When the population standard deviation, is unknown, a hypothesis test for the population mean is conducted the same way as if the population standard deviation were known. The t-distribution is used instead of the conventional normal distribution, which is the only distinction (z-distribution).
Differentiate the function with respect to x. Shot steps
Differentition of [tex]y=log_{2}x^{3}.(5x^{4}+2)[/tex] is [tex]y'=log_{2}x^{3}(20x^{3} )+(5x^{4}+2)\frac{1}{x}[/tex]
What is Differential equation?A differential equation is an equation that contains one or more functions with its derivatives.
Given,
[tex]y=log_{2}x^{3}.(5x^{4}+2)[/tex]
We have to differentiate with respect to x.
y'=xy'+yx'
[tex]x=log_{2}x^{3}[/tex]
[tex]y=5x^{4}+2[/tex]
[tex]y'=log_{2}x^{3}(20x^{3} )+(5x^{4}+2)\frac{1}{x^{3}} .3x^{2}[/tex]
[tex]y'=log_{2}x^{3}(20x^{3} )+(5x^{4}+2)\frac{1}{x}[/tex]
Hence, differentiation of [tex]y=log_{2}x^{3}.(5x^{4}+2)[/tex] is [tex]y'=log_{2}x^{3}(20x^{3} )+(5x^{4}+2)\frac{1}{x}[/tex]
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The weight of oranges growing in an orchard is normally distributed with a mean
weight of 4 oz. and a standard deviation of 0.5 oz. From a batch of 2000 oranges, how
many would be expected to weight less than 5 oz., to the nearest whole number?
Answer:
The weight of oranges growing in an orchard is normally distributed with a mean weight of 6.5 oz. and a standard deviation of 1 oz. Using the empirical rule, determine what interval would represent weights of the middle 99.7% of all oranges from this orchard
Step-by-step explanation:
bran leist ple
Answer:
1954
Step-by-step explanation:
If a continuous random variable X is normally distributed with mean μ and variance σ²:
[tex]\boxed{X \sim \textsf{N}(\mu,\sigma^2)}[/tex]
Given:
mean μ = 4 ozstandard deviation σ = 0.5 ozFirst find the probability that the weight of an orange is less than 5 oz.
[tex]\text{If \;$X \sim \textsf{N}(4,0.5^2)$,\;\;find\;\;P$(X < 5)$}.[/tex]
Method 1
Using a calculator:
[tex]\implies \text{P}(X < 5)=0.977249868[/tex]
Method 2
Converting to the z-distribution.
[tex]\boxed{\text{If\;\;$X \sim$N$(\mu,\sigma^2)$\;\;then\;\;$\dfrac{X-\mu}{\sigma}=Z$, \quad where $Z \sim$N$(0,1)$}}[/tex]
[tex]x=5 \implies Z=\dfrac{5-4}{0.5}=2[/tex]
Using the z-tables for the probability:
[tex]\implies \text{P}(Z < 2)=0.9772[/tex]
To find the expected number of oranges that will weigh less than 5 oz from a batch of 2000, multiply the total number of oranges by the probability calculated:
[tex]\begin{aligned}2000 \times \text{P}(X < 5)&=2000 \times 0.977249868\\&=1954.499736\\&=1954\end{aligned}[/tex]
Therefore, 1954 oranges would be expected to weigh less than 5 oz.
help me answer this please
Answer:
3,952 ft
Step-by-step explanation:
Use the sine function since you need to find the hypotenuse but know the opposite side of the angle, since sine is equal to opposite/hypotenuse.
sin8°=[tex]\frac{550}{c}[/tex]
csin8°=550
c=550/sin8°
c= 3,952
Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 22 days and a standard deviation of 6 days. 64% of all of these types of trials are completed within how many days
Answer:
30 days
Step-by-step explanation:
Look at you z-score table to find the value closest to .6400 (64%)
my table shows this corresponds to z-score + .36 standard deviation ABOVE the mean of 22 days
.36 * 22 = ~ 8 days
added to the mean 8 + 22 = 30 days
Write a quadratic inequality for the graph.
The required quadratic inequality whose graph is given below is
[tex]y > -\frac{1}{4}x^2 -4x +2[/tex]
What is graph of a function?
