Answers
The value of exponential expression ln e⁴ is 4
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given is an exponential expression ln e⁴ we need to simplify it,
So,
we know that,
ln aⁿ = n ln a
and =
ln e = 1
so,
ln e⁴ = 4 ln e
= 4 x 1
= 4
Hence, the value of exponential expression ln e⁴ is 4
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Related Questions
Mathematics question help
Answers
Distance Formula: [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]
Point 1: (9,0)
Point 2: (5,-8)
D = sqrt[ (5 - 9)^2 + (-8 - 0)^2 ]
D = sqrt[ (-4)^2 + (-8)^2 ]
D = sqrt[ 16 + 64]
D = sqrt(80)
Hope this helps!
4 square root of 5
Step-by-step explanation:
Can someone please help me
Researchers would like to assess the overall health of white pine trees in a state park. Which of the following
methods for choosing the trees to assess would be considered a convenience sample?
O A ranger hires employees to assess every tree in the park.
O The 100 trees closest to a ranger station are assessed for damage.
O Agrid map of the park is used, and 100 random points on the grid are chosen and used to select the trees to
assess
O Each tree in the state park is tagged with a number, and 100 random numbers that represent the trees are
selected and assessed for damage.
Answers
Answer:
The 100 trees closest to a ranger station are assessed for damage.
Step-by-step explanation:
Convenience samples are samples taken from only around the focal point.
Option B is correct, The 100 trees closest to a ranger station are assessed for damage.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
A convenience sample is a non-random method of sampling that involves selecting subjects that are easy to access or readily available.
Of the methods listed, the convenience sample is the one where the trees are selected based on their proximity to a ranger station:
The 100 trees closest to a ranger station are assessed for damage.
This method is a convenience sample because it does not involve random selection of trees.
Instead, the trees are chosen based on their proximity to a specific location.
This can introduce bias into the sample, as trees near the ranger station may not be representative of the overall health of white pine trees in the state park.
Hence, Option B is correct, The 100 trees closest to a ranger station are assessed for damage.
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Solve for y. 14y-6(y-3)=22
Answers
Answer:
y=0.5
Step-by-step explanation:
14y-6(y-3)=22
14y-6y+18=22
8y+18=22
8y=4
y=0.5
Then we check our work...
14(0.5)-6((0.5)-3)=22
7-6(-2.5)=22
7+15=22
7+15 does equal 22, so this solution is correct.
1) Respond to the following questions.
What is the relationship between exponential and logarithmic functions?
Describe a real life situation in which exponential functions are used.
Describe a real life situation in which logarithms are used.
Answers
Solve for x.
A. 2
B. 5
C. 0
D. 7
Answers
Answer:
We know that the angle which lineer and divided by |AB| equal to 130°
Step-by-step explanation:
if 130° look at the 2x+260 we can say that 2x+260=260° so X equal to Zero (0)
A ladder 10m long is set against a vertical wall, Calculate the height of the wall where the ladder reached a foot of the ladder is 6m away from the wall.
Answers
Answer:
8m
Step-by-step explanation:
The least-squares regression equation
y = 3 + 1.16x can be used to predict the height of a plant (in centimeters) after x weeks. Suppose the height of a plant was 9.2 centimeters after 5 weeks.
Calculate and interpret the residual for this plant after 5 weeks.
The residual is
✔ 0.4
, which means that the predicted height of the plant is
✔ 0.4 centimeters less
than the actual height of the plant of
✔ 9.2
centimeters.
Answers
Answer:
✔ 0.4
✔ 0.4 centimeters less
✔ 9.2
1.16(5) + 3 = 8.8
9.2 - 8.8 = .4
ED2021
The residual is 0.4
What is regression?
'Regression takes a group of random variables, thought to be predicting Y, and tries to find a mathematical relationship between them. This relationship is typically in the form of a straight line (linear regression) that best approximates all the individual data points.'
According to the given problem,
y = 3 + 1.16x
After 5 weeks, x = 5,
⇒ y = 3 + 1.16(5)
⇒ y = 3 + 5.8
⇒ y = 8.8
Now subtracting y from actual height of plant,
⇒ 9.2 - 8.8
= 0.4
Hence, we can conclude the residual to be 0.4.
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2x+3=60 thì x băng bao nhieu
Answers
Answer:
x=57/2
Step-by-step explanation:
2x+3=60
<=> 2x=57
=> x=57/2
Betadine solution is a 10% povidone-iodine solution. Express this strength both as a fraction and as a ratio.
Answers
Step-by-step explanation:
Fraction =
[tex] \frac{10}{100} = \frac{1}{10} [/tex]
Ratio is 1 : 10
please help with math
Answers
Answer:
98
Step-by-step explanation:
2, 10, 18, 26, 34, 42, 50... 98
Hope this helps. Have a great day!
