Answer:5.03
1.26 are correct
Step-by-step explanation:We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):
5u^2 - 8u + 2 = 0
We can use the quadratic formula to solve for u:
u = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 5, b = -8, and c = 2. Substituting these values, we get:
u = (8 ± sqrt(64 - 40)) / 10
u = (8 ± 2sqrt(6)) / 10
Therefore, either:
What function does this table make
Answer:
f(n) = 3^(n -1)
Step-by-step explanation:
You want a function that describes the relation shown in the table.
AnalysisThe values under Steps are sequential, which makes determining the function a lot easier.
The values listed under Black Triangles don't have a common difference, but they do have a common ratio:
r = 3/1 = 9/3 = 27/9 = 3
Exponential functionFor this function, we'll use 'n' as the independent variable (the number of steps), and we'll call the function 'f'.
For common ratio r and a pair of table values (n, f(n)) = (a, b), the exponential function can be written as ...
f(n) = b·r^(n -a)
With r=3 and (a, b) = (1, 1), this becomes ...
f(n) = 1·3^(n -1)
The multiplier 1 isn't really needed, so we can use ...
f(n) = 3^(n -1)
A student is using wooden blocks to build two towers of different heights. All of the blocks are the same size and have a height of 3/4inch. The short tower is 5 blocks high and the tall tower is 9 blocks high. What is the difference in height, in inches, between the short tower and the tall tower?
The difference in height of short and tall tower is 3 inch.
We have,
length of each block = 3/4 inch
So, the length of 5 block
= 5 x 3/4
= 15/4 inch
and, the length of 9 blocks
= 9 x 3/4
= 27/4 inch
So, the difference in height of short and tall tower is
= 27/4 - 15/4
= 12/4
= 3 inch
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Please help me solve questions 14,15, & 16.
=================================================
Explanation for problem 14
There are 4 aces and 4 copies of "9".
4+4 = 8 cards we want to select out of 52 total
8/52 = (4*2)/(4*13) = 2/13 which points to choice D as the final answer
---------------
Explanation for problem 15
4 kings gives a probability of 4/52 = 1/13.
After the king is chosen, there are 52-1 = 51 cards left since we aren't replacing it. The probability of getting a queen on the second selection is 4/51
(1/13)*(4/51) = 4/663 is the probability of a king, then a queen, with no replacement. We arrive at choice C as the final answer.
----------------
Explanation for problem 16
face card = picture card
face card = Jack, Queen, King
aces are not considered a face card
3*4 = 12 face cards in total
A = 12/52 = (4*3)/(4*13) = 3/13 is the probability of selecting a face card.
That card is then put back (aka replacement) and we still have 52 cards in the deck. We don't drop down to 51.
13 hearts ---> B = 13/52 = 1/4 is the probability of getting a heart
A*B = (3/13)*(1/4) = 3/52 is the probability of getting a face card, then a heart, when replacement is done. The final answer is choice B
QUESTION ONE
(a) If the mean of five values is64, find the sum of the values
(b) If the mean of five values is 8.2 and four of the values are 6, 10, 7, and 12, find the fifth vaue.
(c) Find the mean of 10, 20, 30, 40, and 50.
i) Add 10 to each value and find the mean.
ii) Subtract 10 from each value and find the mean.
iii) Multiply each value by 10 and find the mean.
iv) Divideeach value by 10 and find the mean.
v) Make a general statement about each situation.
QUESTION TWO
a)Find the mean deviation for these data. 5, 9, 10, 11, 11, 12, 15, 18, 20, 22
b)The mean marks in statistics of 100 students in a class was 72 per cent. The mean marks of boys
was 75 per cent, while their number was 70 per cent. Find outthe mean marks of girls in the
cass.
c)The weighted geometric mean of the four numbers 20, 18, 12, and 4 is 11.75. If the weights of
the first three numbers are 1, 3, and 4, respectivey, find the weight of the fourth number
QUESTION THREE
a)For a group of 50 male workers, the mean and standard deviation of their monthly wages
are $6300 and $900 respectively. For a group of 40 female workers, these are $ 5400 and $
600 respectively. Find the standard deviation of monthly wages for the combined group of
workers.
