Step-by-step explanation:
BODMAS
155.5-5.5*20.7
155.5-113.85
=41.65
Answer:
41.65
Step-by-step explanation:
155.5-(5.5*20.7) order of operation
155.5-113.85=
41.65
What is the solution to the equation below?
3log X= log 32+ log 2
X=-8
X=-4
X= 8
With the options:
X=-8
X=-4
X=4
X=8
The correct answer is x=4
The required solution of the given expression is x = 4.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
3log X= log 32+ log 2
logx³ = log 2⁵ + log 2
logx³ = log 2 ⁶
x³ = 2⁶
x = ∛2⁶
x = 4
Thus, the required solution of the given expression is x = 4.
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Why do we square the residuals when using the least-squares line method to find the line of best fit?
We square the residuals when using the least-squares line method to find the line of best fit because we believe that huge negative residuals (i.e., points well below the line) are just as harmful as large positive residuals (i.e., points that are high above the line).
What do you mean by Residuals?We treat both positive and negative disparities equally by squaring the residual values. We cannot discover a single straight line that concurrently minimizes all residuals. The average (squared) residual value is instead minimized.
We might also take the absolute values of the residuals rather than squaring them. Positive disparities are viewed as just as harmful as negative ones under both strategies.
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Verify the equation below with each of the values listed for t to find a solution. 4 = 3t – 2 A. t = –6 B. t = –2 C. t = -1/2 D. t = 2
Hi there!
»»————- ★ ————-««
I believe your answer is:
\(\text{D) }t=2\)
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
\(\boxed{\text{Calculating the Answer...}}\\\\4 = 3t - 2\\-----------\\\rightarrow 3t - 2 = 4\\\\\rightarrow 3t - 2 + 2 = 4 + 2\\\\\rightarrow 3t = 6\\\\\rightarrow\frac{3t = 6 }{3}\\\\\rightarrow \boxed{t = 2}\)
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. How much does a taco cost?
Answer:
The price for a small glass of milk is $0.95, and the price for a breakfast taco is $1.15.
Step-by-step explanation:
Let the price of a taco be x and the price for a small glass of milk be y.
\(x + y = 2.1\)
\(2x + 3y = 5.15\)
Multiply the first equation by 2:
\(2x + 2y = 4.2\)
Subtract the new third equation from the second equation:
\((2x + 3y) - (2x + 2y) = 5.15 - 4.2\)
\(y = 0.95\)
Hence, the price for a small glass of milk is $0.95.
Substitute y into the first equation.
\(x + 0.95 = 2.1\)
\(x = 1.15\)
Therefore, the price for a breakfast taco is $1.15.
Hope this helped!
Answer:
2t + 3m = 5.15
Step-by-step explanation:
Since the problem tells us that the cost of a breakfast taco and a small glass of milk is $2.10, we can write the equation
t + m = 2.10
Since the cost of two tacos and 3 small glasses of milk is $5.15, we can write the equation
2t + 3m = 5.15
Hope this helps. :)
(-7²)×(-2²) is equal to :
(a) 14
(b) -14
(c) 196
(d) -196
Answer:
C
Step-by-step explanation:
-7 x7 = - 49
-2x2= - 4
-49x-4 = 196
Answer and Step-by-step explanation:
(-7²)×(-2²)
49 times 4
(a negative number squared becomes a positive number.
-7 squared is the same thing as -7 times -7, which is 49.
-2 squared is the same thing as -2 times -2, which is 4.
C. 196 is the answer.
3
49
x 4
_____
196
(40 times 4, + 4 times 9)
( 160 + 36 = 196)
#teamtrees #WAP (Water And Plant)
A golf club manufacturer measures the impact elasticity of a new material. This is done by randomly selecting a driver head made from the new material, firing a golf ball at it from an air cannon (under carefully controlled conditions), and making certain measurements of the ball's motion. These measurements are used to calculate a number called the coefficient of restitution of the driver head. Engineers use this procedure 30 times. The sample mean coefficient of restitution is 0.835. Calculate a 99% confidence interval for the true mean coefficient of restitution, assuming the population standard deviation of such coefficients is 0.019. Round your answers to the fourth decimal digit.
The confidence interval for the true mean coefficient of restitution is (29.9911,30.0089).
Given sample mean coefficient of restitution 0.835,population standard deviation of 0.019 and the confidence level of 0.835.
We have to find the confidence interval for the true mean coefficient of restitution.
We can easily find the confidence interval through the formula of margin of error.
Margin of error is the difference between the calculated values and the real values.
Margin of error=z*σ/\(\sqrt{n}\)
where z is the z value of p value,
σ is population mean or sample mean,
n is the sample size.
In our problem the sample size is 30.
z value for the p value of 0.99 is 2.576.
