Answer:
-7 and 7
Step-by-step explanation:
-7+7=0
because they are opposite numbers
Step-by-step explanation:
-7+7= 0
it is hence -7 and 7
The function defined by w(x)=-1.17x+1260 gives the wind speed w(x)(in mph) based on the barometric pressure x (in millibars,mb). a) Approximate the wind speed for a hurricane with the barometric pressure of 900mb. b) Write a function representing the inverse of w and interpret its meaning in context. c) Approximate the barometric pressure for a hurricane with speed 90 mph.
Answer:
a) 207 mph
b) x = (1260-w)/1.17
c) 1000 mb
Step-by-step explanation:
a) Put the pressure in the equation and solve.
w(900) = -1.17(900) +1260 = 207
The wind speed for a hurricane with a pressure of 900 mb is 207 mph.
__
b) Solving for x, we have ...
w = -1.17x +1260
w -1260 = -1.17x
x = (1260 -w)/1.17 . . . . inverse function
__
c) Evaluating the inverse function for w=90 gives ...
x = (1260 -90)/1.17 = 1170/1.17 = 1000 . . . millibars
The approximate barometric pressure for a hurricane with a wind speed of 90 mph is 1000 millibars.
Can anyone please explain? Need some help :)
A regular hexagon is inscribed in a circle with a diameter of 12 units. Find the area of the hexagon. Round your answer to the nearest tenth. (there's no picture included)
Answer:
93.5 square units
Step-by-step explanation:
Diameter of the Circle = 12 Units
Therefore:
Radius of the Circle = 12/2 =6 Units
Since the hexagon is regular, it consists of 6 equilateral triangles of side length 6 units.
Area of the Hexagon = 6 X Area of one equilateral triangle
Area of an equilateral triangle of side length s = [tex]\dfrac{\sqrt{3} }{4}s^2[/tex]
Side Length, s=6 Units
[tex]\text{Therefore, the area of one equilateral triangle =}\dfrac{\sqrt{3} }{4}\times 6^2\\\\=9\sqrt{3} $ square units[/tex]
Area of the Hexagon
[tex]= 6 X 9\sqrt{3} \\=93.5$ square units (to the nearest tenth)[/tex]
Translate the following argument in a standard form categorial syllogims then use venn diagram or rules for syllogim to determine whether each is valid or invalid.
All of the movies except the romantic comedies were exciting. Hence, the action films were exciting,because none of them is a romantic comedies.
Answer:
couldnt tell you
Step-by-step explanation:
jkj
if g (x) = 2x + 2, find g (a + h) - g (a)
Answer:
[tex] g(x) = 2x+2[/tex]
Let's find g(a+h):
[tex] g(a+h)=2*(a+h) +2= 2a +2h +2[/tex]
And now let's find g(a)
[tex] g(a)= 2a+2[/tex]
And now finally:
[tex] g(a+h) = 2a +2h +2 -2a-2 = 2h +2-2= 2h[/tex]
Step-by-step explanation:
We have the following function given:
[tex] g(x) = 2x+2[/tex]
Let's find g(a+h):
[tex] g(a+h)=2*(a+h) +2= 2a +2h +2[/tex]
And now let's find g(a)
[tex] g(a)= 2a+2[/tex]
And now finally:
[tex] g(a+h) = 2a +2h +2 -2a-2 = 2h +2-2= 2h[/tex]
Translate into an equation: The cost of V ounces at $2 per ounce equals $56.
Answer:
V = number of ounces
56 = 2V
Step-by-step explanation:
Answer:28
Step-by-step explanation:V times 2= 56
I don't know what to do.
Answer:
True.
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
We can simply plug in the 3 variables to see if it forms a Pythagorean Triple:
6² + 13² = 14.32²
36 + 169 = 205.062
205 = 205 (rounded), so True.
solve the exponential function 3 to the x-5 = 9
Answer:
x = 7
Step-by-step explanation:
[tex] 3^{x - 5} = 9 [/tex]
[tex] 3^{x - 5} = 3^2 [/tex]
[tex] x - 5 = 2 [/tex]
[tex] x = 7 [/tex]
2(x + 25) HELPPPPP MEEEEE
Answer:
2x+50
Step-by-step explanation:
Distributive property: 2(x)+2(25)
Simplify: 2x+50
Answer: 2x + 50
Step-by-step explanation: In this problem, the 2 distributes through the parenthses, multiplying by each of the terms inside.