b)A study of the age of 100 persons grouped into intervals 20–22, 22–24, 24–26..., revealed
the mean age and standard deviation to be 32.02 and 13.18 respectivey. While checking it
was discovered that the observation 57 was misread as 27. Cacuate the correct mean age and standard deviation
QUESTION FOUR
The weekly sales of two products A and B were recorded as given below:
Product A : 59 75 27 63 27 28 56
Product B : 150 200 125 310 330 250 225
Find out which of the two shows greater fluctuation in sales
(a) Sum of values = Mean × Number of values = 64 × 5 = 320
(b) Sum of values = Mean × Number of values = 8.2 × 5 = 41
Fifth value = Sum of values - sum of known values = 41 - (6 + 10 + 7 + 12) = 41 - 35 = 6
How to solve(c) The resulting middle number when computing 10, 20, 30, 40, 50;that is (10 + 20 + 30 + 40 + 50)/5, totals up to 150 and dividing that number by 5 reflects a mean of 30.
i) Forming an average of 20, 30, 40, 50, 60;that is (20 + 30 + 40 + 50 + 60)/5 provides an outcome of 200 and divided by 5 reveals a mean of 40.
ii) With 0, 10, 20, 30, 40 used, (0 + 10 + 20 + 30 + 40)/5 practices calculation yielding a total of 100 which, split into five parties, imparts a mean of 20.
iii) Taking into consideration the input of 100, 200, 300, 400, 500;whereby (100 + 200 + 300 + 400 + 500)/5 develops a collective of 1500, cut in half produces a mean of 300.
iv) Calculating 1, 2, 3, 4, 5's mean; namely (1 + 2 + 3 + 4 + 5)/5 ascertains a collective amount of 15, divide that figure by five culminates with a mean of 3.
v) Accordingly, the following general assumptions can be made:
i) Introducing a constant to each value augments the mean by that very same constant.
ii) Extracting a constant from all values decrements the mean by such said constant.
iii) Multiplying every value by one constant multiplies the mean by the same specific constant.
iv) Dividing all values by a particular constant divides the mean by that given constant.
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picture look in the picture
Answer:
The measure of angle E is 56°.
8 cupcakes in 1 box = 16 cupcake in X boxes
Answer:
2 boxes
Step-by-step explanation:
8 cupcakes in 1 box = 16 cupcake in x box
We Take
16 ÷ 8 = 2 boxes
So, the answer is 2 boxes.
rancher wants to enclose a rectangular plot of land, but have a divider in the middle. There is 240 feet of fencing available. What dimension will produce the largest area the rancher can make? What is the max area? Dimensions: __________________ Area:___________ --------------------------------------------------------------------------------------------------------- 2. (10 points) From a thin square piece of cardboard 20 in. per side, square corners (x) are cut out so that the sides can be folded up to make a box. What dimensions will yield a box of maximum volume? What is the maximum volume? Dimensions: __________________ Volume:___________ ----------------------------------------------------------------------------------------------------------- 3. (10 points) During a recent oil spill in the gulf, the radius of the spill was increasing at a rate of 10 feet per second. How fast is the circular area of the spill increasing at the moment that the radius is 80 feet? dA = dt __________
The solution is, the two dimensions will be 2121.32 by 1414.2.
Here, we have,
let X and Y be the two dimensions.
Area will be X times Y.
XY = 3000000
Y = 3000000 / X
Perimeter = 2x + 3y
substituting the values:
Perimeter = 2x + 3*3000000 / x
= 2x + 9000000 / x
so, we get,
2 = 9000000 / x^2
x^2 = 9000000 / 2 = 4500000
x = sqrt(4,500,000)
= 2121.32
= 1000 sqrt (4.5)
y = 3000000 / 2121.32
= 1414.2
= 1000 sqrt(2)
so the dimensions will be 2121.32 by 1414.2 .
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complete question:
A rancher wants to fence in an area of 3000000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?
A hippopotamus weighs 2 tons and a crocodile weighs 20 lbs.
How many times as much as the hippopotamus does the crocodile weigh?
The crocodile weighs 0.005 times as much as the hippopotamus.