A uniform 41.0 kg scaffold of length 6.6 m is supported by two light cables, as shown below. A 74.0 kg painter stands 1.0 m from the left end of the scaffold, and his painting equipment is 1.4 m from the right end. If the tension in the left cable is twice that in the right cable, find the tensions in the cables (in N) and the mass of the equipment (in kg). (Due to the nature of this problem, do not use rounded intermediate values in your calculations—including answers submitted in WebAssign.)
Answers
Step-by-step explanation:
Let
[tex]m_p[/tex] = mass of the painter
[tex]m_s[/tex] = mass of the scaffold
[tex]m_e[/tex] = mass of the equipment
[tex]T[/tex] = tension in the cables
In order for this scaffold to remain in equilibrium, the net force and torque on it must be zero. The net force acting on the scaffold can be written as
[tex]3T = (m_p + m_s + m_e)g\:\:\:\:\:\:\:(1)[/tex]
Set this aside and let's look at the net torque on the scaffold. Assume the counterclockwise direction to be the positive direction for the rotation. The pivot point is chosen so that one of the unknown quantities is eliminated. Let's choose our pivot point to be the location of [tex]m_e[/tex]. The net torque on the scaffold is then
[tex]T(1.4\:\text{m}) + m_sg(1.9\:\text{m}) + m_pg(4.2\:\text{m}) - 2T(5.2\:\text{m}) = 0[/tex]
Solving for T,
[tex]9T = m_sg(1.9\:\text{m}) + m_pg(4.2\:\text{m})[/tex]
or
[tex]T = \frac{1}{9}[m_sg(1.9\:\text{m}) + m_pg(4.2\:\text{m})][/tex]
[tex]\:\:\:\:= 423.3\:\text{N}[/tex]
To solve for the the mass of the equipment [tex]m_e[/tex], use the value for T into Eqn(1):
[tex]m_e = \dfrac{3T - (m_p + m_s)g}{g} = 14.6\:\text{kg}[/tex]
The difference between two positive integers is 3. If the smaller is added to the square of the larger, the sum is 129.
Step 2 of 2 : Find the integers by solving the equation.
Answers
Answer:
11 and 8
Step-by-step explanation:
Let the integers be x and y. ATQ y-x=3 and x+y^2=129. Solving it, we will get x=8 and y=11
If my classmate was born on April 9, two thousand and six and I was born on December 24, two thousand and four, how many months, years and days are we apart?
Answers
Answer:
I could be wrong but I calculated 2 years 8 months and 15 days.
2 years
8 months
15 days
On Monday, Main Street station sells 40 tickets.
There are four types of ticket; infant, child, adult and senior.
The bar chart shows the number of infant, child and adult tickets sold.
How many Senior tickets sold ?
Find how many adult tickets were sold than child tickets ?
BOTH QUESTIONS ANSWER NEEDED PLES HELP
Answers
Answer:
0 senior tickets were sold
5 more adult tickets were sold than chil tickets
Step-by-step explanation:
You need to see the frequency of each bar
Answer by Gauthmath
Use the confidence level and sample data to find a confidence interval for estimating the population μ. Round your answer to the same number of decimal places as the sample mean.
Test scores: n = 92, = 90.6, σ = 8.9; 99% confidence
Options:
A.) 88.2 < μ < 93.0
B.) 88.4 < μ < 92.8
C.) 89.1 < μ < 92.1
D.) 88.8 < μ < 92.4
Answers
Answer: Choice A.) 88.2 < μ < 93.0
=============================================================
Explanation:
We have this given info:
n = 92 = sample sizexbar = 90.6 = sample meansigma = 8.9 = population standard deviationC = 99% = confidence levelBecause n > 30 and because we know sigma, this allows us to use the Z distribution (aka standard normal distribution).
At 99% confidence, the z critical value is roughly z = 2.576; use a reference sheet, table, or calculator to determine this.
The lower bound of the confidence interval (L) is roughly
L = xbar - z*sigma/sqrt(n)
L = 90.6 - 2.576*8.9/sqrt(92)
L = 88.209757568781
L = 88.2
The upper bound (U) of this confidence interval is roughly
U = xbar + z*sigma/sqrt(n)
U = 90.6 + 2.576*8.9/sqrt(92)
U = 92.990242431219
U = 93.0
Therefore, the confidence interval in the format (L, U) is approximately (88.2, 93.0)
When converted to L < μ < U format, then we get approximately 88.2 < μ < 93.0 which shows that the final answer is choice A.
We're 99% confident that the population mean mu is somewhere between 88.2 and 93.0
A box with a square base and no top is to be made from a square piece of carboard by cutting 4 in. squares from each corner and folding up the sides. The box is to hold 1444 in3. How big a piece of cardboard is needed
Answers
Answer:
[tex]C=27inch\ by\ 27inch[/tex]
Step-by-step explanation:
Squares [tex]h=4inch[/tex]
Volume [tex]v=1444in^3[/tex]
Generally the equation for Volume of box is mathematically given by
[tex]V=l^2h[/tex]
[tex]1444=l^2*4[/tex]
[tex]l^2=361[/tex]
[tex]l=19in[/tex]
Since
Length of cardboard is
[tex]l_c=19+4+4[/tex]
[tex]l_c=27in[/tex]
Therefore
Dimensions of the piece of cardboard is
[tex]C=27inch\ by\ 27inch[/tex]
The area of a rectangle is 63 ft^2, and the length of the rectangle is 11 ft more than twice the width. Find the dimensions of the rectangle.