At first it is important to know about function
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Graph of a function f(x) is the collection of all point of the form (x, f(x))
Let the equation be [tex]y = ax^2 + bx + c[/tex]
The graph passes through (0, 2)
Putting x = 0 and y = 2
c = 2
[tex]y = ax^2 + bx + 2[/tex]
The graph passes through (-12, 14) and (-4, 14)
[tex]14 = (-12)^2a + (-12)b+2\\144a - 12b = 14 - 2\\12(12a- b) = 12\\12a - b = \frac{12}{12}\\12a - b = 1 ... (1)[/tex]
Also
[tex]14 = (-4)^2a + (-4)b + 2\\16a - 4b = 14 - 2\\16a - 4b = 12\\4(4a - b) = 12\\4a - b = \frac{12}{4}\\4a - b = 3 .... (2)[/tex]
Subtracting (2) from (1),
8a = -2
[tex]a = -\frac{2}{8}[/tex]
[tex]a = -\frac{1}{4}[/tex]
Putting the value of a in (2)
[tex]4 \times -\frac{1}{4} - b =3\\-1 - b = 3\\b = -3 - 1\\b = -4[/tex]
The required equality is
[tex]y = -\frac{1}{4}x^2 -4x +2[/tex]
Since the shaded region is the outer region and the line is given dotted,
The required quadratic inequality is
[tex]y > -\frac{1}{4}x^2 -4x +2[/tex]
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what is 1234000 times squared
Answer:
1.522756e+12
Step-by-step explanation:
Answer the question in the image below.
Answer:
(a) x = 2
(b) 7 + 5√2
Step-by-step explanation:
Part (a)Given terms of a geometric sequence:
[tex]a_1=\sqrt{x}-1[/tex][tex]a_2=1[/tex][tex]a_3=\sqrt{x}+1[/tex]The common ratio of a geometric sequence is found by dividing consecutive terms. Therefore:
[tex]\implies \dfrac{a_3}{a_2}=\dfrac{a_2}{a_1}[/tex]
Substitute the given terms into the equation and solve for x:
[tex]\implies \dfrac{\sqrt{x}+1}{1}=\dfrac{1}{\sqrt{x}-1}[/tex]
[tex]\implies (\sqrt{x}-1)(\sqrt{x}+1)=1[/tex]
[tex]\implies x+\sqrt{x}-\sqrt{x}-1=1[/tex]
[tex]\implies x-1=1[/tex]
[tex]\implies x=2[/tex]
Part (b)General form of a geometric sequence:
[tex]\boxed{a_n=ar^{n-1}}[/tex]
where:
[tex]a_n[/tex] is the nth term.a is the first term.r is the common ratio.n is the position of the term.Substitute the found value of x into the expressions for the given terms:
[tex]a_1=\sqrt{2}-1[/tex][tex]a_2=1[/tex][tex]a_3=\sqrt{2}+1[/tex]Find the common ratio:
[tex]\implies r=\dfrac{a_3}{a_2}=\dfrac{\sqrt{2}+1}{1}=\sqrt{2}+1[/tex]
Therefore, the equation for the nth term is:
[tex]\boxed{a_n=(\sqrt{2}-1)(\sqrt{2}+1)^{n-1}}}[/tex]
To find the 5th term, substitute n = 5 into the equation:
[tex]\implies a_5=(\sqrt{2}-1)(\sqrt{2}+1)^{5-1}[/tex]
[tex]\implies a_5=(\sqrt{2}-1)(\sqrt{2}+1)^{4}[/tex]
[tex]\implies a_5=(\sqrt{2}-1)(\sqrt{2}+1)^2(\sqrt{2}+1)^2[/tex]
[tex]\implies a_5=(\sqrt{2}-1)(3+2\sqrt{2})(3+2\sqrt{2})[/tex]
[tex]\implies a_5=(\sqrt{2}-1)(9+12\sqrt{12}+8)[/tex]
[tex]\implies a_5=(\sqrt{2}-1)(17+12\sqrt{2})[/tex]
[tex]\implies a_5=17\sqrt{2}+24-17-12\sqrt{2}[/tex]
[tex]\implies a_5=7+5\sqrt{2}[/tex]
find the unlabeled sides and calculate the lenths.
Answer:
v = 9√2 ; u = 18
Step-by-step explanation:
angle 45 degrees = the legs are congruent
v = 9√2
u = [tex]\sqrt{(9\sqrt{2} )^2+{(9\sqrt{2})^2}} = \sqrt{2(9\sqrt{2)}^2} = \sqrt{2 (81 *2) }= \sqrt{4 * 81}= 2 * 9 = 18[/tex]
Answer:
v = 9√2u = 18Step-by-step explanation:
a triangle with an angle of 90° and an angle of 45° is an isosceles right triangle, so V equals 9√2.
to find u we use the Pythagorean theorem
u = √(9√2)²+(9√2)²
semplifyu = 9 + 9
u = 18
Nao and Arban drive to work.