To determine how many times as much as the hippopotamus a crocodile weighs, we need to compare the weights of both animals. However, they are currently in different units, so we need to convert them to a common unit.
We can convert the weight of the hippopotamus from tons to pounds by multiplying by 2,000, since there are 2,000 pounds in a ton. This gives us:
Hippopotamus weight = 2 tons × 2,000 pounds/ton = 4,000 pounds
Now that both weights are in pounds, we can compare them. To determine how many times as much as the hippopotamus the crocodile weighs, we can divide the weight of the crocodile by the weight of the hippopotamus. This gives us:
Crocodile weight / Hippopotamus weight = 20 pounds / 4,000 pounds = 0.005
Alternatively, we could say that the hippopotamus weighs 200 times as much as the crocodile.
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PLEASE HELP (WILL GIVE BRAINLIEST)
Answer:
144π = (1/2)(4/3)π(r^3)
144 = (2/3)(r^3)
r^3 = 216, so r = 6 mm, meaning the diameter is 2 × 6 mm = 12 mm.
Match these values of r with the accompanying scatterplots:
−0.405,
−0.998,
−1,
−0.743,
and
0.743.
The matching table is given in the image below:
What is a Scatter Plot?A scatter plot, an undeniably essential chart for visualizing the correlation between two variables, is constructed by putting one variable on the x-axis and another one alongside the y-axis, with each individual data point symbolizing both associated values.
Scatter plots are not only indispensable when inspecting trends and peculiarities in a given set of data but can likewise be applied to examine the relationship or link between the two components.
Essentially imperative to fields such as economics, engineering, and statistics, these diagrams are efficiently drawn up through popular software applications like Excel or Python.
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(a) The equation of a straight line, 4, is given as y=-²x = ³
(i) State the gradient of the line, l₁.
(ii)The point A (b, 4) lies on the line l₁. Determine the value of b.
(iii) A line, 12, passing through the point (0,-5), is perpendicular to l₁. Find the equation of the straight line l2.
£1 = $1.41
£1= €1.15
$1= €?
We can use unit conversion to find the value of $1 in Euros:
\begin{aligned}
£1 &= $1.41 \\
\frac{£1}{1.15} &= \frac{$1.41}{x} \\
x &= \frac{$1.41}{\frac{£1}{1.15}} \\
&= $1.7278
\end{aligned}
Therefore, $1 is equal to €1.7278.
Find the tangent of the smaller acute angle in a right triangle with side lengths 8, 15, and 17
Answer: the tangent of the smaller acute angle in this right triangle is 8/15.
Step-by-step explanation:
Since the side lengths of the correct triangle are given as 8, 15, and 17, able to see that the sides with lengths 8 and 15 are the legs of the proper triangle, and the side with length 17 is the hypotenuse.
We know that the littler intense point θ is inverse the shorter leg of length 8. Hence, the digression of θ is:
tan(θ) = opposite/adjacent = 8/15
How much will you have in our retirement account at the end of 2 years if you contribute $3,000 a year and have a 100% employer match? Assume a 9% annual return on your investments and end-of-year contributions.
0 $12,540.00
0 $6,000.00
4,12,44,176,890
which is odd one ?
Answer:
890 as it is not divisible by 4
The function f(x) = 1.85x^2 models the cost of a square carpet, where x is the length in feet. Find the average rate of change for f, to the nearest tenth, over the interval 10 ≤ x ≤ 20.
Answer:
I helped you last time so I'll help you again.
Step-by-step explanation:
We can find the average rate of change of f(x) over the interval [10, 20] using the formula:
average rate of change = (f(b) - f(a))/(b - a)
where a = 10 and b = 20.
So, we have:
f(a) = f(10) = 1.85(10)^2 = 185
f(b) = f(20) = 1.85(20)^2 = 740
average rate of change = (740 - 185)/(20 - 10) ≈ 55.5
Therefore, the average rate of change of f(x) over the interval [10, 20] is approximately 55.5.
What is the sum of 3.0 x 4.1 x 5.5
Answer: 67.65
Step-by-step explanation:
Multiply 3.0*4.1 and you get 12.3
Then take that sum and multiply it by the 5.5
So 12.3*5.5=67.65
for a new customer top golf charges $10 for a player card and $2 per hour.