Margin of error=2.576*0.019/\(\sqrt{30}\)
=0.048944/5.4772
=0.0089
Upper level=mean +margin of error
=30+0.0089
=30.0089
Lower level=Mean-margin of error
=30-0.0089
=29.9911.
Hence the confidence interval for the true mean coefficient of restitution is (29.9911,30.0089).
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You hear on the news that over the next 5 years the inflation rate will skyrocket to 12% if today a new blu-ray movie costs $19.99 assuming continuous compounding how much will the same disk cost in 5 years?
The Blu-ray movie will cost approximately $36.42 in 5 years with an inflation rate of 12% and continuous compounding.
To calculate the future cost of the Blu-ray movie in 5 years with an inflation rate of 12% and continuous compounding, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = Future value
P = Present value
e = Euler's number (approximately 2.71828)
r = Annual interest rate (in decimal form)
t = Time period in years
In this case, the present value (P) is $19.99, the inflation rate (r) is 12% or 0.12, and the time period (t) is 5 years. Substituting these values into the formula, we get:
A = 19.99 * e^(0.12 * 5)
Calculating the exponent first:
0.12 * 5 = 0.6
Then:
e^0.6 ≈ 1.82212
Finally:
A = 19.99 * 1.82212 ≈ 36.42
Using the formula for continuous compound interest, we calculated that a Blu-ray movie that costs $19.99 today will cost approximately $36.42 in 5 years, assuming an inflation rate of 12% and continuous compounding.
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Solve this system of linear equations. Separate
the x- and y-values with a comma.
-4x + 2y = 12
- 13x + 3y = 46
12x+24 is equivalent to 4(3x+6) because...
Answer:
you use disputation
Step-by-step explanation:
4 times 3x = 12x
4 times 6 = 24
In 1994, an outbreak of illness due to ice cream contaminated with the bacteria salmonella occurred in the United States. The outbreak affected an estimated 224,000 people. If the total population in the U.S. at that time was 260,000,000, which is the best estimate for the percentage of people who were affected?
According to the question, the best estimate for the percentage of people who were affected by the outbreak is approximately 0.086%.
To estimate the percentage of people affected by the outbreak, we can use the following formula:
\(\[\text{Percentage} = \left(\frac{\text{Affected}}{\text{Total population}}\right) \times 100\]\)
Given that the number of affected people is 224,000 and the total population is 260,000,000, we can substitute these values into the formula:
\(\[\text{Percentage} = \left(\frac{224,000}{260,000,000}\right) \times 100\]\)
Calculating this expression, we find:
\(\[\text{Percentage} \approx 0.086 \%\]\)
Therefore, the best estimate for the percentage of people who were affected by the outbreak is approximately 0.086%.
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Given the function y=-\frac{3\sqrt{x^5}}{4},y=− 4 3 x 5 , find \frac{dy}{dx}. dx dy . Express your answer in radical form without using negative exponents, simplifying all fractions.
Given:
The function is:
\(y=-\dfrac{3\sqrt{x^5}}{4}\)
To find:
The value of \(\dfrac{dy}{dx}\).
Solution:
We have,
\(y=-\dfrac{3\sqrt{x^5}}{4}\)
It can be written as
\(y=-\dfrac{3}{4}x^{\frac{5}{2}}\) \([\because \sqrt[n]x=x^\frac{1}{n}]\)
Differentiate with respect to x.
\(\dfrac{dy}{dx}=-\dfrac{3}{4}\times \dfrac{5}{2}x^{\frac{5}{2}-1}\) \([\because \dfrac{d}{dx}x^n=nx^{n-1}]\)
\(\dfrac{dy}{dx}=-\dfrac{15}{8}x^{\frac{5-2}{2}}\)
\(\dfrac{dy}{dx}=-\dfrac{15}{8}x^{\frac{3}{2}}\)
\(\dfrac{dy}{dx}=-\dfrac{15}{8}\sqrt{x^3}\)
Therefore, the value of \(\dfrac{dy}{dx}\) is \(-\dfrac{15}{8}\sqrt{x^3}\).
Volume of a pentagonal prism is 360 inches cubed. The height of prism is 3 inches. What is the area of the pentagon base?
The pentagonal prism with volume 360 in³ and height of 3 inches have a base area of 120 in²
What is a pentagonal prism?A pentagonal prism is a prism that has two pentagonal bases like top and bottom and five rectangular sides.
