Answer:I have the same problem
Step-by-step explanation
sold 72 books. if ratio of books to bookmarks is 9:2, how many bookmark was sold?
Answer:
16 bookmarks were sold
Answer:
40
Step-by-step explanation:
They sold 9 book marks for every 2 books (9:2 ratio).
72/9 = 2/x
Cross multiply. 72 * x = 72x
9 * 2 = 18
72 divided by 18 = 40
A blue boat and a red boat are on the same side of a lake and are 18 miles apart. The blue boat is 30 miles from a lighthouse on the opposite side of the lake. The angle formed by the boats and the lighthouse, and whose vertex is at the blue boat, measures 120°. Find the distance from the red boat to the lighthouse. What is the angle made from the lighthouse to the two boats?
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Answer:
red boat distance: 42 milesangle at lighthouse: 22°Step-by-step explanation:
The Law of Cosines can be used to find the distance from the red boat to the lighthouse.
b² = l² +r² -2lr·cos(B)
b² = 18² +30² +2·18·30·cos(120°) = 1764
b = √1764 = 42
The distance from the red boat to the lighthouse is 42 miles.
__
The angle at the lighthouse can be found using the law of sines.
sin(L)/l = sin(B)/b
L = arcsin(l/b·sin(B)) = arcsin(18/42·sin(120°)) ≈ 21.79°
The angle between the boats measured at the lighthouse is about 22°.
Graph the following piecewise function and then find the domain.
f(x)= 3x^2+1 if -4x
Answer:
B
Step-by-step explanation:
The domain goes from -4 to 9. It would not be brackets since the actual points are not on the graph so it would be parentheses.
Surface Area of Pyramids
Instructions: Find the surface area of each figure. Round your answers to the nearest tenth, if necessary.
9514 1404 393
Answer:
288 km²
Step-by-step explanation:
The surface area is the sum of the area of the square base and the area of the four triangular faces.
SA = (10 km)² + 4(1/2)(10 km)(9.4 km) = 288 km²
____
The area formulas for a square and a triangle are ...
A = s² . . . . area of a square of edge length s
A = 1/2bh . . . . area of a triangle with base b and height h
Solve the equation for x 11x=110
Abigail buys two cartons of strawberries. One carton has 191919 berries and the other carton has 262626 berries. She wants to divide the berries into bags so there are exactly 666 berries in each bag.
How many bags will have 666 berries?
Answer:
682
Step-by-step explanation:
191,919 + 262,626
454545 ÷ 666 = 682.5
Thus meaning 682 bags will have 666 berries and one bag will have 333 berries.
HELP PLEASE, WILL GIVE BRAINLYIST NOW
Answer:
Step-by-step explanation:
I think you got it correct. The reciprical of this function is y = x.
Can you please help me
Answer:
you will add the numerator and the denominator and or you look for lowest common factor
Identify the domain of the graph given below.
Answer:
(-∞,∞) is the domain.
2 is the range
Step-by-step explanation:
write your answer in simplest radical form
Answer:
q = [tex]\sqrt{2}[/tex]
Step-by-step explanation:
Using the sine ratio in the right triangle and the exact value
sin30° = [tex]\frac{1}{2}[/tex] , then
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{q}{2\sqrt{2} }[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2q = 2[tex]\sqrt{2}[/tex] ( divide both sides by 2 )
q = [tex]\sqrt{2}[/tex]
What is the largest product that can be made from whole numbers that add up to 100?
Answer:
Step 1: Find the largest product
50 + 50 = 100
50 * 50 = 2500
Answer: I believe that the largest product is 2500
If the triangle above is translated two units to the right, what is the correct coordinate for A'?
Answer: 0, 5
Step-by-step explanation: a translation is just like sliding the object in this case a triangle/point on the triangle. so the point it is at now is -2, 5 because it is 2 to the left and 5 up. and if you go to the right 2. then you are adding 2 to the x value. so -2 +2 = 0. which is how you get 0, 5
What is the distance between (-5,-5) and (-9,-2)
Answer:
A (5)
Step-by-step explanation:
The distance is the slope/gradientIn the pythogaras theorem [tex]c^{2} = a^{2} + b^{2}[/tex],c represents the slope and a and b represent the two shorter sides of the right angled triangle ( x,y)
x = -9 - (-5 ) = -9 +5 = -4y = -2 - (-5) = -2 +5 = 3[tex]c^{2}[/tex] = [tex]-4^{2} + 3^{2}[/tex]
= 16 + 9
= 25,
therefore [tex]\sqrt{c^{2} }[/tex] = [tex]\sqrt{25}[/tex]
c = 5
Find the slope of the line
Slope=m=_____
Answer:
4
Step-by-step explanation:
Slope = y2-y1/x2-x1
We need to find two points on the graph, let's take these two points:
(x1, y1) (X2,y2)
(0,-6) and (2,2)
(2-(-6)/ (2-0) = 8/2 = 4
Answered by Gauthmath
Mr jones rolls a 6 sided cube mumbered 1,2,3,4,5,6, what is the probability he rolls a three.