Nao drives 95 miles in 2.5 hours.
Arban drives 128 km in 1 hour 15 min.
Work out the difference between their average speeds in km/h.
1 mile = 1.6 km
Thank You.
Answer:
41.6 km/h
Step-by-step explanation:
Nao drives 95mi/2.5hr or 38 miles per hour, or 60.8 km/h
1 hr 15 min is the same as 1.25 hours
Arban drives 128km/1.25hr or 102.4 km/h
The difference is 102.4-60.8 = 41.6
I need help with my math homework, it is pre-algebra, and it's about similar figures.
Answer:
1) 5
2) 3
3) 2
4) 10
5) 7
6) 36
7) 110
8) 100
9) 40
10) 8
11) 30
12) 60
13) 12
14) 63
15) 77
16) 5
Step-by-step explanation:
Answer:
1) x=5; 2) x=3; 3) x=2; 4) x=10; 5) x=7; 6) x=36; 7) x=110; 8) x=100; 9) x=40; 10) x=8; 11) x=30; 12) x=12; 13) x=12; 14) x=63; 15) x=77; 16) x=5
Step-by-step explanation:
I can't explain every problem, but I will do the first three.
1) We divide the sides by 4 to get x=5
2)We divide by 3 to get x=3
3)Divide by 4 to get x=2
Solve the system for 25 points
Answer: its gonna be D
Step-by-step explanation:
its just zeros
Make v subject of the formula T= v divided 6+5
The representation of the given equation 'v' as subject of the formula v = 6 ( T - 5 ).
What is meant by mathematical expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Dividends are made by multiplying them. When you divide 12 into three equal groups of 4, you get four in each group if 3 groups of 4 add up to 12.The main goal of division is to produce equal groups or to establish the number of individuals in each group after a fair distribution.In mathematics, division is the process of dividing a number into equal parts and determining the most possible number of equal parts.For example, 15 is divided into 3 groups of 5 when multiplied by 3.Given,
T = v / 6 + 5
substract 5 on both the sides, we get
⇒ T - 5 = v / 6 + 5 - 5
⇒ v / 6 = T - 5
Now represent 'v' as a subject of the formula we get,
v = 6 ( T - 5)
Hence, v = 6 (T - 5 ) is the representation of the given equation 'v' as subject of the formula.
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Prove by Mathematical Induction that 1 / 1 ×2 + 1 / 2 ×3 + 1 / 3 × 4 + ... + 1 / n ( n + 1 ) = n / n + 1
The required proof by Mathematical Induction of 1 / 1 ×2 + 1 / 2 ×3 + 1 / 3 × 4 + ... + 1 / n ( n + 1 ) = n / n + 1 has been in the solution.
To begin, we suppose that the assertion is correct for some integer k.
⇒ 1/1. 2 + 1/2 . 3 + . . . + 1/k . (k+1) = k/(k+1) ....(i)
As per Mathematical Induction, the required solution would be as:
Let the LHS be Sk.
Consider the series with one more term, when k = k+1.
We must demonstrate that Sk+1 has the same form as equation (i) but with k substituted by k+1.
Then,
Sk+1 = Sk + 1/(k+1)(k+2)
= k/(k+1) + 1/(k+1)(k+2)
= [k(k+2) + 1] / (k+1)(k+2)
= (k2+2k +1) / (k+1)(k+2)
= (k+1)2 / (k+1)(k+2)
= (k+1) / (k+2)
= (k+1) / ((k+1)+1)
And this has the same form as equation (i) but with k+1 in place of k.
As a result, if it is true for n=k, it must also be true for n=k+1.
When n=1, S1 = 1/1. 2 = 1/2 = 1/1(1+1), hence the assertion is correct.
As a result of the preceding demonstration, it must be true for n= 1+1 = 2.
as well as for n=2+1=3 and so forth for all n numbers.
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The function f(w) is graphed below. What is true about the graph on the interval from point a to point b?
The graph of the function f(x) is negative and decreasing from point a to point b.
What is a graph?The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.
These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.
From the given graph of f(x) it is decreasing as it is going downwards in the interval from a to b where x is increasing and the graph is negative also in the interval a to b as it is in the negative y-axis.
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Help! Trig Homework. Will give brainliest!!!
