1)r = 18.2
2) Square root of 56 = 7.48
3)Square of -4.7 = 22.09
4) Square of 7.6 = 57.76
5) -tz = l/r
6) r = -2/5
Factoring
To include something when you are doing a calculation, or when you are trying to understand something: People are earning more, but when inflation is factored in, they are no better off.
1) r=6r-91 (Factoring)
r-6r = - 91
-5r = -91
r = 91/5
r = 18.2
Square Root
Square root, in mathematics, a factor of a number that, when multiplied by itself, gives the original number. For example, both 3 and –3 are square roots of 9.
2) -2r" -146 = -34 (Square Roots}
- 2r’’ = -34 + 146
- 2r’’ = 112
-r’’ = 112/2
-r’’= 56
r’’ = - 56
Square root of 56 = 7.48
3) r-14r-53 = 9 (Completing the Square)
- 13r = 9+53
- 13r = 62
- r = 62/13
r = - 4.7
Square of -4.7 = 22.09
4) 3r*+6r-62 =7 (Completing the Square)
9r = 7+62
r = 69/9
r = 7.6
Square of 7.6 = 57.76
5) -rtZr=l (Quadratic Formula)
- r(tz) = l
- tz = l/r
6) 5r =-2 (Quadratic Formula)
r = -2/5
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a wodden plnk 15
[tex] \sqrt{3} [/tex]
m long rests on a wall in such a way that it mskes an angel with ground at 15m away from the foot of the wall. find the angle made by the plank with the ground
Step-by-step explanation:
when you look at that right-angled triangle that is created by the plank as Hypotenuse (the side opposite of the 90° angle), and the distance on the ground from the wall and the height on the wall (from ground to the plank) as the legs, we know that the Hypotenuse (the plank) is the radius of the trigonometric circle we can draw there, and the 15 m ground distance from the wall is
cos(our angle) × radius
15×sqrt(3) × cos(our angle) = 15
cos(our angle) = 1/ sqrt(3) = 0.577350269...
our angle = 54.73561032...°
How do you solve 2^x=4.5?
The solution of the given equation is:
[tex]\frac{log 9}{Log 2} - 1[/tex] = 2.16992500144
Logarithm:
Logarithm, an exponent or power that must be raised to obtain a particular number. Mathematically, if bx = n then x = logb n then x is the logarithm of n to base b. Example: 23 = 8; so 3 is the base 2 logarithm of 8, or 3 = log2 8. Similarly, 2 = log10 100 because 102 = 100. The latter kind of logarithm (that is, the base 10 logarithm) is called the ordinary logarithm or the Briggs logarithm and simply write log n.
Invented in the 17th century to speed up calculations, logarithms greatly reduced the time required to multiply large numbers. These were the basis of numerical computation for over 300 years until the mechanical calculator of the late 19th century and his 20th century computer sophistication made it obsolete for large-scale calculations. However, the natural logarithm (with base e ≅ 2.71828 and written ln n) continues to be one of the most useful functions in mathematics, being applied to mathematical models in the physical and biological sciences.
According to the question:
2ˣ=4.5
Take the logarithm of both sides of the equation
log2ˣ = log9 / 2
x . log2 = log9 − log2
divide both sides of the equation by log 2:
[tex]\frac{x Log 2}{Log 2} = \frac{Log 9 - Log 2}{Log 2}[/tex]
⇒ x = [tex]\frac{log 9}{Log 2} - 1[/tex]
⇒ x = 2.16992500144.
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At the beginning of the year, the number of books owned by a library was 10,000. Since then, it has grown by 1% each month.
Which expressions represent the number of books, in thousands, owned by the library 5 years later if it continues to grow at that rate?
A) 10x ((1+0.01)^12)^5
B) 10x(1+0.01^12) ^60
C) 10x (1.01)^5
D) 10x(1.01)^60
E) 10x (0.01)^60
.
Grocery Store A is selling bananas for $0.75 for 12 pound. Grocery Store B is selling 5 pounds of bananas for $3.75. Which store is offering the best unit rate?
Store B is offering the best unit rate for bananas.
What is Rate?
A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.
When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.
Grocery Store A is selling bananas for $0.75 for 12 pounds.
The unit rate will be = 0.75/12 = 0.06
Grocery Store B is selling 5 pounds of bananas for $3.75.
The unit rate will be = 3.75/5 = 0.75
Hence, Store B is offering the best unit rate for bananas.
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the edison electric institute has published figures on the number of kilowatt hours used annually by various home appliances. it is claimed that a vacuum cleaner uses an average of $46$ kilowatt hours per year. if a random sample of $12$ homes included in a planned study indicates that vacuum cleaners use an average of $42$ kilowatt hours per year with a standard deviation of $11.9$ kilowatt hours, do these data suggest that at the $0.05$ significance level the mean annual usage of vacuum cleaners is less than $46$ kilowatt hours? assume the population distribution of usage in kilowatt hours to be normal.