Answer:1.5
Step-by-step explanation:
Which function represents a exponential decay. Plz help need answer for my exam!
Answer:
the last one
Step-by-step explanation:
Plz help me find side x and y thanks
Answer:
2sqrt3
Step-by-step explanation:
Since this seems to be a 45, 45, 90 triangle, x and y are the same.
The hypoteneuse is always the side lengths *sqrt2
We divide the hypoteneuse by sqrt 2 and get sqrt12
sqrt12 simplified is 2sqrt3
3. Solve the system of equations using the elimination method.
5x + 2y = 9
-5x + 4y = 3
please give detailed steps!!
Answer:
x = 1
y = 2
Step-by-step explanation:
5x + 2y = 9
-5x + 4y = 3
==> 6y = 12 ==> y = 12/6 ==> y = 2.
we replace y by its value in the first or the second equation, so will have:
5x + 2×2 = 9
5x + 4 = 9
5x = 5
x = 1
A dairy needs 291 gallons of milk containing 6% butterfat. How many gallons each of milk containing 7% butterfat and milk containing 4% butterfat must be used to obtain the desired 291 gallons?
Answer:
Step-by-step explanation:
Each gallon of 7% milk contains 0.07 gallon of butterfat.
Each gallon of 4% milk contains 0.04 gallon of butterfat.
291 gallons of 6% milk contain 291×0.06 = 17.46 gallons of butterfat.
Let x be the number of gallons of 7% milk used. 291-x is the number of gallons of 4% milk used.
0.07x + 0.04(291-x) = 17.46
0.03x + 11.64 = 17.46
x = 200
Use 200 gallons of 7% and 91 gallons of 4%.
Questions
1) Identify the missing features of this map ?
2) Write north , south , east or west to complete each sentence?
a) The rowboats are _____ of the campfire .
b) The camping trailers are _______ of the tent .
c) The cabins are ______ of the tents
d) The campfire is ______ of the camping trailers
e) The island is _____ of the cabins .
Do answer
Answer:
it is missing a scale because it should be at the bottom of the map
Help please. I need the answer
The incomplete work of a student to solve an equation is shown below:
Step 1: 4x + 12 = 4
Step 2: ?
Step 3: x = −8 ÷ 4
Step 4: x = −2
What is the missing Step 2?
4x = 8
4x = 16
4x = −16
4x = −8
Find a vector v that is perpendicular to the plane through the points
A=(5,−4,4), B=(−5,0,−3), and C=(−4,2,−5).
v =
The value of vector v that is perpendicular to the plane through the points is,
⇒ v = (6, - 27, - 24)
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Points are,
A = (5,−4,4), B = (−5,0,−3), and C = (−4,2,−5).
Hence, We get;
AB = [- 10, 4, - 7]
AC = [-9, 6, -9]
So, The value of vector v that is perpendicular to the plane through the points is,
⇒ v = AB x AC
⇒ v = (- 10, 4, - 7) x (- 9, 6, - 9)
⇒ v = (6, - 27, - 24)
Thus, The value of vector v that is perpendicular to the plane through the points is,
⇒ v = (6, - 27, - 24)
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What is the value of the expression, written in standard form?
Answer:
200
Step-by-step explanation:
6.6/3.3 = 2
10^-2 - (-4) = 10^2
The answer is 2 * 10^2 or 200.
PLS HELP
Evaluate the piecewise function at the indicated values from the domain
==========================================================
Explanation:
Piecewise functions are admittedly a bit confusing at first if you aren't familiar with them.
However, they aren't too bad. Effectively we have two functions going on depending on what the input is.
If the input x is less than 0, then we go for the top row and say [tex]f(x) = x^2[/tex]
OR
If the input x is greater than 0, then we go for the bottom row to say [tex]f(x) = \sqrt[3]{x}[/tex]
-------------------------------
In this case, the input is x = -8. So we go for the first row since this x value satisfies x < 0.
We would then say:
[tex]f(x) = x^2\\\\f(-8) = (-8)^2\\\\f(-8) = 64\\\\[/tex]
Which points us to choice A as the final answer.
Answer:
f(-8) = 64
Step-by-step explanation:
Input -8 into one of the formulas (either will work) and the answer should be 64. therefore, if x is -8, f(-8) would equal 64.