Answers
answer this question ASAP
Answers
Answer:
972pi in ^3
Step-by-step explanation:
We need to find the volume of the sphere
V = 4/3 pi r^3
The diameter is 18
r = d/2 = 18/2 = 9
V = 4/3 pi ( 9)^3
V = 972pi in ^3
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)
Answers
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]
What is the mean of the following list of extra credit points earned on a statistics test?
10,8,18,17,7
Answers
Answer:
12
Step-by-step explanation:
Given the data :
X : 10,8,18,17,7
The mean value of scores obtained can be obtained thus :
Mean = ΣX / n
n = sample size = 5
Mean = ΣX / n = (10+8+18+17+7) / 5
Mean = 60 / 5 = 12
Can someone please help
Me
Answers
Answer:
$3735
Step-by-step explanation:
2/5 = 8/20
8/20 + 7/20 = 15/20 = 3/4
3/4*4980 = 3735
What is the equation
Answers
Answer:
y=3x+1
Step-by-step explanation:
Determine slope with two coordinates and use it in the formula
Write 36 as a product of its prime factors.Write the factors in order,from smallest to largest.
Pls Help me!!!!
Answers
Answer:
2×2×3×3
Step-by-step explanation:
Answer:
2×2×3×3
Step-by-step explanation:
36=3×12
12=3×4
4=2×2
=3×3×2×2
Hope this helps! <3
please help solve for y!
Answers
As both angles are supplementary
[tex]\\ \Large\sf\longmapsto 3x+(2x+3y)=180°[/tex]
[tex]\\ \Large\sf\longmapsto 3x+2x+3y=180[/tex]
[tex]\\ \Large\sf\longmapsto 5x+3y=180[/tex]
[tex]\\ \Large\sf\longmapsto 3y=180-5x[/tex]
[tex]\\ \Large\sf\longmapsto y=\dfrac{180-5x}{3}[/tex]
And
[tex]\\ \Large\sf\longmapsto 3x=90[/tex]
[tex]\\ \Large\sf\longmapsto x=\dfrac{90}{3}[/tex]
[tex]\\ \Large\sf\longmapsto x=30[/tex]
Now
Putting value[tex]\\ \Large\sf\longmapsto y=\dfrac{180-5x}{3}[/tex]
[tex]\\ \Large\sf\longmapsto y=\dfrac{180-5(30)}{3}[/tex]
[tex]\\ \Large\sf\longmapsto y=\dfrac{180-150}{3}[/tex]
[tex]\\ \Large\sf\longmapsto y=\dfrac{30}{3}[/tex]
[tex]\\ \Large\sf\longmapsto y=10[/tex]
Which is the solution to-x/2<-4
A x<-8
B x2-8
C x <8
D x 8
Answers
Answer:
A.x<-8
Step-by-step explanation:
=1/2x<−4
=2*(1/2x)< (2)*(-4)
= x<-8
The point (3,-4) is on the terminal side of an angle 0. What is cos 0?
А. 3/4
В. -3/4
C. 3/5
D. -3/5 E. 3
Answers
9514 1404 393
Answer:
C. 3/5
Step-by-step explanation:
The distance from the origin to the given point is ...
d = √(3² +(-4)²) = √(9+16) = 5
The cosine of the angle is the ratio of the x-coordinate to this value:
cos(θ) = x/d
cos(θ) = 3/5
9.03 divided by 899.8 is closest to? a.0.01 b.0.001 c.1 d.100
Answers
9.03 divided by 899.8 is closest to a.0.01
Answer: a) 0.01
Step-by-step explanation:
Find the missing length
Answers
Answer:
x=5.9
i think this the answer
Kiểm tra 800 hạt gạo của một lô gạo người ta thấy có 750 hạt nguyên, 25 hạt tấm lớn, 25 hạt tấm bé. Hãy tìm khoảng tin cậy của tỉ lệ hạt nguyên của lô gạo nói trên với độ tin cậy 95%. Cho U(0,025) = 1,96, U(0,05) = 1,645.
Answers
Answer:
what is your Language I think it is Russian I don't understand Russian I only understand Nepali,English and Japanese
A poll of 400 people from Dobbs Ferry showed 250 preferred chocolate raspberry coffee while 170 out of 350 in Irvington preferred the same flavor. To test the hypothesis that there is no difference in preferences in the two villages, what is the alternate hypothesis
Answers
Answer: The alternate hypothesis would disprove the null hypothesis and state that there are a significant difference in preferences/proportions between the two villages.
For instance, let's say:
p₁ = proportion of preference from Dobbs Ferryp₂ = proportion of preference from IrvingtonThe null hypothesis would be that p₁ = p₂, while the alternative hypothesis would be that p₁ ≠ p₂.
