a side lengths of 12 and is dilated to a shape with 4
The scale factor of a figure with a shape with a side length of 12 and is dilated to a shape with 4 is 1/3.
What is a scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
Given that a figure with side length of 12 units is being dilated in a figure with side length of 4.
In this case, the scale factor = 4/12 = 1/3
Hence, The scale factor of a figure with a shape with a side length of 12 and is dilated to a shape with 4 is 1/3.
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HELP the price of gasoline purchased varies directly with the number of gallons purchased if 10 gallons of gasoline are purchased for$23 what will be the price of 50 gallons be?
Answer:
Step-by-step explanation:
It will be 115$
Answer: the answer is $21.7391304348 or round to $21.74 is the cost for 50 gallons
Step-by-step explanation: I did the calculations and it costs $2.30 a gallon
Can somone help me with this will mark u brainliest
The simplest radical form of √(11/(x + 4)) when x is 16 is; ¹/₁₀√55
How to simplify surds in radical form?Surds are actually the expressions of the number, and often use radicals. Meanwhile, the radical is just the symbol used to express the square root.
We are given the expression of the surd as;
√(11/(x + 4))
We want to solve this for when x = 16. Thus, we plug in 16 for x in the surd to get;
√(11/(16 + 4))
= √(11/20)
Now, we can rewrite the fraction in the bracket to have the denominator as a perfect square by multiplying both numerator and denominator by 5 to get;
√(55/100)
Square root of 100 is 10 and as such we now have;
√(55/100) = ¹/₁₀√55
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At a party, 60 drank malt, 48 drank beer, 36 drank cocacola, 20 drank both beer and cocacola, 18 drank both cocacola and malt, 15 drank malt and beer and 12 drank all the three. If there are 100 in the party, is the data consistent?
Answer:
no because 60+48+36 is 144
Step-by-step explanation:
please mark brainliest
The total number of people is 144. The data is not consistent.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that at a party, 60 drank malt, 48 drank beer, 36 drank cocacola, 20 drank both beer and cocacola, 18 drank both cocacola and malt, 15 drank malt and beer and 12 drank all the three.
The total number of the people in the party,
60+48+36 is 144
But it is given in the question that there are 100 in the party.
Therefore, the total number of people is 144. The data is not consistent.
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Help me please!!!!!
The matrix
[tex]MN = \left[\begin{array}{ccc}-2&1&0\\17&2&-3\\11&12&-5\end{array}\right][/tex]
The given matrix is
[tex]M = \left[\begin{array}{ccc}1&0\\-4&3\\2&5\end{array}\right][/tex]
[tex]N = \left[\begin{array}{ccc}-2&1&0\\3&2&-1\\\end{array}\right][/tex]
The Order of M = (3×2)
The Order of N = (2×3)
Since the number of columns of M is equal to the number of rows, the multiplication of M and N is possible,
The order of the matrix formed is MN = ( 3 × 3 )
So,
[tex]MN = \left[\begin{array}{ccc}-2+0&1+0&0+0\\8+9&-4+6&0-3\\-4+15&2+10&0-5\end{array}\right] \\\\MN = \left[\begin{array}{ccc}-2&1&0\\17&2&-3\\11&12&-5\end{array}\right][/tex]
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Terry sees this offer.
Refurbished phone
35% OFF
Now only £78
How much was the phone before the discounted price?
Answer: The phone was £120 before the discount.
Angles ABC and CBD are a linear pair. If m∠CBD=90°, what is m∠ABC in degrees?
NO LINKS OR FILES.
Measurement of ∠ ABC is 90°
What is Linear pair?A linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.
Given that ∠ CBD and ∠ ABC are linear pairs,
Therefore, m∠ CBD + m∠ ABC = 180°
m∠ ABC = 180° - 90° = 90°
Hence, Measurement of ∠ ABC is 90°
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Find the value of x. Then find the measure of each angle and write the answers in ascending order.
The measured interior angles of the triangle are 40°, 60°, and 80° in ascending order.