The cost for a new customer to rent a bay for 6 hours at Top Golf is $22, which includes a $10 player card fee and a $12 bay rental fee at $2 per hour.
Let's let "x" be the total cost for a new customer to rent a bay for 6 hours.
We know that there is a flat fee of $10 for the player card, and then an additional $2 per hour for the bay rental.
So, the equation for the cost "x" can be written as
x = 10 + 2(6)
The expression 2(6) represents the cost of the bay rental for 6 hours. We can simplify the expression by multiplying 2 and 6, which gives us
x = 10 + 12
Now, we can combine like terms to find the final cost
x = 22
Therefore, the cost for a new customer to rent a bay for 6 hours at Top Golf is $22.
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--The given question is incomplete, the complete question is given
" For a new customer top golf charges $10 for a player card and $2 per hour. Write and solve a linear equation to find the cost for a new customer to rent a bay for 6 hours."--
Look at the picture
According to the information, we can infer that the area of the triangle is: 19 1/4ft²
How to calculate the area of the triangle?To calculate the area of the triangle, we need to use the formula for the area of a triangle:
Area = (1/2) x base x heightwhere,
Base = 5 1/2 ftHeight = 7 ft.How to find the height of the triangle?To find the height of the triangle, we need to use the Pythagorean theorem, which relates the slant height, height, and half the base:
(slant height)^2 = (height)^2 + (1/2 base)^2Substituting the given values, we get:
(1/3)^2 = (7)^2 + (1/2 x 5 1/2)^2(1/9) = 49 + (15/4)(1/9) = (196/4 + 15/4)(1/9) = (211/4)Multiplying both sides by 36, we get:
4 = 844.44...So the height of the triangle is approximately 2.04 ft.
Now we can plug in the values for the base and height into the formula for the area:
Area = (1/2) x 5 1/2 x 7Area = 19.25 square feetArea = 19 1/4ft²Therefore, the area of the triangle is approximately 19.25 square feet.
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f(x)=3x-15 g(x)=1/3x+15
find f(g(x))
g(f(x))
are they inverses if do, why?
The values for the composition of functions are:
a. (f o g)(x) = -x³ - x + 1
b. (g o f)(x) = -x³ - x - 1
Here, we have,
to Determine the Value of Composite Functions:
The value of composite functions are determined by first finding the output of the inner function, which would be used as the input of the outer functions to derive the value of the composite functions.
Given the following:
f(x) = x³ + x + 1
g(x) = -x
a. To find (f o g)(x), substitute g(x) as the inner function for x into f(x):
(f o g)(x) = (-x)³ + (-x) + 1
Simplify
(f o g)(x) = -x³ - x + 1
b. To find (g o f)(x), substitute f(x) as the inner function for x into g(x):
(g o f)(x) = -(x³ + x + 1)
Distribute by -1
(g o f)(x) = -x³ - x - 1
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complete question:
If f(x)=x³+x+1 and g(x)=-x, find (f°g)(x) and (g°f)(x).
(f°g)(x)=
If a solid has 6 faces and 12 edges, how many vertices does it have? A. 10 vertices B. 9 vertices C. 7 vertices D. 8 vertices
Answer: D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
(ILL GIVE YOU 100 POINTS!!)
The work of a student to solve the equation 4(2x − 4) = 8 + 2x + 8 is shown below: Step 1: 4(2x − 4) = 8 + 2x + 8
Step 2: 6x − 8 = 16 + 2x
Step 3: 6x − 2x = 16 + 8
Step 4: 4x = 24
Step 5: x = 6
In which step did the student first make an error and what is the correct step?