Answer:
[tex]\frac{4\pi }{5}[/tex]
Step-by-step explanation:
the 2 angles lie on the x- axis and sum to π , then the curved arrow angle is
π - [tex]\frac{\pi }{5}[/tex] = [tex]\frac{5\pi }{5}[/tex] - [tex]\frac{\pi }{5}[/tex] = [tex]\frac{4\pi }{5}[/tex]
Somebody please help
Answer:
The answer to your question is,
D. Reflect over the x-axis and reflect over the y-axis
Step-by-step explanation:
I Hope this helps :)
Answer:
C. Reflect over the X axis and translate 6 units left
Step-by-step explanation:
That is the only one that works
A, B, and D are close but don't line up. For one rectangle to line up with another, it had to be in the same place with the same letters at the same corners. For option C, a reflection across the X axis means that rectangle ABCD will flip across the horizontal line. (it matches A'B'C'D now) then a translation 6 units left just moves it six boxes left. It should match A"B"C"D now :)
Cube length is 5 inches what is the shape of its face
By rounding to one significant figure, estimate the answers to these questions:
a) 59 +25
b) 6820
71
c)
91 × 18
58
Answer:
A. 90 B.690000 C.180000Step-by-step explanation:
A. 60 + 30 = 90
B. 690000
C. 90 x 2000 = 180000
PLEASE HELP ME WITH MY WORK “A function is graphed below. On which interval of a is the average rate of change of the function the greatest?”
The required greatest rate of change is at x = 7 to x = 10. Option A is correct.
Given that,
The function is graphed. On which interval of a is the average rate of change of the function the greatest is to be determined.
Rate of change is defined as the change in value with rest to the time is called rate of change.
Here,
The average rate for,
x = 7 tot x = 10
Rate = 56 - 8 / 10 -7
Rate = 16
While the other pair has an average rate of 4, 4.46
Thus, the required greatest rate of change is at x = 7 to x = 10. Option A is correct.
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The following is a street map of a beighbourhend. Study the street map and answer the questions
1.21 How many houses are there in this neighbourhood?
1.2.2 Which building is located next to the park? 1.2.3 Which business appears more than all the other businesses?
1.2.4 The bar (graphic or line) scale shows the distance of the bar in real life Measure the length of the bar in centimetres
1.2.5 Hence, use your measurement in QUESTION 1.24 to explain the scale of this street map 12.6 How many more houses are in the street at the top than the street at the bottom?
1.2.1 There are 18 houses in the neighborhood.
1.2.2 The building located next to the park is the hospital.
1.2.3 The business which appears more than all the other businesses in the neighborhood is the Cafe.
1.2.4. The bar scale measures 25 centimeters.
1.2.5 Based on the above measurement, the scale of this street map has a scale factor of 0.005468, compared to the original distance of the neighborhood.
1.2.6 There are 3 more houses in the street at the top than the street at the bottom.
What is the scale factor?The scale factor is the ratio between two scales of an object.
The scale factor shows how larger or smaller the new scale is compared to the old scale (original measurement).
The formula for the scale factor is as follows:
Scale factor = Dimension of the new scale ÷ Dimensions of the original scale.
1 yard = 91.44 centimeters
50 yards = 4,572 centimeters (91.44 x 50)
The original (larger) dimension of the neighborhood = 50 yards or 4,572 centimeters
Scale (smaller) dimension of the map = 25 centimeters
Scale factor = Smaller dimension/Larger dimensions
= 25/4,572
= 0.005468
The number of houses at the top street = 8
The number of houses at the center street = 5
The number of houses at the bottom street = 5
The total number of houses in the neighborhood = 18
The difference between the top street houses and the bottom street houses = 3 (8 - 5)
The number of cafes = 2
The number of parks = 1
The number of other businesses = 1 each
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The function f(x) is shown on the graph.
Which type of function describes f(x)?
Exponential
Logarithmic
Polynomial
Rational
Answer: Rational
Step-by-step explanation:
The function is not continuous, so the function cannot be exponential, logarithmic, or exponential.
This means the only possibility is that the function is rational.
Write the expression as a logarithm of a single expression.
log 5+ log 18- log 9
Answer: log(10)
Step-by-step explanation:
Based on the laws of logarithm attached below, the expression can be rewritten as:
[tex]log(5)+log(18)-log(9)=log(5*18)-log(9)\\\\=log(90)-log(9)=log(\frac{90}{9})=log(10)[/tex]
Convert 3492 in to yards
Answer:
97 yards
Step-by-step explanation:
conversion factor 36 in = 1 yard
(3492/1 in)(1yd/36in)
3492/36 yd = 97 yards
Answer:
97 yards
Step-by-step explanation:
First, convert inches to feet:
3492in / 12in = 291 ft
(12 inches in one foot)
Then, convert feet to yards:
291ft / 3ft = 97 yds
(3 feet in one yard)
What does the a b and c effect in this equation when used onto a graph? (Just general explanation)
The line x1 = b/2a serves as the axis of symmetry for the graph of a quadratic equation with the form y1 = ax1²+bx1+c.