So we have 2(x) + 2(25) which simplifies to 2x + 50.
The world’s population is currently estimated at 7,125,000,000. What is this to the nearest billion? billion
Answer:
7,000,000,000
Step-by-step explanation:
since the closest number is less than 5 (1<5) you round down making the nearest billion 7
Answer:
7,000,000,000 OR 7 Billion
Step-by-step explanation:
Since the 1 is millions place and its less than 5, you need to round down meaning that 7,125,000,00 rounded to the nearest billion is 7 billion.
5x +3y=210 x+y=60 Witch can represent a linear equation
Answer:
both
Step-by-step explanation:
Both of the equations shown here are linear equations in standard form.
5x + 3y = 210
x + y = 60
Human body temperatures are normally distributed with a mean of 98.2oF and a standard deviation of 0.62oF. Find the temperature that separates the bottom 12% from the top 88%.
Answer:
The temperature that separates the bottom 12% from the top 88% is 97.5°F.
Step-by-step explanation:
We are given that human body temperatures are normally distributed with a mean of 98.2°F and a standard deviation of 0.62°F.
Let X = human body temperatures
So, X ~ Normal([tex]\mu= 98.2,\sigma^{2} = 0.62^{2}[/tex])
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean human body temperature = 98.2°F
[tex]\sigma[/tex] = stnadard deviation = 0.62°F
Now, we have to find the temperature that separates the bottom 12% from the top 88%, that means;
P(X < x) = 0.12 {where x is the required temperature}
P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{x-98.2}{0.62}[/tex] ) = 0.12
P(Z < [tex]\frac{x-98.2}{0.62}[/tex] ) = 0.12
Now, the critical value of x that represents the bottom 12% of the area in the z table is given as -1.1835, that is;
[tex]\frac{x-98.2}{0.62} = -1.1835[/tex]
[tex]{x-98.2}= -1.1835\times 0.62[/tex]
[tex]x = 98.2 -0.734[/tex] = 97.5°F
Hence, the temperature that separates the bottom 12% from the top 88% is 97.5°F.
State if the triangles in each pair are similar. If so, State how you know they are similar and complete the similarity statement.
Answer:
Answer is option 2
Step-by-step explanation:
We know that Angle M = Angle G (given in diagram)
We also know that Angle L in triangle LMN is equal to Angle L in triangle LGH
As two angles are equal in both triangles they are similar.
But why is it Triangle LGH instead of Triangle HGL?
As we know M=G therefore they should be in the same place in the name Of the triangle. In triangle LMN M is in the middle therefore Angle G should also be in the middle
What is the amount of oil for a sports car? 5 gallons, 5 quarts or 5 cups
Answer:
Option A.
Step-by-step explanation:
We need to find the amount of oil for a sports car.
We know that,
1 quart = 4 cups
1 gallon = 4 quarts = 16 cups
Since, quart and cup are small units and they are not sufficient for a sports car because sports car needs more oil, therefore the amount of oil for a sports car is 5 gallons.
Therefore, the correct option is A.
Which of the following theorems verifies that HIJ MLN?
Answer:
HL (try HL, I believe that's the right answer)
Answer:
HL
Step-by-step explanation:
BRO TRUST ME
Pls help me help me pls guys
Answer:
C
Step-by-step explanation:
[tex]-5x-49\geq 113[/tex]
[tex]-5x\geq 162[/tex]
[tex]x\leq -32.4[/tex]
(Multiplying or dividing by a negative flips the sign).
Andrew plans to retire in 36 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on past returns. He learns that over the entire 20th century, the real (that is, adjusted for inflation) annual returns on U.S. common stocks had mean 8.7% and standard deviation 20.2%. The distribution of annual returns on common stocks is roughly symmetric, so the mean return over even a moderate number of years is close to Normal.
(a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 36 years will exceed 11%?
(b) What is the probability that the mean return will be less than 5%?