Given that, the volume of a pentagonal prism is 360 in³, with a height of 3 inches,
We need to find the area of the base,
We know that, the volume of a pentagonal prism is =
V = 1/4 √(5(5+2√5)·a²h
Where a is the base edge and h is the height,
360 = 1/4·3 √(5(5+2√5)·a²
1/4·√(5(5+2√5)·a² = 120
Since, the base of a pentagonal prism is a pentagon, and the area of a pentagon = 1/4 √(5(5+2√5)·a²
And we have,
1/4 √(5(5+2√5)·a² = 120
Therefore, the base area is 120 in²
Hence, the pentagonal prism with volume 360 in³ and height of 3 inches have a base area of 120 in²
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Research has shown that IQ scores have been increasing for years (Flynn, 1984, 1999). The phenomenon is called the Flynn effect and the data indicate that the increase appears to average about 7 points per decade. To examine this effect, a researcher obtains an IQ test with instructions for scoring from 10 years ago and plans to administers the test to a sample of n = 25 of today’s high school students. Ten years ago, the scores on this IQ test produced a standardized distribution with a mean of μ = 100 and a standard deviation σ = 15. If there actually has been a 7-point increase in the average IQ during the past 10 years, then find the power of the hypothesis test for each of the following.
a. The researcher uses a two-tailed hypothesis test with α = .05 to determine if the data indicate a significant change in IQ over the past 10 years.
b. The researcher uses a one-tailed hypothesis test with α = .05 to determine if the data indicate a significant increase in IQ over the past 10 years.
A. The power of the two-tailed hypothesis test with α = .05 is 0.53.
B. The power of the one-tailed hypothesis test with α = .05 is 0.95.
What is hypothesis test?A hypothesis test is used to make decisions about a population based on sample data. It involves specifying a null hypothesis, collecting data, and then assessing the data to either reject or accept the null hypothesis.
A. The power of the two-tailed hypothesis test is calculated using the formula:
Power=
1- β=1- (1-α)\(^{1/2}\)
=1- (1-0.05)\(^{1/2}\)
=0.525
=0.53
This means that the researcher has an 53% chance of correctly rejecting the null hypothesis that there has been no change in the IQ over the past 10 years.
B. The power of the one-tailed hypothesis test is calculated using the formula:
Power=
1- β=1- α
=1- 0.05
= 0.95
This means that the researcher has a 95% chance of correctly rejecting the null hypothesis that there has been no increase in the IQ over the past 10 years.
This is a higher power than the two-tailed test because the one-tailed test focuses on detecting an increase in the IQ, while the two-tailed test can detect both an increase or decrease in the IQ.
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What is the value of x in the figure below?
Answer:
I blieve that X would be 9 , good luck ^^
25 POINTS!!! Please help with 12 and 13
Answer:
um
Step-by-step explanation:
When a sprinkler is installed in the ground, the spray of water goes up and falls in the pattern of a parabola. The height, in inches, of a spray of water is given by the equation ℎ()=160−162 where is the number of feet away from the sprinkler head the spray is. What is the height of the spray 2 feet away from the sprinkler head?
Answer:
96feet
Step-by-step explanation:
Given the height, in inches, of a spray of water is given by the equation ℎ(x)=160−16x^2
x is the number of feet away from the sprinkler head the spray
To get the height of the spray 2 feet away from the sprinkler head, we will simply substitute x =2 into the function and et the height h as shown;
From the equation
ℎ(x)=160−16x^2
h(2) = 160-16(2)²
h(2) = 160-16(4)
h(2) = 160-64
h(2) = 96feet
Hence the height will be 96feet if the spray is 2feet away from the sprinklers head
22.204 divided by 5,2
Answer: 4.27
Step-by-step explanation: I used a calculator.
Write an equation in standard form of a line that goes through these two points (3, 4) and (5, -5). Please help and explain it because I want to learn how to do this.
Answer:
first find the slope
finding slope
y2-y1/x2-x1
-5-4/5-3
-9/2
then the slope is -9/2 or -4.5
then y=mx+b
y=-4.5x+b
then replace y=-4.5x+b
replace y by 4 and x by 3
4=-4.5times 3 +b
4=-13.5+b
b=17.5
then the equation is y=4.5x+17.5
if you have any question ask me thank you
The price of televisions has dropped dramatically over the last three years. Three years ago a 32 inch television was $500. This year the tv was on sale for $199. What is the percent change?
A percentage is a way to describe a part of a whole. The percentage change in the price of the TV will be 60.2%.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
As it is mentioned that the price of the tv 3 years ago was $500, while the current price of the tv is $199. Therefore, the percentage change in the price of the tv can be written as,
\(\rm Percentage\ change = \dfrac{\text{Initial value - Final value}}{Initial\ value} \times 100\%\)
\(\rm Percentage\ change = \dfrac{\$500-\$199}{\$500} \times 100= 60.2\%\)
Hence, the percentage change in the price of the TV will be 60.2%.
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Find how many years it takes for money to quadruple when invested at an annual interest rate of 1.8% compounded continuously.
Answer:
It takes 38.5 years for money to quadruple when invested at an annual interest rate of 1.8% compounded continuously.
What ms the answer plss
Write a function P(x) that can be used to determine the profit for sales of x fixtures.The profit is the difference between the revenue function, R(x), and the cost function, C(x), shownR(x) = 252C(x) = 1500 + 1035x + 1500O 15x + 1500O 15x - 15000 -15x - 1500
P(X)= R(X) - C(X)
Substituing the functions on the P(X) functions:
P(X)=25x-(1500+10x)
P(X)=25x-1500-10x
Solving:
P(x)=15x-1500, The answer would be the third option!
Under what order of operations are the set of interger closed
Answer: The set of integers is closed for addition, subtraction, and multiplication but not for division.
Suppose the average battery life is 10 hours. (i) [5 pts]. find the probability that the iphone will not die before t hours. this probability is often called the reliability of the device.
The probability that the iPhone will not die before t hours, given an average battery life of 10 hours, can be calculated using the exponential distribution. The reliability of the device is equal to the probability of surviving beyond t hours, which is given by the equation \(\[P(T > t) = e^{-\lambda t}\]\), where \(\(\lambda\)\) is the rate parameter. In this case, since the average battery life is 10 hours, \(\(\lambda = \frac{1}{10}\)\). Therefore, the probability of reliability is \(\[P(T > t) = e^{-\frac{t}{10}}\]\).
To find the probability of reliability, we use the exponential distribution formula. The exponential distribution is commonly used to model the time until an event occurs, such as the battery dying in this case. The rate parameter, \(\(\lambda\)\), is the reciprocal of the average time until the event occurs.
In this scenario, the average battery life is given as 10 hours. Therefore, the rate parameter \(\(\lambda\)\) is \(\(\frac{1}{10}\)\). The probability that the iPhone will not die before t hours is calculated by finding the complement of the probability that it will die before t hours.
The complement of the event "the iPhone will die before t hours" is "the iPhone will survive beyond t hours." This is represented as \(\(P(T > t)\)\), where T is the time until the battery dies.
Substituting the value of \(\(\lambda\)\) into the exponential distribution formula, we get \(\(P(T > t) = e^{-\frac{t}{10}}\)\). This equation gives us the probability that the iPhone will not die before t hours, which is the reliability of the device.
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X/19 = 4
what is x please help i don`t under stand this equation
p.s. xover 19 =4
Is ozone harmful to health?
Ozone can be both harmful and beneficial to health, depending on its location in the atmosphere and the levels at which it is present.
In the stratosphere (the layer of the atmosphere that is located about 10-50 kilometers above the Earth's surface), ozone is a beneficial gas that protects life on Earth by absorbing harmful ultraviolet (UV) radiation from the sun. However, at ground level, ozone can be harmful to health, particularly for people with respiratory problems such as asthma.
Exposure to high levels of ozone can irritate the respiratory system and cause coughing, throat irritation, and chest pain. It can also worsen bronchitis, emphysema, and other lung diseases. Ozone can also reduce lung function and inflame the linings of the lungs, leading to more serious health problems.
It is important to note that ground-level ozone is not emitted directly into the air, but is formed when pollutants from sources such as vehicle exhaust, power plants, and industrial facilities react with sunlight and heat.
Therefore, Ozone can be both harmful and beneficial to health.
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Find the area of the trapezoid
3cm, 3cm, 8cm
The area of the trapezoid is the amount of space on it, and the value of the area is 16.5 square cm
How to determine the area?The given parameters are:
Parallel sides = 3cm and 8 cm
Height = 3cm
The area is then calculated using:
Area = 0.5 * (Sum of parallel sides) * Height
So, we have:
Area = 0.5 * (3 + 8) * 3
Evaluate
Area = 16.5
Hence, the area of the trapezoid is 16.5 square cm
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Jason eats 10 ounces of candy in 5 days. How many pounds does he eat per day? (Recall: 16 ounces = 1 pound) Do not include units (pounds per day) in your answer.
Answer:
Jason eats 1/8=0.125 pounds of candy per day and it will take him 8 days to eat 1 pund of candy Hope Im not wrong
Step-by-step explanation:
Given the scatter plot, choose the function that best fits the data.
f(x) = 2^x
f(x) = 2x
f(x) = −2x
f(x) = 2x^2
The given scatter plot depicts the exponential function. Therefore, option 1 f(x) = 2ˣ is the correct one.
A scatter plot is a particular kind of graphic diagram that uses Cartesian coordinates to show the values of two variables for a collection of data.
We write y as the function of x as y=f(x). Here, f is considered the name of the function and x is the value of the function. To check which function depicts the given scatter plot, we have to substitute the values for x and find the function. Then, plot the graph.
By doing we get, the plot for f(x) = 2ˣ is equivalent to the given scatter plot. Because this graph depicts the exponential function where the graph passes through the point (0,1). Therefore, option 1 correctly depicts the given plot. Option 2 depicts the identity function and 4 depicts squaring or quadratic function.
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If the tax rate is 8.3% what is the tax on 196.44