Answer:
5 cases
10 additional units
Step-by-step explanation:
Given that :
Total number of units needed = 60 units
Total number of units per case = 14
Hence, the total number of cases required will be :
Number of units needed / number of units per case
Number of cases required = 60 / 14 = 4.285 (this means that 5 cases are required as 4 cases won't be up to 60 units)
With 5 cases, we have exceeded the required units needed :
Additional units will be : (14 * 5) - 60
Additional units = 70 - 60 = 10 units
[tex]Solve. Clear fraction first.6/5 + 2/5 x = 89/30 + 7/6 x + 1/6[/tex]
Step-by-step explanation:
we have denominators 5, 6 and 30.
the smallest number that is divisible by all 3 is clearly 30.
so, we have to multiply everything by 30 to eliminate the fractions.
180/5 + 60/5 x = 89 + 210/6 x + 30/6 =
36 + 12x = 89 + 35x + 5
-58 = 23x
x = -58/23
What is the area of a square with a side length of 32 yards?
Answer:
A=1024 yd.^2
Step-by-step explanation:
A=s^2
Substitute,
A=32^2
So,
A=1024 yd.^2
Answer:
1024 yd²
Step-by-step explanation:
Since it's a square, the side lengths will all be the same length. Due to this, you can square the given value to find the area.
A(Square) = 32² = 1024
HELP PLEASE!!!
Oak wilt is a fungal disease that infects oak trees. Scientists have discovered that a single tree in a small forest is infected with oak wilt. They determined that they can use this exponential model to predict the number of trees that will be infected after t years.
f(t)=e^0.4t
Question:
Rewrite the exponential model as a logarithmic model that calculates the # of years, g(x) for the number of infected trees to reach a value of x.
The logarithmic model is:
[tex]g(x) = \frac{\ln{x}}{0.4}[/tex]
-------------
We are given an exponential function, for the amount of infected trees f(x) after x years.To find the amount years needed for the number of infected trees to reach x, we find the inverse function, applying the natural logarithm.-------------
The original function is:
[tex]y = f(x) = e^{0.4x}[/tex]
To find the inverse function, first, we exchange y and x, so:
[tex]e^{0.4y} = x[/tex]
Now, we have to isolate y, and we start applying the natural logarithm to both sides of the equality. So
[tex]\ln{e^{0.4y}} = \ln{x}[/tex]
[tex]0.4y = \ln{x}[/tex]
[tex]y = \frac{\ln{x}}{0.4}[/tex]
Thus, the logarithmic model is:
[tex]g(x) = \frac{\ln{x}}{0.4}[/tex]
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I need help ASAP please and thank you
9514 1404 393
Answer:
C. 4 +√(x+5)
Step-by-step explanation:
The sign between the terms changes to form the conjugate. The radical contents are unchanged.
The conjugate of 4 -√(x+5) is 4 +√(x+5).
_____
Additional comment
The utility of a conjugate is that the product of a number and its conjugate is the difference of two squares. The squares are intended to remove an undesirable feature of the number, its imaginary part or its irrational part, for example. Here, the product of the number and its conjugate would be ...
(a -b)(a +b) = a² -b²
4² -(√(x+5))² = 16 -(x +5) = 11 -x . . . . no longer contains a root
Find the area of the triangle with vertices (0,0,0),(−4,1,−2), and (−4,2,−3).