Answer:
a) 24.82% probability that the mean annual return on common stocks over the next 36 years will exceed 11%
b) 13.57% probability that the mean return will be less than 5%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
[tex]\mu = 8.7, \sigma = 20.2, n = 36, s = \frac{20.2}{\sqrt{36}} = 3.3667[/tex]
(a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 36 years will exceed 11%?
This is 1 subtracted by the pvalue of Z when X = 11.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{11 - 8.7}{3.3667}[/tex]
[tex]Z = 0.68[/tex]
[tex]Z = 0.68[/tex] has a pvalue of 0.7518
1 - 0.7518 = 0.2482
24.82% probability that the mean annual return on common stocks over the next 36 years will exceed 11%
(b) What is the probability that the mean return will be less than 5%?
This is the pvalue of Z when X = 5.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{5 - 8.7}{3.3667}[/tex]
[tex]Z = -1.1[/tex]
[tex]Z = -1.1[/tex] has a pvalue of 0.1357
13.57% probability that the mean return will be less than 5%
What is the surface area of this regular pyramid? A. 230 in2 B. 304 in2 C. 480 in2 D. 544 in2
Answer:
B: 304in^2
Step-by-step explanation:
One triangle face: (8)(15) ÷ 2 = 60
Four triangle faces: 60 x 4 = 240
Bottom Face: (8)(8) = 64
Total Surface Area: Four triangle faces + Bottom Face
Total Surface Area: 240 + 64
Total Surface Area: 304in^2
A postal service will accept a package if its length plus its girth is not more than 96 inches. Find the dimensions and volume of the largest package with a square end that can be mailed.
Answer:
Dimension - 16in by 16in by 32inVolume - 8,192in³Step-by-step explanation:
Let the length and width of the rectangular package be x and y respectively. Since end of the package is a square, the perimeter of the package will be expressed as P = 4x+y and the volume will be expressed as V = x²y
If a postal service will accept a package if its length plus its girth is not more than 96 inches, then the perimeter is equivalent to 96 inches.
96 = 4x+y
y = 96-4x
Substituting the value of x into the formula for calculating the volume, we will have;
V(x) = x²(96-4x)
V(x) = 96x²-4x³
To get the dimensions and volume of the largest package, we will find V'(x) and equate it to zero.
V'(x) = 192x-12x²
192x-12x² = 0
Factoring out x;
x(192-12x) = 0
x = 0 and 192-12x = 0
12x = 192
x = 192/12
x = 16
This shows that we have a maximum value at x = 16 and minimum at x = 0
To get y, we will substitute x = 16 into the expression y = 96-4x
y = 96-4(16)
y = 96-64
y = 32
- The dimensions of the largest package is therefore 16in by 16in by 32in
- Volume of largest package = x²y = 16²*18 = 8,192in³
You wish to take out a $200,000 mortgage. The yearly interest rate on the loan is 4% compounded monthly, and the loan is for 30 years. Calculate the total interest paid on the mortgage. Give your answer in dollars to the nearest dollar. Do not include commas or the dollar sign in your answer.
Answer:
$143,739
Step-by-step explanation:
We must apply the formula for P0 and solve for d, that is,
P0=d(1−(1+rk)−Nk(rk).
We have P0=$200,000,r=0.04,k=12,N=30, so substituting in the numbers into the formula gives
$200,000=d(1−(1+0.0412)−30⋅12)(0.0412),
that is,
$200,000=209.4612d⟹d=$954.83.
So our monthly repayments are d=$954.83. To calculate the total interest paid, we find out the entire amount that's paid and subtract the principal. The total amount paid is
Total Paid=$954.83×12×30=$343,738.80
and therefore the total amount of interest paid is
Total Interest=$343,738.80−$200,000=$143,738.80,
which is $143,739 to the nearest dollar.
The interest paid is 2912683 dollars.
What is compound interest ?Compound interest is calculated for the principle taken as well as previous interest paid.
According to the given question Principle amount (P) taken from the bank is 2000000 dollars.
The yearly interest rate (r) compounded monthly is 4%.
Time in years (n) is 30.