What is graphing quadratic equation ?A parabola is the name for a quadratic function's graph.
Finding the vertex for the given equation is the first step in drawing a parabola graph. To accomplish this, use the formulas x=-b/2a and y=f(-b/2a). When the quadratic equation is stated in the vertex form, f(x) = a(x-h)2 + k, where (h, k) is the parabola's apex, the graph is plotted.
Let y equal the phrases on both sides of the equal sign as the first step.
Step 2: Graph the two newly formed functions.
Step 3: Estimate the location(s) where the function graphs intersect.
Hence a quadratic equation with the form y1 = ax1²+bx1+c is graphed, and the line x1 = b/2a acts as the axis of symmetry.
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Which event is least likely to occur?
1. Rolling a multiple of 3 on a twelve-sided die, numbered from 1 to 12.
2. Spinning a spinner is divided into four equal-sized sections colored red/green/yellow/blue and lands on red or blue.
3. Winning a raffle that sold a total of 100 tickets, if you buy 62 tickets.
4. Reach into a bag full of 15 strawberry chews and 65 cherry chews without looking and pulling out a strawberry chew.
The event that is least likely to occur among the given events after finding their probabilities is; Event number 4
What is the probability of selection?1) From 1 to 12, the multiples of 3 are;
3, 6, 9 12. They are 4 in number and so;
P(roll a multiple of 3) = 4/12 = 0.333
2) Spinner is divided into 4 equal sized sections made up of red/green/yellow/blue. Thus probability that it lands on red or blue.;
P(red) = 1/4
P(blue) = 1/4
Thus;
P(red or blue) = (1/4) + (1/4)
P(red or blue) = 1/2 = 0.5
3) Total number of tickets = 100
Number bought = 62
Thus, probability of winning = 62/100 = 0.62
4) Number of strawberry chews = 15
Number of cherry chews = 65
Total number of chews = 15 + 65 = 90
Probability of pulling out a strawberry chew is;
P(Strawberry chew) = 15/90 = 0.167
The least likely to occur has the least probability which is number 4.
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Find two positive numbers whose difference is 28 and whose product is 2720.
Answer:
68 and 40
Step-by-step explanation:
x - y = 28
x * y = 2720
x = 28 + y
(28+y)y = 2720
28y+y^2 = 2720
y^2 + 28y - 2720 = 0
discriminant = 28^2 - 4(-2720) = 784 + 10 880 = 11 644
we are searching only the positive value
y = (-28 + 108)/2 = 80/2 = 40
x = 28 + 40 = 68
Convert 7.5 miles to yd
Answer:
13200
Step-by-step explanation:
7.5 x 1760 = 13200
How to find a relationship on a graph.
The equation that represents the relationship on the graph attached below is: y = 4/5x + 3.
How to Find the Relationship on a Linear Graph?Given a linear graph like the one attached below, showing the relationship between x and y, the equation that represents the relationship between x and y in the given graph can be expressed as: y = mx + b, where m is the slope (m) and b is the y-intercept (b) of the graph.
In the given image, the line intercepts the y-axis at 3, therefore the y-intercept of the graph is b = 3.
The slope of the graph (m) = change in y / change in x = (11 - 7)/(10 - 5)
m = 4/5
To write the equation of the relationship, substitute m = 4/5 and b = 3 into y = mx + b:
y = 4/5x + 3
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16.
1
Breakfasts cost $7.50. Find 10
the customer's total cost for
ordering 100 breakfasts.
Explain the number of zeros
and the placement of the
decimal in your answer using
a place value chart.
17
Answer:
The total of 100 breakfasts that cost $7.50 would be $750 and the placement of the decimal point would be moved 2 spaces to the right.
Step-by-step explanation:
Breakfasts cost $7.50. Find the customer's total cost for ordering 100 breakfasts. Explain the number of zeros and the placement of the decimal in your answer using a place value chart.
7.50(100)
Brainliest Please?
Help me please!!!!!!
Answer:
mixed number: 12 2/5
improper fraction: 62/5
Step-by-step explanation:
