ANSWER
1,440
EXPLANATION
We have that 4 boys are competing and also 5 girls are competing. 3 medals are given to the boys and 3 medals are given to the girls.
For the boys, the gold medal can be awarded to one of 4 boys, then the silver medal can be awarded to 3 boys because 1 of them already got the gold medal. Finally, the bronze medal can be awarded to one of 2 boys, since the gold and silver medals are already taken. The number of ways the medals can be given to the boys is,
[tex]permutations_{boys}=4\cdot3\cdot2=24[/tex]This situation is similar for the girls, but in this case, there are 5 girls in total,
[tex]permutations_{girls}=5\times4\times3=60[/tex]The total ways the six medals can be given is,
[tex]permutations_{boys}\times permutations_{girls}=24\times60=1,440[/tex]Hence, there are 1,440 ways to give the six medals to the 4 boys and 5 girls.
In the diagram below of triangle DEF, G is a midpoint of DE and H is a midpoint of EF. IfGH = 50 -- 87, and DF = 9x + 0, what is the measure of GH? E H D F
GH = 18
Explanations:From the diagram:
DF = 9x + 0
GH = 50 - 8x
Since G is a midpoint of DE and H is a midpoint of EF, using the midpoint theorem:
DF = 2GH
9x + 0 = 2 (50 - 8x)
9x = 100 - 16x
9x + 16x = 100
25x = 100
x = 100/25
x = 4
Substituting the value of x into GH = 50 - 8x
GH = 50 - 8(4)
GH = 50 - 32
GH = 18
A restaurant offers a $12 dinner special that has 4 choices for an appetizer, 11 choices for an entree, and 3 choices for a dessert. How many different meals are available when you select an appetizer, an entree, and a dessert?
In an all boys school, the heights of the student body are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. What is the probability that a randomly selected student will be taller than 71 inches tall, to the nearest thousandth?
The probability that a randomly selected student will be taller than 71 inches tall is 0.010.
We use z score formula to calculate :
z = (x-μ)/σ
where,
z = standard score
x = observed value
μ = mean of students height
σ = standard deviation of students height
x = 63 inches
μ = 70 inches
σ = 3 inches
For x shorter than 63 inches we calculate
Z = (x - μ)/σ
then put the given values in above equation.
= (63 - 70)/3
= -2.33333
Probability value is :
P(x<63) = 0.0098153
Approximately to the nearest thousandth = 0.010
The probability that a randomly selected student will be taller than 71 inches tall is 0.010.
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m(25+2)(x-7)(4%-8)"y =
From the figure we can obtain 2 equations:
[tex](2y+2)+(4x-8)=180[/tex]and
[tex](9x-7)+(4x-8)=180[/tex]first lets simplify both equations:
for the first;
[tex]2y+4x=186[/tex]and for the second one:
[tex]9x+4x=195\Rightarrow13x=195\Rightarrow x=\frac{195}{13}=15[/tex]Now we have that x=15 and we can substitute x for 15 in the first equation to find y:
[tex]2y+4(15)=186\Rightarrow2y=126\Rightarrow y=63[/tex]so the final answe is: x=15 and y=63
factor out 2x^4 = 9x^2
Solution
Step 1
Rearrange the equation
[tex]2x^{4\text{ }}-9x^2=0[/tex]Step 2
factorise the equation
[tex]x^2(2x^2-9)=0[/tex]Hence by factorization, the answer is
x^2(2x^2 - 9) = 0
A circle has a circumference of 10 inches. Find its approximate radius, diameter and area
Answer:
Radius = 1.59 in
Diameter = 3.18 in
Area = 7.94 in²
Explanation:
The circumference of a circle can be calculated as:
[tex]C=2\pi r[/tex]Where r is the radius of the circle and π is approximately 3.14. So, replacing C by 10 in and solving for r, we get:
[tex]\begin{gathered} 10\text{ in = 2}\pi r \\ \frac{10\text{ in}}{2\pi}=\frac{2\pi r}{2\pi} \\ 1.59\text{ in = r} \end{gathered}[/tex]Then, the radius is 1.59 in.