Answer:
0.5*sqrt33
Step-by-step explanation:
A(0,0,0) B(-4,1,-2), c(-4,2,-3)
Vector AB is (-4-0,-1-0, -2-0)= (-4,-1,-2) The modul of AB is sqrt (4squared+
+(-1) squared+ (-2) squared)= sqrt (16+1+4)=sqrt21
Vector AC is (-4,2,-3) The modul of vector AC is equal to sqrt ((-4)squared+ 2squared+(-3)squared)= sqrt(16+4+9)= sqrt29
Vector BC is equal to (-4-(-4), 2-1, -3-(-2))= (0,1,-1)
The modul of BC is sqrt (1^2+(-1)^2)=sqrt2
Find the angle B
Ac^2= BC^2+AB^2-2*BC*AB*cosB
29= 2+21-2*sqrt2*sqrt21*cosB
29= 2+21-2*sqrt42*cosB
cosB= -3/ sqrt42
sinB= sqrt( 1-(-3/sqrt42)^2)=sqrt33/42= sqrt11/14
s=1/2* (sqrt2*sqrt21*sqrt11/14)=1/2*sqrt(42*11/14)= 0.5*sqrt33
Determine if the described set is a subspace. Assume a, b, and c are real numbers. The subset of R3 consisting of vectors of the form [a b c] , where at most one of a , b and c is non 0.
The set is a subspace.
The set is not a subspace.
If so, give a proof. If not, explain why not.
Answer:
Not a subspace
Step-by-step explanation:
(4,0,0) and (0,4,0) are vectors in R3 with zero or one entries being nonzero, but their sum, (4,4,0) has two nonzero entries.
convert the following to decimal fractions 99 by 5
Answer:
divide 99 by 5
99/5= 19.8
please help me
find x
9514 1404 393
Answer:
x = 6√2
Step-by-step explanation:
The side ratios in an isosceles right triangle are ...
1 : 1 : √2
These will be the same as ...
x : x : 12
so, ...
x = 12/√2
x = 6√2
A plane flying horizontally at an altitude of 3 mi and a speed of 460 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 4 mi away from the station (Round your answer to the nearest whole number.) 368 X mi/h Enhanced Feedback Please try again. Keep in mind that distance - (altitude)2 + (horizontal distance)? (or y = x + n ). Differentiate with respect to con both sides of the equation, using the Chain Rule, to solve for the given speed of the plane is x.
Answer:
[tex]\frac{dy}{dt}=304mi/h[/tex]
Step-by-step explanation:
From the question we are told that:
Height of Plane [tex]h=3mi[/tex]
Speed [tex]\frac{dx}{dt}=460mi/h[/tex]
Distance from station [tex]d=4mi[/tex]
Generally the equation for The Pythagoras Theorem is is mathematically given by
[tex]x^2+3^2=y^2[/tex]
For y=d
[tex]x^2+3^2=d^2[/tex]
[tex]x^2+3^2=4^2[/tex]
[tex]x=\sqrt{7}[/tex]
Therefore
[tex]x^2+3^2=y^2[/tex]
Differentiating with respect to time t we have
[tex]2x\frac{dx}{dt}=2y\frac{dy}{dt}[/tex]
[tex]\frac{dy}{dt}=\frac{x}{y}\frac{dx}{dt}[/tex]
[tex]\frac{dy}{dt}=\frac{\sqrt{7}}{4} *460[/tex]
[tex]\frac{dy}{dt}=304.2614008mi/h[/tex]
[tex]\frac{dy}{dt}=304mi/h[/tex]
If x/4-y/6=1/6 and y/z=1/2, then what is the value of 3x-z?
A. 4
B.6
C. 3
D. 2
E. None
Người ta chiếu xạ liều 3000 Rơn ghen vào một quần thể ruồi dấm ở thế hệ F1: Chiếu xạ 1000 con ruồi dấm không cho ăn đường thì có 80 con bị đột biến và chiếu xạ 1000 con ruồi dấm có cho ăn đường thì có 120 con bị đột biến. Cho ăn đường có ảnh hưởng đến tỉ lệ đột biến của ruồi giấm không, với mức ý nghĩa 5%? Giá trị kiểm định là
Answer:
gggggggggggggggggggggrrrrrrrrrrrttyuuiiiii
please help me with both questions
Answer:
(b) 829 seconds
(c) 13.8 minutes
Step-by-step explanation:
(b) 2.48×10⁸/2.99×10⁵ = 829 seconds
(c) 829/60 = 13.8 minutes
The graph of a linear function is given below. What is the zero of the function?
Answer:
Need to see the problem, but the "zero of the function" is the x value when y=0.
Substitute '0' for y.