What is a Triangle?Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.
The triangle has interior angles are:
(2x)°, (3x)° and (4x)°
As we know that the sum of interior angles is 180 degrees in the triangle.
According to the given figure,
(2x)° + (3x)° + (4x)° = 180°
Apply the addition operation in the above equation,
9x = 180
x = 180/9
x = 20°
Thus, The triangle has interior angles are:
(2x)° = 2 × 20° = 40°
(3x)° = 3 × 20° = 60°
(4x)° = 4 × 20° = 80°
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Estimate the answer to 4.8 x 47.1
Answer:
235
Step-by-step explanation:
When estimating the product of two decimals, first round the decimals to their nearest whole numbers.
If the number in the tenth place is less than 5, round down to the nearest whole number.If the number in the tenth place is 5 or more, round up to the nearest whole number.Therefore,
4.8 ≈ 547.1 ≈ 47So an estimate of the product of the two decimals is:
[tex]\implies 4.8 \times 47.1 \approx 5 \times 47[/tex]
Partition 47 into tens and units:
[tex]\implies 5 \times 47 = 5 \times (40 + 7)[/tex]
Apply the distributive property of multiplication over addition:
[tex]\begin{aligned}\implies 5 \times (40 + 7) &= (5 \times 40) + (5 \times 7)\\&=200+35\\&=235\end{aligned}[/tex]
Therefore:
[tex]\boxed{4.8 \times 47.1 \approx 235}[/tex]
two foods contain proteins, carbohydrates, and fats. food a costs $1 per pound and contains 30% protein, 10% fat, and 50% carbohydrates. food b costs $1.50 per pound and contains 20% protein, 4% fat, and 75% carbohydrates. what is a combination of x pounds of food a and y pounds of food b that provides at least 1 1 2 pounds of protein, 3 3 4 pounds of carbohydrates, and 1 5 pound of fat at the lowest cost? (x, y)
A combination of x pounds of food a and y pounds of food b that provides at least 1 1 2 pounds of protein, 3 3 4 pounds of carbohydrates, and 1 5 pound of fat lowest cost is at (x,y) is (3,2).
Define function.A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Given,
Function:
C = x + 1.5y
Subjected to:
30x + 20y ≥ 13/10 ×100 ≥ 130
10x + 4y ≥ 1/5 × 100 ≥ 20
50x + 75y ≥ 3 × 100 ≥ 300
Feasible region:
(0, 13/2), (3,2) (6,0)
C = x + 1.5y
(0, 13/2) ⇒ C = 0+ (1.5)(13/2)
(0.13/2) ⇒ C = 9.75
(3,2) ⇒ C = 3+ (1.5)(2)
(3,2) ⇒ C = 6
(6,0) ⇒ C = 6 + 0
(6,0)⇒ C = 6
A combination of x pounds of food a and y pounds of food b that provides at least 1 1 2 pounds of protein, 3 3 4 pounds of carbohydrates, and 1 5 pound of fat lowest cost is at (x,y) is (3,2).
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c) Which of these
numbers is a square number?
A: 4x10^5
B:9x10^4
C:4x10^3
D:9x10^3
F(x)=x^2+1 what is f(f(x))?
Answer:
f(f(x)) = [tex]x^{4}[/tex] + 2x² + 2
Step-by-step explanation:
to evaluate f(f(x)), substitute x = f(x) into f(x)
f(f(x))
= f(x² + 1)
= (x² + 1)² + 1 ← expand factor using FOIL
= [tex]x^{4}[/tex] + 2x² + 1 + 1
= [tex]x^{4}[/tex] + 2x² + 2
Answer:
[tex]f[f(x)]=x^4+2x^2+2[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=x^2+1[/tex]
To find the composite function f[f(x)], substitute the function f(x) in place of the x in function f(x):
[tex]\begin{aligned}\implies f[f(x)]&=f(x^2+1)\\&=(x^2+1)^2+1\\&=(x^2+1)(x^2+1)+1\\&=x^4+x^2+x^2+1+1\\&=x^4+2x^2+2\end{aligned}[/tex]
How long will it take for $3, 900 to double if it is invested at 8% annual interest compounded 2 times a year?