Now, the diameter is twice the radius, so the diameter is equal to:
Diameter = 2 x r = 2 x 1.59 in = 3.18 in
On the other hand, the area can be calculated as:
[tex]A=\pi\cdot r^2[/tex]So, replacing r = 1.59 in, we get:
[tex]\begin{gathered} A=3.14\times(1.59)^2 \\ A=3.14\times2.53 \\ A=7.94in^2 \end{gathered}[/tex]Therefore, the answer are:
Radius = 1.59 in
Diameter = 3.18 in
Area = 7.94 in²
Determine the period
I hate acellus
Answer:
my answer i got is y=2x+9
Answer:
5
Step-by-step explanation:
They are asking for the Period. The Period goes from one peak to the next (or from any point to the next matching point). To me it looks like that value is 5 for this graph.
In a charity triathlon, Mark ran half the distance and swam a quarter of the distance when he took a quick break to get a drink of Gatorade he was just starting to bite the remaining 12 miles what was the total distance of the race?
Solving a present makes your problem using a system of linear equations
Answer:
Explanation:
How would you use the Pythagorean Theorem to find the missing length in the triangle shown? Find the missing length.
The given triangle is a right angle triangle. The pythagorean theorem is expressed as
hypotenuse^2 = one leg^2 + other leg^2
From the diagram,
hypotenuse = AB = c
one leg = BC = 9
other leg = AC = 12
By applying the pythagorean theorem, we have
[tex]\begin{gathered} c^2=9^2+12^2\text{ = 81 + 144} \\ c^2\text{ = 225} \\ c\text{ = }\sqrt[]{225} \\ c\text{ = 15} \end{gathered}[/tex]The missing length is 15 cm
Which of the following is only true sometimes? A. The sum of a rational number and a rational number is rational. B. The sum of a rational number and an irrational number is irrational. C. The product of an irrational number and an irrational number is irrational. D. The product of a nonzero rational number and an irrational number is irrational.
The sum of a rational number and a rational number is rational. ALWAYS
The sum of a rational number and an irrational number is irrational.
The product of an irrational number and an irrational number is irrational. SOMETIMES
For example, the product of multiplicative inverses like √2 and 1/√2 will be 1
The product of a nonzero rational number and an irrational number is irrational.
4. A stone nudged off the Royal Gorge Bridge near Cañon City, Colorado, falls 1053 feet before hitting water. Because its speed increases as it falls, the distance ittravels each second increases. During the first second, it drops 16 feet. During the next second, it drops an additional 48 feet. During the third second, it drops another80 feet. The distances traveled each second form an arithmetic sequence:16, 48, 80,...Part 1: How far does the stone fall during the 5th second? Find and use the explicitformula.a. What is the first term of the sequence?b. What is d, the common difference?c. Write the explicit formula in function notation. Use f(n) = f(1) + (n - 1)d, wheref(1) represents the first term.d. Use the explicit formula to find the distance the stone travels in the 5th second.Part II: The table below shows the values in the sequence you already know. Use the explicit formula or the common difference to complete the table for the first 7 seconds. Time (s) 1 2 3 4 5 6 7 Distance (ft) 16 48 80 | | 144 | | | | Part ||| : Use the table from part 2 to answer the questions a. The values in the table form a(n)___ sequence and the term numbers are shownb. The term values are shown in the in the____row, and the term numbers are shown in the ___ row. c. This sequence is associated with a(n)___function d. The domain of the function is the set of time values:___
The formula for determining the nth term of an arithmetic sequence is expressed as
f(n) = f(1) + (n - 1)d
Where
f(1) represents the first term
d represents the common difference
n represents the number of terms
From the information given,
f(1) = 16
d = 48 - 16 = 80 - 48 = 32
a) The first term of the sequence is 16
b) the common difference is 32
c) The explicit is
f(n) = 16 + 32(n - 1)
d) To find the distance the stone travels in the 5th second, it means that n = 5
Thus
f(5) = 16 + 32(5 - 1)
f(5) = 16 + 32 * 4
f(5) = 144
the distance the stone travels in the 5th second is 144 feet
The question is in the picture, couldn’t fit the last graph so sent it in a separate picture
Explanation:
Concept:
To figure out if a graph is a function, we will use the vertical line test below
The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines.