An insurance company offers its policyholders a number of different premium payment options. For a randomly selected policyholder, let X 5 the number of months between successive payments. The cdf of X is as follows:
0 x<1
0.30 1< x <3
F(x)= 0.40 3< x <4
0.45 4< x <6
0.60 6< x <12
1 12< x
Required:
a. What is the pmf of x?
b. Using just the cdf, compute P(3< x <6)and P(4< x)
Answer:
(a)
[tex]\begin{array}{cccccc}x & {1} & {3} & {4} & {6} & {12} \ \\ P(x) & {0.30} & {0.10} & {0.05} & {0.15} & {0.40} \ \end{array}[/tex]
(b)
[tex]P(3 \le x \le 6) = 0.30[/tex]
[tex]P(4 \le x)=0.60[/tex]
Step-by-step explanation:
Given
[tex]F(x) = \left[\begin{array}{ccc}0& x<1 &\\0.30&1 \le x<3 &\\0.40&3 \le x < 4& &0.45 &4 \le x<6 &\\0.60 & 6 \le x < 12 & & 1 & 12 \le x\end{array}\right[/tex]
Solving (a): The pmf
This means that we list out the probability of each value of x.
To do this, we simply subtract the current probability value from the next.
So, we have:
[tex]\begin{array}{cccccc}x & {1} & {3} & {4} & {6} & {12} \ \\ P(x) & {0.30} & {0.10} & {0.05} & {0.15} & {0.40} \ \end{array}[/tex]
The calculation is as follows:
[tex]0.30 - 0 = 0.30[/tex]
[tex]0.40 - 0.30 = 0.10[/tex]
[tex]0.45 - 0.40 = 0.05[/tex]
[tex]0.60 - 0.45 = 0.15[/tex]
[tex]1 - 0.60 = 0.40[/tex]
The x values are gotten by considering where the equality sign is in each range.
[tex]1 \le x < 3[/tex] means [tex]x = 1[/tex]
[tex]3 \le x < 4[/tex] means [tex]x = 3[/tex]
[tex]4 \le x < 6[/tex] means [tex]x=4[/tex]
[tex]6 \le x < 12[/tex] means [tex]x = 6[/tex]
[tex]12 \le x[/tex] means [tex]x = 12[/tex]
Solving (b):
[tex](i)\ P(3 \le x \le 6)[/tex]
This is calculated as:
[tex]P(3 \le x \le 6) = F(6) - F(3-)[/tex]
From the given function
[tex]F(6)= 0.60[/tex]
[tex]F(3-) = F(1) = 0.30[/tex]
So:
[tex]P(3 \le x \le 6) = 0.60 - 0.30[/tex]
[tex]P(3 \le x \le 6) = 0.30[/tex]
[tex](ii)\ P(4 \le x)[/tex]
This is calculated as:
[tex]P(4 \le x)=1 - F(4-)[/tex]
[tex]P(4 \le x)=1 - F(3)[/tex]
[tex]P(4 \le x)=1 - 0.40[/tex]
[tex]P(4 \le x)=0.60[/tex]
Find the value of the trigonometric ratio. sin A
Answer:
sin A = 4/5
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin A = opp / hyp
sin A = 24/ 30
Dividing the top and bottom by 6
sin A = 4/5
sinØ=Perpendicular/Hypotenuse
sinA=BC/ACsinA=24/30sinA=4/5The shorter leg of a right triangle is 5 meters. The hypotenuse is 1 meter longer than the longer leg. Find the
length of the longer leg.
The other leg is
meters.
Answers:
longer leg = 12 meters
hypotenuse = 13 meters
==========================================================
Explanation:
Let's say the triangle has sides a,b,c such that a < b < c
a = 5 = short legb = unknown long legc = b+1 = hypotenuseUse the pythagorean theorem to solve for b
[tex]a^2 + b^2 = c^2\\\\5^2 + b^2 = (b+1)^2\\\\25 + b^2 = b^2+2b+1\\\\25 + b^2-b^2-2b-1 = 0\\\\-2b+24 = 0\\\\-2b = -24\\\\b = -24/(-2)\\\\b = 12[/tex]
The longer leg is 12 meters in length.
c = b+1 = 12+1 = 13
The hypotenuse is 13 meters long.
We have a 5-12-13 right triangle.
The math teacher and cheerleading coach have teamed up to help the students do better on their math test. The cheer coach, using dance move names for the positioning of their arms, yells out polynomial functions with different degrees.
For each position the coach yells out, write the shape by describing the position of your left and right arm.
a1. Constant Function:
a2. Positive Linear Function:
a3. Negative Linear Function:
a4. Positive Quadratic Function:
a5. Negative Quadratic Function:
a6. Positive Cubic Function:
a7. Negative Cubic Function:
a8. Positive Quartic Function:
a9. Negative Quartic Function:
When it comes time to take the test not only do the students have to describe the shape of the polynomial function, you have to find the number of positive and negative real zeros, including complex. Use the equation below:
[tex]f(x)=x^5-3x^4-5x^3+5x^2-6x+8[/tex]
b. Identify all possible rational zeros.
c. How many possible positive real zeros are there? How many possible negative real zeros? How many possible complex zeros?
d. Graph the polynomial to approximate the zeros. What are the rational zeros? Use synthetic division to verify these are correct.
e. Write the polynomial in factor form.
f. What are the complex zeros?