a Step 2; 8x − 4 = 2(6 + x + 6)
b Step 2; 8x − 16 = 16 + 2x
c Step 3; 6x − 2x = 16 − 8
d Step 3; 6x + 2x = 16 + 8
Answer:
step 2 is wrong
Step-by-step explanation:
4 multiply by 2x = 8x4 multiply by -4 = -16CORRECT STEP4(2x - 4) = 8 + 2x + 88x - 16 = 8 + 2x + 88x - 16 = 2x + 16 6x = 32x = 32/6 = 5 ( approximately )Here, The work of a student to solve the equation :
[tex]4(2x - 4) = 8 + 2x + 8[/tex]
The steps for calculating the value of x are :
Step 1: [tex]4(2x - 4) = 8 + 2x + 8[/tex]
Step 2: [tex]6x - 8 = 16 + 2x[/tex]
Step 3: [tex]6x - 2x = 16 + 8[/tex]
Step 4: [tex]4x = 24[/tex]
Step 5: [tex]x = 6[/tex]
Step 2 is incorrect, as the student instead of multiplying, adds the number as:
[tex]4(2x - 4) = 8 + 2x + 8[/tex]
Here, the correct step is:
[tex]\boxed{\bold{8x - 16 = 16 + 2x}}[/tex]
[tex]6 x = 32[/tex]
[tex]x = 5.33[/tex]
So, the error is in STEP 2 and the correct option is (B).
Simplify the expression: 8y + 4 - 3y + 12
The simplified expression is:
8y + 4 - 3y + 12 = 5y + 16
How to simplify the expression?Remember the distributive property:
A*(B + C) = A*B + A*C
Now let's look at our expression, it is:
8y + 4 - 3y + 12
We can reorder the terms to get:
8y - 3y +4 + 12
Now we can take y as a common factor:
(8 - 3)y + 4 + 12
Now simplify the two operations:
(8 - 3)y + 4 + 12 = 5y + 16
That is the expression simplified.
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Alicia bitman,age
30,plans to purchase a $50,000 whole-life policy what is the annual premium
The annual premium is $192.5.
We have,
Number of units to be purchased by Alicia:
= 50,000 / 1,000
= 50 units
At age 30, the cost per $1,000 unit of insurance is $3.85 for a female.
= Number of units purchased x Premium per $1,000
= 50 x 3.85
= $192.5
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Volume of Prism 2 3/4, 5 1/2, 3 2/5
Volume of the prism given is 51 [tex]\frac{17}{40}[/tex].
The volume of the prism is given by the formula,
Volume of the prism = Base area × height
Base area = 2 3/4 × 5 1/2
= 11/4 × 11/2
= 121 / 8
Volume of the prism = 121 / 8 × 3 2/5
= 121/8 × 17/5
= 2057/40
= 51 17/40
Hence the volume of the prism is 51 [tex]\frac{17}{40}[/tex].
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The table below shows the U.S. National Debt (in trillions of dollars) by year
Year 1960 1970. 1980 1990 1995 2000 2005 2010 2014
Debt .29 .37 .91 3.23 4.97 5.67 7.93 13.96 17.82
Find an exponential model for the national debt. Use the model to estimate the National Debt for the year 2015. Compare it with the actual value found in the table
The terms given in US national debt in standard form when converted to scientific notation form will be 2.86 * 10^11, 3.70 * 10^11, 9.07 * 10^11, 3.23 * 10^12, 5.67 * 10^12 and 1.35 * 10^13 respectively.
Scientific notation if the process of conversion of very large numbers which are otherwise inconvenient to read into decimal form raised to some power of 10.
During this conversion, the numbers in standard form are written such that only one place value before decimal is left and written as coefficient and all other numbers are then counted and written in the form of base 10 raised to some exponent value.
The coefficient value must be such that its value lies between 1 and 9 and less than 10. Thus, the following numbers can be written as follows in scientific form.
286330760848.37 = 2.86 * 10^11
370918706949.93 = 3.70 * 10^11
907701000000.00 = 9.07 * 10^11
3233313451777.25 = 3.23 * 10^12
5674178209886.86 = 5.67 * 10^12
13561623030891.79 = 1.35 * 10^13
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Classify the following into finite and infinite set
(i) The set of months in a year
(ii)The set of stars in the galaxy
(iii)The set of even integers
(iv)The set of odd integers
(v)The set of alphabets
i) finite set, ii) infinite set, iii) infinite set, iv) infinite set, and v) finite set are the required solutions.
A Set is a collection of objects with similar properties. There are different types of set two of them are finite and infinite set.
Finite set- A set is called a finite set when the elements inside the set are countable or where we can know the starting and the ending of the elements. For example- A set of players in a cricket team.