Enter in exact calculations or round to 3 decimal places.
It will take___years to double.
How long will it take if the interest is compounded continuously?
Compounded continuously, it would only take___ years.
The number of years to double the investment is 8.824 years.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
We have,
P = $3,900
R = 8%
n = 2
A = 2P = 2 x 3,900 = $7,800
Now,
A = P [tex](1 + r/n)^{nt}[/tex]
7,800 = 3,900 [tex](1 + 0.04)^{2t}[/tex]
78/39 = [tex](1.04)^{2t}[/tex]
2 = [tex](1.04)^{2t}[/tex]
Taking logs on both sides.
log 2 = 2t log(1.04)
0.30 = 2t x 0.017
0.30/0.017 = 2t
17.65 = 2t
Divide both sides by 2.
t = 17.65 / 2
t = 8.824 years.
Thus,
The number of years to double the investment is 8.824 years.
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in a recent study, it was found that 87.3% of all homes have a large-screen tv. a sample of 28 homes is selected. the data follows a binomial distribution. a) what is the mean of the distribution? (round your answer to 3 decimals.)
The mean of the distribution is 24.444.
Given, that 87.3% of all homes have a large-screen tv. a sample of 28 homes is selected.
Now, we have to find the mean of the distribution
As, we know
E(x) = np
where, n is the sample and p is the probability of success
So, n = 28 and p = 87.3% = 0.873
Now, on using the formula we get,
E(x) = (28)(0.873)
E(x) = 24.444
So, the mean of the distribution is E(x) = 24.444
Hence, the mean of the distribution is 24.444.
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A bag contains 8 beads.
. 2 of the beads are blue.
. 1 of the beads is green.
. 3 of the beads are purple.
. The rest of the beads are red.
Jules takes a bead from the bag at random. Optional working
c) What is the probability that this bead
is purple or red?
Answer:
the probability would be taking a purple one. there are only 2 red beads
3/2 or 2/3
The probability that the two beads selected from the bag at random is purple or red is 5/8.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Total number of beads = 8
2 of the beads are blue.
1 of the beads is green.
3 of the beads are purple.
Red beads = 8 - (2 + 1 + 3) = 8 - 6 = 2
Now,
The probability that the two beads selected are purple or red.
= Probability that the two beads are purple + Probability that the two beads are red.
= 3/8 + 2/8
= 5/8
Thus,
The probability that the two beads selected are purple or red is 5/8.
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Having trouble solving this
Answer:
[tex]r = 2279.41[/tex]
Supposed the original quality is 1,500 and the new quality is 1,650 what should be the first step in solving for the percent increase what is the percent increase
The first step is to find the increase in quantity.
The percentage increase is 10%.
How to calculate the percentage?From the information, the original quality is 1,500 and the new quality is 1,650.
The first step is to find the increase in quality will be:
= New quantity - Old quantity
= 1650 - 1500
= 150
The percentage increase will be:
= Increase / Old Quantity × 100
= 150 / 1500 × 100
= 10%
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Suppose we want to choose 4 letters, without replacement, from 17 distinct letters. How many ways can this be done, if the order of the choices is not taken into consideration
Thus, the number of ways in which to choose 4 letters, without replacement, from 17 distinct letters is 57,120.
Define the term permutation?The term permutation applies to a mathematical computation of a number of possible arrangements of a given collection. Simply said, a permutation is a term that defines the amount of different ways something can be organized or arranged.Total distinct letters are 17.
There are 17 alternatives for the initial letter if there are 17 letters.
There are just 16 alternatives left once you remove the letter.
Each time you remove a letter, the bag contains one fewer letter.
Number of ways = 17 x 16 x 15 x 14
Number of ways = 57,120
Thus, if the sequence of the alternatives is irrelevant, there are 57,120 options.