We know, in the case of compound interest compounded yearly is
A = P(1 + r/100)ⁿ.
So, Amount compounded monthly will be
A = P[ 1 + (r/12)/100]¹²ⁿ.
A = 2000000[ 1 + (4/12)/100]¹²ˣ³⁰.
A = 2000000[ 1 + 0.003]³⁶⁰.
A = 2000000[ 1.003]³⁰⁰.
A = 2000000(2.456).
A = 4912583.
∴ The total interest paid on the mortgage is (4912683 - 2000000) = 2912683.
earn more about compound interest here :
https://brainly.com/question/14295570
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Express it in slope-intercept form.
Hey there! :)
Answer:
y = 1/4x - 3.
Step-by-step explanation:
Use the slope-formula to find the slope of the line:
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Plug in two points from the line. Use the points (-4, -4) and (0, 3):
[tex]m = \frac{-3 - (-4)}{0 - (-4)}[/tex]
Simplify:
m = 1/4.
Slope-intercept form is y = mx + b.
Find the 'b' value by finding the y-value at which the graph intersects the y-axis. This is at y = -3. Therefore, the equation is:
y = 1/4x - 3.
The formula to convert Fahrenheit to Celsius is C - 5 (F - 32). Convert 30°C to
Fahrenheit. Round to the nearest degree.
A. 30°F
B. -1°F
C. 112°F
D. 86°F
Answer:
D. *6F
Step-by-step explanation:
C=(F-32)*5/9
30=(F-32)*5/9
F = (30*9)/5+32
F = 86
Write the equation in the form Ax + By = C. Find an equation of a line passing through the pair of points (4,7) and (3,4).
Answer:
[tex] 3x - y = 5 [/tex]
Step-by-step explanation:
The two pint equation of a line:
[tex] y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) [/tex]
We have
[tex] x_1 = 4 [/tex]
[tex] x_2 = 3 [/tex]
[tex] y_1 = 7 [/tex]
[tex] y_2 = 4 [/tex]
[tex] y - 7 = \dfrac{4 - 7}{3 - 4}(x - 4) [/tex]
[tex] y - 7 = \dfrac{-3}{-1}(x - 4) [/tex]
[tex] y - 7 = 3(x - 4) [/tex]
[tex] y - 7 = 3x - 12 [/tex]
[tex] 5 = 3x - y [/tex]
[tex] 3x - y = 5 [/tex]
Joan's Nursery specializes in custom-designed landscaping for residential areas. The estimated labor cost associated with a particular landscaping proposal is based on the number of planting trees, shrubs, and so on to be used for the project. For cost-estimating purposes, managers use two hours of labor time for planting of a medium-sized tree. Actual times from a sample of 10 plantintings during the past month follow (times in hours):
1.7, 1.5, 2.6, 2.2, 2.4, 2.3, 2.6, 3.0, 1.4, 2.3
With a 0.05 level of significance, test to see whether the mean tree-planting time differs from two hours.
A. State the null and alternative hypotheses.
B. Compute the sample mean.
C. Compute the sample standard deviation.
D. What is the p-value?
E. What is your conclusion?
Answer:
A) Null and alternative hypothesis
[tex]H_0: \mu=2\\\\H_a:\mu\neq 2[/tex]
B) M = 2.2 hours
C) s = 0.52 hours
D) P-value = 0.255
E) At a significance level of 0.05, there is not enough evidence to support the claim that the mean tree-planting time significantly differs from two hours.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the mean tree-planting time significantly differs from two hours.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=2\\\\H_a:\mu\neq 2[/tex]
The significance level is 0.05.
The sample has a size n=10.
The sample mean is M=2.2.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.52.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.52}{\sqrt{10}}=0.1644[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{2.2-2}{0.1644}=\dfrac{0.2}{0.1644}=1.216[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=10-1=9[/tex]
This test is a two-tailed test, with 9 degrees of freedom and t=1.216, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=2\cdot P(t>1.216)=0.255[/tex]
As the P-value (0.255) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.05, there is not enough evidence to support the claim that the mean tree-planting time significantly differs from two hours.