Solve for x
Answer: D
Step-by-step explanation:
What is the simplified form of the following expression? Assume x > 0.
3
2x
16x
2x
4/24x²
2x
4/2443
16x4
124²
Answer:
fourth root of 24 x cubed/16x to the power four
The half-life of a radioactive substance is 20 years. If you start with some amount of this substance, what fraction will remain in 180 years?
Answer:
1/512
Step-by-step explanation:
Let staring fraction = x
Half-life = 20 years ; this is the time taken for an element to decrease to half of its original size
Hence,
After 20 years - - - > x/2
After 40 years - - - - > x/2 ÷ 2 = x/2 * 1/2 = x /4
After 60 years - - - - > x/4 ÷ 2 = x/4 * 1/2 = x/8
After 80 years - - - - -> x/8 ÷ 2 = x/8 * 1/2 = x / 16
After 100 years - - - > x/16 * 1/2 = x/32
After 120 years - - - - > x/32 * 1/2 = x/64
After 140 years - - - - -> x / 64 * 1/2 = x / 128
After 160 years - - - - - > x / 128 * 1/2 = x/256
After 180 years - - - - > x/256 * 1/2 = x / 512
Hence, the fraction after 180 years = 1/512
Venn diagrams: unions, intersections, and complements
Attached is the photo reference
Answer:
a) 0
b) 2,3,4,5,6,7
c)3,4,6,7
Step-by-step explanation:
Round 5,821 to the nearest thousands place:
Answer:
6000 hope this helps
if the question is 5,422 then the round figure is 5000
but the question is 5,821 its above 5500 will be 6000
kabura bought a piece of cloth 3 metres long. The material shrunk by 1% after washing. What was the new length of the cloth
Answer:
2.97m
Step-by-step explanation:
1% of 3m =1/100×3=0.03
0.03m of cloth was shrunk,
So, New lenght : 3-0.03=2.97m
Solve for
x
Round to the nearest tenth, if necessary.
9514 1404 393
Answer:
x = 5.0
Step-by-step explanation:
The tangent relation is helpful:
Tan = Opposite/Adjacent
tan(50°) = x/4.2
x = 4.2·tan(50°) ≈ 5.0054 . . . . multiply by 4.2
x ≈ 5.0
Question 6 of 10
The domain of a function f(x) is x = 0, and the range is ys -1. What are the
domain and range of its inverse function, '(x)?
Answer: y = 0 and x = -1
What is the image point of (4, -6) after a translation right 5 units and up 4 units?
Answer:
(9,-2)
Step-by-step explanation:
5 is the x coordinate, and 4 is the y coordinate. When you go right a certain amount of units, you add those units to your x coordinate. If you were to go left a certain amount of units, you'd subtract them. Since we're going right, 5 + 4 = 9. When you go up a certain amount of units, you add those units to you y coordinate. If you were to go down a certain amount of units, you'd subtract them. Since we're going up, -6 + 4 = -2. So, x = 9 and y = -2, or (9,-2)
Please help explanation if possible
Answer:
18.84 feet. let me know if you have ay other questions.
Step-by-step explanation:
The way to find the formula for circumference is kinda complicated so it is best to ust memorize the formula, which is 2πr. or 2 times pi times the radius.
Your problem gives you the formula, but instead of 2 and r in it you have d, which is the diameter.
The diameter of the circle is 2 times the radius, so that's why it is replaced.
the radius is the distance from the center fo the circle to one edge, and the diameter is the distance through the circle passing through its center. so it's the center to one end plus the center to another end. or r+r which is also 2r.
So d = 2r, so in this problem d =6 feet.
So now the formula πd = 3.14*6 feet = 18.84 feet
MY NOTES Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) f(x) = 2x2 − 4x + 3, [−1, 3
Answer:
b) [tex]c=1[/tex]
Step-by-step explanation:
From the question, we are told that:
Function
[tex]F(x)=2x^2-4x+9[/tex]
Given
Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that f(a) = f(b), then f′(x) = 0 for some x with a ≤ x ≤ b.