Step-by-step explanation:
a1. The shape will be a vertical or horizontal line.
a2. The shape will be shaped like a diagonal line increasing as we go right.
a3. The shape will be shaped like a diagonal line decreasing as we go right.
a4. The shape will be shaped like a U facing upwards.
a5.The shape will be shaped like a U facing downwards.
a6. The shape will look like a S shape and it increases as we go right.
a7. The shape will look like a S shape and it decreases as We go right.
a8. The shape look like a W shape and it facing upwards.
a9. The shape look a W shape facing downwards.
We are given function.
[tex]x {}^{5} - 3x {}^{4} - 5x {}^{3} + 5x {}^{2} - 6x + 8[/tex]
b. We can test by the Rational Roots Test,
This means a the possible roots are
plus or minus(1,2,4,8).
c. If we apply Descrates Rule of Signs,
There are 3 possible positive roots or 1 possible positive root.There are also 1 possible negative root.There is also 1 possible complex root.d. Use Desmos to Graph the Function. Some roots are (-2,1,4).
e.
[tex](x {}^{2} + 1) (x - 1)(x - 4)(x + 2)[/tex]
f. The complex zeroes are
i and -i
Polynomial [tex]f(x) = x^{5} -3x^{4} - 5x^{3} + 5x^{2} - 6x + 8[/tex] in factor form: (x-1)(x+2)(x-4)(x-i)(x+i)
What is a polynomial?A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
Shape of the graph for the following polynomial:
Constant function - straight line parallel to x axis.Positive linear function - straight line slanting upwards from left to right.Negative linear function - straight line slanting downwards from left to right.Positive quadratic function - U shaped curve opening upwardsNegative quadratic function - U shaped curve opening downwardsPositive cubic function - right hand curved upwards, left hand curved downwards.Negative cubic function - Left hand curved upwards, right hand curved downwards. Positive quartic function - W shaped facing upwardsNegative quartic function - W shaped facing downwardsFinding zeros of the polynomial given:
[tex]f(x) = x^{5} -3x^{4} - 5x^{3} + 5x^{2} - 6x + 8[/tex]
By factor theorem, if f(t) = 0, t is a zero of the polynomial.
Taking t = 1.
f(1) = 1 - 3 - 5 + 5 - 6 + 8 = 0
(x - 1) is a factor of the polynomial f(x).
Divide f(x) by (x-1) using long division to find the other factors.
f(x)/(x-1) = [tex]x^{4} -2x^{3}-7x^{2} -2x-8[/tex] is also a factor of f(x).
Factorizing it further:
g(x) = [tex]x^{4} -2x^{3}-7x^{2} -2x-8[/tex]
g(-2) = 16 + 16 - 28 + 4 - 8 = 0
(x + 2) is a factor of g(x) and thus f(x).
g(x)/(x+2) = [tex]x^{3} - 4x^{2} +x - 4[/tex] is a factor of f(x).
Factorizing it further:
k(x) = [tex]x^{3} - 4x^{2} +x - 4[/tex]
k(4) = 64 - 64 + 4 - 4 = 0
(x - 4) is a factor of k(x) thus of f(x).
k(x)/(x-4) = [tex]x^{2} +1[/tex]
Factorizing it further:
l(x) = [tex]x^{2} +1[/tex] = (x + i)(x - i)
Zeros of f(x) = 1, -2, 4, ±i
Rational zeros : 1, -2, 4
Positive real zeros: 1, 4
Negative real zeros: -2
Complex zeros: ±i
Polynomial in factor form: (x-1)(x+2)(x-4)(x-i)(x+i).
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An analyst has developed the following probability distribution for the rate of return for a common stock.
Scenario Probability Rate of Return
10 0.34 -19%
20 0.48 8%
30 0.18 26%
a. Calculate the expected rate of return. Round your answer to 2 decimal places.
b. Calculate the variance and the standard deviation of this probability distribution. Use the percentage values for your calculations (for example 10% not 0.10). Round intermediate calculations to 4 decimal places.
Answer:
a) 2.06
b) variance = 270.90 , std = 275.14
Step-by-step explanation:
a) Determine Expected rate of return
attached below is the calculated table for the solution provided
∴ Expected rate of return = ∑ Xp(x) = -6.46 + 3.84 + 4.68 = 2.06
b) Determine the variance and standard deviation
Variance ( Vx ) = E(x)^2 - [ Expected rate of return ]^2
= 275.14 - ( 2.06 )^2 ≈ 270.90
standard deviation = √ variance = √270.90 = 16.459
note : E(x)^2 = ∑ x^2 p(x) = 275.14