From the first graph we can see that the vertical line cuts the points at on intersection
The Second graph is given below as
Its has two intersections on both sides of the graph
The third graph is given below as
It has two intersections on the ride hand side of the graph
The Fourth graph ios given below as
Its has two intersection on the right hand side of the graph
In conclusion,
A graph is said to be a function if one value of x has a separate value of y
Therefore,
The final answer is
The FIRST OPTION is the correct answer
What is the slope of this line? :(
Answer:
y=1/4x+1
Step-by-step explanation:
Answer:
m=1/4
Step-by-step explanation:
Got it correct
Exam Content
Question 25
Approximately how many years would it take money to grow from $5,000 to $10,000 if it could earn 6% interest?
It would take 16.66 years to grow from $5,000 to $10,000 if it could earn 6% interest.
Time it would take money to grow from $5,000 to $10,000
The prinicipal amount is $ 5000
The total amount is $ 10000
The rate of interest is 6%
Interest = Amount - principal
interest = 10000 - 5000 = 5000
By putting the simple interest formula
SI = prt/100
where p is the principal, r is the rate of interest and t is the time period
SI = 5000 x 6% x t/100
5000 = 5000 x 6 x t / 100
5000 x 100= 5000 x 6 x t
t = 100/6
t = 16.66
Therefore, it would take 16.66 years to grow from $5,000 to $10,000 if it could earn 6% interest.
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What transformation would cause the change from ABC to A'B'C'?
Answer:
D. 1/4
Explanation:
When the coordinates of A, B, and C are multiplying by 1/4 we get A', B', and C'.
For example,
[tex]\frac{1}{4}\times A(-8,4)=A^{}(-\frac{8}{4},\frac{4}{4})[/tex][tex]\therefore A(-8,4)\rightarrow A^{\prime}(-2,1)[/tex]The same goes for B and C.
Hence, the transformation that gives us A'B'C' from ABC is Choice D DIlation using k = 1/4.
Which expression is equivalent to (2-3x) (2+3x) ?
Answer:
[tex]4-9x^{2}[/tex]
Step-by-step explanation:
in the first parenthesis, multiply the FIRST number (2 - 3x) by the numbers in the OTHER parenthesis. (2 + 3x)
[tex](2-3x)(2+3x)[/tex]
it would look like:
[tex]2(2) = 4\\2(3x) = 6x[/tex]
Next, multiply the SECOND number (2 - 3x) by the numbers in the OTHER parenthesis. (2 + 3x)
[tex]-3x(2) = -6x\\-3x(3x) = 9x^2[/tex]
Now, add like terms. Your answer should either be:
[tex]4+6x-6x+9^2[/tex] OR [tex]4 -9x^2[/tex]
Daylyn wants to win headphones . In addition to his grandmother and uncle, some friends of his agree that each one will give him a $5 donation . Some other friends agree that each one will pay him $0.25 for every correct answer. The number of friends who donate $ 5 to Daylyn is 3 times the number who pays him for correct answers. Write and solve an equation to find the number of friends who must pay him $0.25 for each correct answer in order for Daylyn to meet his goal
Let
x ------> number of friends of his agree that each one will give him a $5 donation
y -----> the number of friends who must pay him $0.25 for each correct answer
so
to win headphones-------> $350
we have that
x=3y -------> equation A
5x+0.25y=350 -------> equation B
substitute equation A in equation B
5(3y)+0.25y=350
solve for y
15y+o.25y=350
15.25y=350
y=22.95
therefore
the answer is 23 friends who must pay him $0.25 for each correct answerVictoria, Cooper, and Diego are reading the same book for theirlanguage arts class. The table shows the fraction of the bookeach student has read. Which student has read the leastamount? Explain your reasoning.
Given:
Completion of reading in fractions:
[tex]\text{Victoria}=\frac{2}{5};\text{Cooper}=\frac{1}{5};\text{Diego}=\frac{3}{5}[/tex]Since the denominators,
[tex]\text{The least value of the three given values is }\frac{1}{5}[/tex]Therefore, Cooper has read the least amount.
Which of the following is a perfect cube?118481
From the options given we will have that a perfect cube is:
[tex]1^3=1\ast1\ast1=1[/tex]So, 1 is the perfect cube.