Infinite set- A set is called an infinite set when the elements inside the set are uncountable or where the ending of the elements is not known. For Example- A set of positive numbers.
Here in the question the option (i) and (v) are finite sets because the no.of months in the year and no.of alphabets are countable or finite. Option (ii), (iii), and (iv) are infinite sets as no.of stars in the galaxy, even integers, and odd integers are uncountable.
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Answer:
the set of months in a year is finite
the set of star in the Galaxy is finite
the set of even integers is infinite
the set of odd integers is infinite
the set of alphabet is finite
Step-by-step explanation:
1) the set of month in a year is finite because they are limit and we can count them easily
2) the set of star in the galaxy is finite cause there are zillions of stars
3) the set of even integer is infinite because numbers are unlimit or infinite
4) the set of odd integers is infinite cause numbers are infinite ir they have not limit
5) the set of alphabet is finite because we can count them limitedly
Vocabulary
1. The remainder is the number that remains after the division is
complete. Use an R to indicate the remainder.
Tia has 26 walnuts. She gives 7 walnuts to each friend. How many friends get
7 walnuts? How many walnuts are left over?
Use the array to find 26+7. Circle the groups of 7.
There are
groups of 7.
left over.
There are
2647-
friends each get 7 walnuts.
walnuts left over.
000000
000000
0.0
000
O
There are
2. Juan puts 57 oranges in bags. Each bag holds 6 oranges. Use the array to divide.
To find 57 +6, circle groups of
5746-
How many full bags of oranges are there?
How many oranges are not in bags?
How many bags does Juan need to put all the oranges in bags?.
3. How many craft sticks will be left over if 9 friends equally share a
package of 85 craft sticks?
000000
OOO
000
000
O
000000
000000
000000
000000
4. A group of 43 people are going to a concert. If 6 people fit in each
car, how many cars will they need to take?
000000
000000
On the Back!
6. Find the number of equal groups and the number left over for
88 +3. Show your work.
bags
000
5. Bess has 19 sunflowers that she is putting into vases. She will put 4 sunflowers in
each vase. How many vases will have 4 flowers?
The number of friends that get 7 walnuts is 3 and there are 5 walnuts are left over
Sharing walnuts among friendsHere, we have
Walnuts = 26Walnuts to each friend = 7So, we have
Friends = 26/7 = 3 R 5
This means that 3 friends get 7 walnuts and there are 5 walnuts are left over
Putting oranges in bagsHere, we have
Oranges = 57
Oranges in each bags = 6
So, we have
Bags 57/6 = 9 R 3
This means that there are 9 full bags of oranges, 3 oranges are not in the bag and Juan needs 10 bags in total
Crafts in sticksHere, we have
Craft sticks = 85
Friends = 9
So, we have
Sticks left = 85\9
Evaluate
Sticks left = 4
Hence, there will be 4 sticks left
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Using the picture, give the term that best describes
each of the following.
C.
1.
E
D
B
G
F
H
BC
3. DH
4. EH 5. OG 6. GF
7. B
2. Term not applicable to this diagram
The labelled parts are described as follows
1. BC - Tangent
3. DH - Chord
4. EH - Diameter
5. G - center of the circle
6. GF Radius of the circle
7. B. a point of tangency
What is tangent and chord of a circleTangent: Referenced as a point of tangency, a tangent to a circle is a line that meets the circumference at one solitary area while never penetrating inside its bounds. To explain further, this line is perpendicular to the radius of the circle right at the tip of contact.
Chord: Referring to such an element, a chord of a circle is a straight piece between two areas that lay along the circumference. Without having any relation to the middle of the target object, it has both of its extremities on the peripheral border.
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HELP ME ASAP PLS. If 19,432 divided by x equals 48 with a remainder of 232. What is X?
The value of x, given that when it divides a number, there is a quotient and a remainder, is 400
How to find the value of x?To find the value of divisor, we can use a variant of the division algorithm formula :
Divisor = ( Dividend - Remainder ) / Quotient
x is the divisor
Dividend = 19, 432
Remainder = 232
Quotient = 48
This means that the value of x is:
x = ( 19, 432 - 232 ) / 48
x = 19, 200 / 48
x = 400
In conclusion, x is 400.
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