Generally, the Function above is a polynomial that can be Differentiated and it is continuous
Where
-F(x) is continuous at (-1,3)
-F(x) Can be differentiated at (-1.3)
-And F(-1)=F(3)
Therefore
F(x) has Satisfied all the Requirements for Rolle's Theorem
Differentiating F(x) we have
[tex]F'(x)=4x-4[/tex]
Equating F(c) we have
[tex]F'(c)=0[/tex]
[tex]4(c)-4=0[/tex]
Therefore
[tex]c=1[/tex]
You measure 49 turtles' weights, and find they have a mean weight of 80 ounces. Assume the population standard deviation is 6.1 ounces. Based on this, construct a 99% confidence interval for the true population mean turtle weight. Round your answers to 2 decimal places.
Answer:
The 99% confidence interval for the true population mean turtle weight is between 77.76 and 82.24 ounces.
Step-by-step explanation:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.575\frac{6.1}{\sqrt{49}} = 2.24[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 80 - 2.24 = 77.76 ounces.
The upper end of the interval is the sample mean added to M. So it is 80 + 2.24 = 82.24 ounces.
The 99% confidence interval for the true population mean turtle weight is between 77.76 and 82.24 ounces.
Consider the given statement. Determine whether its is equivalent to the given statement, a negation, or neither. Attached is the photo reference.
Answer:
1. Negation
2. Equivalent
3. Neither
4. Neither
Step-by-step explanation:
p ^ ~q
~q → p~
~q ∨ p
~p ∨q
Police estimate that 25% of drivers drive without their seat belts. If they stop 6 drivers at random, find theprobability that more than 4 are wearing their seat belts.
Answer:
%17.80
Step-by-step explanation:
17.8% is the probability that more than 4 are wearing their seat belts.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that Police estimate that 25% of drivers drive without their seat belts.
If they stop 6 drivers at random we need to find the probability that more than 4 are wearing their seat belts.
For each driver stopped, there are only two possible outcomes. Either they are wearing their seatbelts, or they are not.
he drivers are chosen at random, which mean that the probability of a driver wearing their seatbelts is independent from other drivers.
Police estimate that 25% of drivers drive without their seat belts.
This means that 75% wear their seatbelts, so P=0.75
If they stop 6 drivers at random, find the probability that all of them are wearing their seat belts.
[tex]P(X=x)=C_{n,x} p^{x} (1-p)^{n-x}[/tex]
[tex]P(X=6)=C_{6,6} 0.75^{6} (1-0.75)^{0} =0.1780[/tex]
Hence, 17.8% is the probability that more than 4 are wearing their seat belts.
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find the surface area of the prism HURRY
Answer:
Does the answer help you?
What is the 11th term of this geometric sequence?: 16384, 8192, 4096, 2048
Answer:
16
Step-by-step explanation:
1) Find out r of the sequence. The first term(a1) is 16384, the second term (a2) is 8192.
8192=16384*r. r= 0.5
2) Use the rule that an=a1*r^(n-1)
a11=a1*r^10
a11= 16384*((0.5)^10)= 16384/ (2^10)=16.
In an interview for a secretary position at the dealer, a typist claims a tying speed of 45 words per minute. On
On the basis of 70 trials, she demonstrated an average speed of 43 words per minute with a standard deviation of 15 words per minute.
Test at 5% significance level on the typist’s claim.
Using the hypothesis test for one sample mean, There is NO SIGNIFICANT EVIDENCE to support the typist's claim
[tex]H_{0} = 45\\H_{1} < 45\\\\[/tex]
The test statistic :
T = (x - μ) ÷ (s/√(n))
T = (43 - 45) ÷ (15/√70)
T = - 2 ÷ 1.7928429
T = -1.12
At α = 0.05
Pvalue :
Degree of freedom, df = 70 - 1 = 69
Pvalue = 0.1333
Decision region :
Reject [tex]H_{0}[/tex] if Pvalue < α
0.1333 > 0.05
Since Pvalue > α We fail to reject the Null
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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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