Two students measured a box in class. They used a digital scale and found that the mass was 400 grams. They then measured the box found the length is 2cm, the width is 2cm, and the height is 1cm. What is the density of the object
Explanation
Step 1
the density of an object is given by:
[tex]\begin{gathered} density=\frac{mass_{object}}{volume_{object}} \\ \end{gathered}[/tex]Let
mass: 400 grams
length's box=2 cm
width´s box= 2 cm
height's box= 1 cm
Step 2
find the volume of the box
[tex]\begin{gathered} \text{Volume}=\text{ length}\cdot width\cdot height \\ \text{replacing} \\ \text{Volume= 2 cm }\cdot\text{ 2 cm }\cdot\text{ 1 cm} \\ \text{Volume}=\text{ 4 cubic cm} \end{gathered}[/tex]Step 3
finally, replace the values of mass and volume in the density equation
[tex]\begin{gathered} density=\frac{mass_{object}}{volume_{object}} \\ density=\frac{400\text{ grm}}{4cm^3} \\ \text{density}=100\frac{gr}{cm^3} \end{gathered}[/tex]I hope this helps you
-1514,2 – 30r2y3 + 45ryjent of517is 3(x^3)y + 6x(y^2) - 3.1. Whe3(x^3)y - 6x(y^2) +9Res-3(x^3)y + 6x(y^2) - 33(x^2)y + 5x(y^2) - 93(x^3)y + 5x(y^2) + 3
To find the quotient of the first part, we can start by noticing that all the factors on the denominator are present in all terms of the numerator, so we can factor those out and cancel with the denominator ones:
[tex]\frac{15x^4y^2-30x^2y^3+45xy}{5xy}=\frac{5xy\cdot3x^3y+5xy\cdot(-6xy^2)+5xy\cdot9}{5xy}=\frac{5xy\cdot(3x^3y-6xy^2+9)}{5xy}=3x^3y-6xy^2+9[/tex]So, the first dropdown option is
[tex]3x^3y-6xy^2+9[/tex]Also, this is the quotient, so we will use it for the second part.
The second part says that if we divide by one of the options (let's call it a), we will get:
[tex]\frac{3x^3y-6xy+9}{a}=x^3y-2xy^2+3[/tex]As we can see, no terms on the final result has fractional coefficient, so the number a has to be a common factor of all the terms coefficients. the coefficients are 3, -6 and 9, so the only common factors are 1 and 3, so the answer should be 3:
[tex]\frac{3x^3y-6xy+9}{3}=\frac{3(x^3y-2xy+3)}{3}=x^3y-2xy^2+3[/tex]So, the second dropdown option is 3.
HELP PLEASE!!!!!!!!!!! ILL MARK BRAINLIEST
The rational number - 91 / 200 is a number between the decimal numbers - 0.45 and - 0.46.
How to determine a rational number between two decimal numbers
In this problem we find two decimal numbers, of which we need to find a rational number between these numbers. Please notice that the decimal numbers are also rational numbers. First, we transform each decimal number into rational numbers:
- 0.45 = - 45 / 100
- 0.46 = - 46 / 100
Second, find a possible rational number between the two ends by the midpoint formula:
x = (1 / 2) · (- 45 / 100) + (1 / 2) · (- 46 / 100)
x = - 45 / 200 - 46 / 200
x = - 91 / 200
Then, the rational number - 91 / 200 is a number between - 0.45 and - 0.46.
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a bottle of ketchup holds 0.95 liters how maney milliliters does it hold?
Explanation:
The relation between liters and milliliters is:
[tex]1\text{ liter}=1000\text{ milliliters}[/tex]we have to multiply the liters by 1000
Answer:
The answer is 950 milliliters
Mr. Alvarez is laying square paver blocks in sections in rows that look like steps.Section 1 has 3 rows that look like steps, the section is 6 blocks wide, and the bottom step is 8 blocks long. Section 2 has 4 rows that look like steps, the Section is 8 blocks wide, and the bottom step is 10 blocks long. Each Section after that is 2 blocks wider and 2 blocks longer.Drag the numbers to complete the table. Numbers may be used once, more than once, or not at all.