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Sheri has $15,200 to invest in mutual funds and in bonds. sheri has selected a mutual fund that earns 1% a year and a bond that earns 4% a year. if she wants to earn $548 at the end of the first year, how much does she need to invest into each type of account?
Sheri should invest $2000 in mutual fund and $13,200 in bond.
Let the amount to be invested in mutual fund be x. So, the amount to be invested in bond will be (15,200 - x). Forming the equation now -
1%×x + 4%×(15,200 - x) = 548
x/100 + 60,800/100 - 4x/100 = 548
60,800 - 3x = 54800
3x = 60800 - 54800
3x = 6000
x = 6000 ÷ 3
x = 2000
Amount to be invested in mutual fund = $2000
Amount to be invested in bond = 15,200 - 2000
Amount to be invested in bond = $13,200
Sheri should invest $2000 and $13,200 in mutual fund and bond respectively.
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22. A box containing 40 marbles weighs 280 grams. When 30 marbles are added, the box weighs 430 grams. How many grams does the box weigh when empty? A 80 B 120 C 150 D 490 E 710
Answer:
A/ 80 grams
Step-by-step explanation:
We know that 430 - 280 = 150, so each marble weights 5 grams. Then we take 5 times 40 = 200 grams. Then we take 280 subtract 200 = 80 grams
p x 3,700=4,070
There was a % percent increase in the number of visitors.
There was 110% percent increase in the number of visitors.
Percent:
Basically, percentage refers the number or ratio that can be expressed as a fraction of 100.
Given,
p x 3,700=4,070
There was a % percent increase in the number of visitors.
Here we need to find the increase in the percentage.
While we looking into the given question we have identified that,
The Old population = 3700
And the new population = 4070
So, the value of P is calculated as,
=> p = 4070/3700
=> p = 1.1
When we convert this into percent then we get 110% as increase.
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The probability that a male’s foot is between 10 and 12. 5 inches is ___%
P(10
The probability of a foot of male being between 10 and 12. 5 inches is 59%.
Define the term normal distribution?The normal distribution approximates any real-valued random distribution which clusters around one single mean value. A cumulative frequency is a procedure that determines if the total amount of information in such a data set is less than and equal to a specific value.The z score of the distribution is found as-
z = (x - μ)/σ
In which,
μ = mean = (11)
σ = standard distribution (1.5)
The likelihood that a male's foot measures between 10 and 12. 5 inches.
P(10 < x < 12.5)
For x = 10
z = (10 - 11) / 1.5
z = -0.67
check the p-value fro z score table.
p (z = -0.67) = 0.2514
For x = 12.5
z = (1.5 - 11)/1.5
z = 1
p (z = 1) = 0.8413
P(10 < x < 12.5) = 0.8413 - 0.2514
P(10 < x < 12.5) = 0.5899
P(10 < x < 12.5) = 58.99%
P(10 < x < 12.5) = 59%.
Thus, the likelihood of a male's foot being between 10 and 12. 5 inches is 59%.
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The complete question is attached in figure.
Determine which integer will make the inequality 5x + 6 ≤ 2x + 15 false.
S:{−2}
S:{5}
S:{2}
S:{−5}
Answer:
the correct she answer should be 5
Step-by-step explanation:
31 <= 25 is falseThe solution set for the given inequality is {.......-4, -3, -2, -1, 0, 1, 2, 3}, so the for x=5 the inequality is false. Therefore, the correct answer is option B.
The given inequality is 5x+6≤2x+15.
Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Here, the inequality can be solved as follows
5x+6≤2x+15
Subtract 6 on both the sides of the inequality, we get
5x+6-6≤2x+15-6
5x≤2x+9
Subtract 2x on both the sides of the inequality, we get
5x-2x≤2x+9-2x
3x≤9
Divide 3 on both the sides of the inequality, we get
x≤3
Here, solution set is {.......-4, -3, -2, -1, 0, 1, 2, 3}
So, the for x=5 the inequality is false.
Therefore, the correct answer is option B.
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