Sample mean and standard deviation:
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{10}(1.7+1.5+2.6+. . .+2.3)\\\\\\M=\dfrac{22}{10}\\\\\\M=2.2\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{9}((1.7-2.2)^2+(1.5-2.2)^2+(2.6-2.2)^2+. . . +(2.3-2.2)^2)}\\\\\\s=\sqrt{\dfrac{2.4}{9}}\\\\\\s=\sqrt{0.27}=0.52\\\\\\[/tex]
How many bits does it take to identify uniquely every person in the United States (the current population is about 300 million)?
Answer:
what's a bit
Step-by-step explanation:
Find the value of X
Answer:
14
Step-by-step explanation:
Chords the same distance from the center of the circle have the same length. You are shown that half the chord length is 7, so the whole chord length is
x = 14.
The number 128 is divided into two parts in the ratio 7:9. Find the absolute difference between the two parts.
The graph of y =ex is transformed as shown in the graph below. Which equation represents the transformed function?
Answer:
B. e^x+3
Step-by-step explanation:
Y=e^x
the graph is moving 3 units up
y= y+3
y=e^x+3
answer = y=e^x+3
Answer: B
Step-by-step explanation:
In ABC,if sin A=4/5 and tan A=4/3, then what I s cos A?
Researchers studied the mean egg length (in millimeters) for a particular bird population. After a random sample of eggs, they obtained a 95% confidence interval of (45,60) in millimeters. In the context of the problem, which of the following interpretations is correct, if any?
A. We are 95% sure that an egg will be between 45 mm and 60 mm in length.
B. For this particular bird population, 95% of all birds have eggs between 45 mm and 60 mm.
C. We are 95% confident that the mean length of eggs for this particular bird population is between 45 mm and 60 mm.
D. We are 95% confident that the mean length of eggs in the sample is between 45 mm and 60 mm.
E. None of the above is a correct interpretation.
Answer:
C. We are 95% confident that the mean length of eggs for this particular bird population is between 45 mm and 60 mm.
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
For 95% confidence interval, it means that we are 95% confident that the mean of the population is between the given upper and lower bounds of the confidence interval.
For the case above, the interpretation of the 95% confidence interval is that we are 95% confident that the mean length of eggs for this particular bird population is between 45 mm and 60 mm.
An appliance dealer sells three different models of upright freezers having 13.5, 15.9, and 19.1 cubic feet of storage. Let X = the amount of storage space purchased by the next customer to buy a freezer. Suppose that X has pmf:
Answer:
a) E(X) = 16.09 ft³
E(X²) = 262.22 ft⁶
Var(X) = 3.27 ft⁶
b) E(22X) = 354 dollars
c) Var(22X) = 1,581 dollars
d) E(X - 0.01X²) = 13.470 ft³
Step-by-step explanation:
The complete Correct Question is presented in the attached image to this solution.
a) Compute E(X), E(X2), and V(X).
The expected value of a probability distribution is given as
E(X) = Σxᵢpᵢ
xᵢ = Each variable in the distribution
pᵢ = Probability of each distribution
Σxᵢpᵢ = (13.5×0.20) + (15.9×0.59) + (19.1×0.21)
= 2.70 + 9.381 + 4.011
= 16.092 = 16.09 ft³
E(X²) = Σxᵢ²pᵢ
Σxᵢ²pᵢ = (13.5²×0.20) + (15.9²×0.59) + (19.1²×0.21)
= 36.45 + 149.1579 + 76.6101
= 262.218 = 262.22 ft⁶
Var(X) = Σxᵢ²pᵢ - μ²
where μ = E(X) = 16.092
Σxᵢ²pᵢ = E(X²) = 262.218
Var(X) = 262.218 - 16.092²
= 3.265536 = 3.27 ft⁶
b) E(22X) = 22E(X) = 22 × 16.092 = 354.024 = 354 dollars to the nearest whole number.
c) Var(22X) = 22² × Var(X) = 22² × 3.265536 = 1,580.519424 = 1,581 dollars
d) E(X - 0.01X²) = E(X) - 0.01E(X²)
= 16.092 - (0.01×262.218)
= 16.0926- 2.62218
= 13.46982 = 13.470 ft³
Hope this helps!!!