12
14
36 blocks
56 blocks
108 blocks
Explanation:The length of section 1 = 8
The length increases by 2 uits as the section increases
Section 2 length of block = length of section 1 + 2 =
= 8 + 2
length of block = 10
Section 3 length of block = length of section 2 + 2
= 10 + 2
length of block = 12
Section 4 length of block = length of section 3 + 2
= 12 + 2
length of section = 14
Number of blocks needed:
if the blocks are counted,
For section 1 there are 6 rows . So we count the total number of blocks on each of them
= 4 + 4 + 6 + 6 + 8 + 8
Section 1 = 36 blocks
For section 2, we count the number of blocks on each row
= 4 + 4 + 6 + 6 + 8 + 8 + 10 + 10
section 2 = 56 blocks
For sectoion 3: The length and width increases by 2 respectively
previous length + 2 = 10 + 2 = 12
Due to the increase we would have two length of 12
= 4 + 4 + 6 + 6 + 8 + 8 + 10 + 10 + 12 + 12 = 80
Already given = 80
For section 4: The length and width increases by 2 respectively
previous length + 2 = 12 + 2 = 14
The increase causes an addition of two length of 14 blocks
Total blocks = 4 + 4 + 6 + 6 + 8 + 8 + 10 + 10 + 12 + 12 + 14 + 14
Total blocks for Section 4 = 108
A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 12.5 ft by 13.5 ft by 13 ft. The container is entirely full. If, on average, its contents weigh 0.18 pounds per cubic foot, and, on average, the contents are worth $7.18 per pound, find the value of the container’s contents. Round your answer to the nearest cent.
The volume of a right rectangular prism is given by
[tex]V=\text{height}\times length\times width[/tex]From the given information, we know that
[tex]\begin{gathered} \text{ height=13.5 ft} \\ \text{ length=13 ft} \\ \text{width = 12.5 ft} \end{gathered}[/tex]So, the volume is given by
[tex]V=13.5\times13\times12.5ft^3[/tex]which gives
[tex]V=2193.75ft^3[/tex]Now, since the content weigh 0.18 pound per cubic foot and worth $7.18 per pound, the value of the container is given by,
[tex]\text{ Value=}2193.75\times0.18\times7.18[/tex]Therefore, by rounding to the nearest cent, the answer is:
[tex]\text{Value}=\text{ \$2835.20}[/tex]Soue se compound inequality and give your answer in intentel notation- 10 AND-80-72-1
S= (-4, 1 ]
1) Solving that compounded inequality
4x +6 > -10 and -8x+7 ≥ -1
2) Let's start by 4x +6 > -10
4x +6 > -10 Subtracting 6 from both sides
4x > -10-6
4x > -16 Dividing both sides by 4
x > -4
And with -8x+7 ≥ -1
-8x+7 ≥ -1 Subtract 7 from both sides
-8x ≥ -1 -7
-8x ≥ -8 Multiply by -1
8x ≤ 8
x ≤ 1
3) Graphing the solution interval:
So the solution is the interval S= (-4, 1 ] not including x= -4 and including the value x = 1
4) The half-life of a medication is the amount of time for half of the drug to be eliminated from the body. The half-life of Advil or ibuprofen is represented by the equation 2 ) 5 . 0 ( t M R = , where R is the amount of Advil remaining in the body, M is the initial dosage, and t is time in hours.
Based on the half-life, 35.36 mg will remain at 6:00P PM in the body
The amount of the medication that will remain at 6:00P PM?The details that complete the question are added as an attachment
From the question, we have
Initial dosage = 200 mg
This means that
M = 200
Also, we have
Initial time =1 : 00 pm
This means that the number of hours, is
n = 6pm - 1pm
n = 5
Recall that the function is given as
R = M(0.5)ⁿ/²
So, we have the following equation
R = 200 x (0.5)⁵/²
Evaluate the quotient of the exponents
So, we have the following equation
R = 200 x (0.5)².⁵
Evaluate the products
R = 35.36 mg
Using the above computation as a guide, we have the remaining amount to be 35.36 mg
Hence, the amount of the medication that will remain at 6:00P PM is 35.36 mg
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7-Which beans are the better deal? Kidney Beans $1.18 per lb O Lima Beans $213 for 2 lbs 76-What is the Unit Price for the better deal? Round to the nearest hundredth) Put your answer in the form 0.00 or .00, so if answer is 43 cents, its 0.43 or.43, if there is a dollar amount like 1.50, do not add zeros in front).
Given :
Two kinds of Beans :
1. Kidney Beans $1.18 per lb
The unit price = $1.18
2. O Lima Beans $213 for 2 lbs
The unit price = 2.13/2 = 1.065
Rounding to the nearest hundredth
So,
The unit
What is x in x/4=1.8/5
Answer:
x = 1.44
Step-by-step explanation:
Multiply both sides by 4 to get rid of the denominator on the LHS(Left hand Side) of the equation and you get x
(x/4) x 4 = 1.8/5 x 4
x = 1.44