The test statistic is less than - 1.796
Hypothesisi test
H0: μ = 46
Ha: μ < 46
This is a lower tailed test
mean = 42
standard deviation = 11.9
sample size n = 12
The level of significance α = 0.05
degree of freedom df = n - 1 = 12 - 1 = 11
Test statistic = (x - mean)/(standard deviation / √n) = (42 - 46)/(11.9 / √12) = - 1.164
Test statistic = - 1.164
Using t- table, we can observe that the p - value is between 0.10 and 0.15
Using excel we find p - value = P(t < - 1.796)
p value = 0.1344
H0: μ < 46, rejection rule is
Reject H0 if test statistic < - 1. 796
Therefore, we reject the hypothesis as the test statistic is less than - 1.796
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Question 9 Which of the following distributions has a mean that varies? I. The population distribution II. The distribution of sample data III. The sampling distribution of the sample mean
O ll only
O IIl only
O I only
O all three distributions
O II and III
II and III only distributions has a mean that varies
The mean of a distribution is a measure of the central tendency of the data, and it can vary depending on the sample being analyzed.
For the population distribution, the mean is a fixed value that is calculated using all of the data in the population. The mean of the population distribution does not vary.
For the distribution of sample data, the mean is calculated using the data in the sample. If you take different samples from the same population, the mean of each sample will be different, so the mean of the distribution of sample data varies.
For the sampling distribution of the sample mean, the mean is calculated using the means of multiple samples. The mean of the sampling distribution is known as the population mean. As with the distribution of sample data, the mean of the sampling distribution varies depending on the samples that are used to calculate it.
Therefore, the mean of the distribution of sample data and the sampling distribution of the sample mean both vary, while the mean of the population distribution does not vary.
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g a data analyst is working with the world happiness data in tableau. what tool do they use to select the area on the map representing finland? 1 point radial rectangular lasso pan
You can select numerous impressions with the Tableau Lasso Selection tool by tracing a freehand shape around them.
How do they choose the region on the map that Tableau uses to represent Finland? You can select numerous impressions with the Tableau Lasso Selection tool by tracing a freehand shape around them.To display only the nations with a World Happiness score of 3.5 or lower, utilize the Filter tool.By tracing a freehand form around several marks with the Lasso tool, you can choose a group of them.When you wish to include only some marks and eliminate others around them, this tool is helpful.Based on the common values, Tableau creates the view of blended data.For instance, Tableau will match data on "Purple" from the main and "Purple" from the secondary if Color is the linking field in both data sources.To learn more about Lasso Selection refer
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Which of the following is not a similarity criterion for two triangles ASA SAS SSS ASA?
(D) ASA is not a similarity criterion for two triangles.
What is the similarity criterion for two triangles?If two triangles fit one of the following descriptions, they are similar: Angles in two pairs that are corresponding are equal.
The ratio of three sets of corresponding sides is three.
The comparable angles between two pairs of corresponding sides are equal and proportional.
You can use three triangle-specific theorems to quickly distinguish similar triangles.
There are three theorems that can be used to determine whether two triangles are similar: Angle - Angle (AA), Side - Angle - Side (SAS), and Side - Side - Side (SSS).
The triangles' potential similarity criteria are Angle-Angle-Angle (AAA), Side-Angle-Side (SAS), and Side-Side-Side (SSS).
Angle-side-angle (ASA) is thus a choice from the available possibilities to check the congruence of the triangle rather than its similarity.
Therefore, (D) ASA is not a similarity criterion for two triangles.
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Correct question:
Which of the following is not a similarity criterion for two triangles
(A) ASA
(B) SAS
(C) SSS
(D) ASA?
Marcos volunteered for a total of 40.2 hours. If he volunteered 0.6 for hours each day, for how many days did he volunteer
Answer:
67 days
Step-by-step explanation:
40.2/0.6 = 67
Answer: 67 days
Which equation has the same solution as 4-2(x-5)=x-19
(A) 2(x+5)= -8.
(B) 3(x-3)=9
(C) x+2=2x-3
(D) 3x-4=2x+7
Answer:
3x-4=2x+7 thus: (D)
x = 11
Step-by-step explanation:
Solve for x:
3 x - 4 = 2 x + 7
Subtract 2 x from both sides:
(3 x - 2 x) - 4 = (2 x - 2 x) + 7
3 x - 2 x = x:
x - 4 = (2 x - 2 x) + 7
2 x - 2 x = 0:
x - 4 = 7
Add 4 to both sides:
x + (4 - 4) = 4 + 7
4 - 4 = 0:
x = 7 + 4
7 + 4 = 11:
Answer: x = 11
___________________________
Solve for x:
4 - 2 (x - 5) = x - 19
-2 (x - 5) = -2 x + 10:
(-2 x + 10) + 4 = x - 19
Add like terms. 4 + 10 = 14:
-2 x + 14 = x - 19
Subtract x from both sides:
(-2 x - x) + 14 = (x - x) - 19
-2 x - x = -3 x:
-3 x + 14 = (x - x) - 19
x - x = 0:
-3 x + 14 = -19
Subtract 14 from both sides:
(14 - 14) - 3 x = -14 - 19
14 - 14 = 0:
-3 x = -14 - 19
-14 - 19 = -33:
-3 x = -33
Divide both sides of -3 x = -33 by -3:
(-3 x)/(-3) = (-33)/(-3)
(-3)/(-3) = 1:
x = (-33)/(-3)
The gcd of -33 and -3 is -3, so (-33)/(-3) = (-3×11)/(-3×1) = (-3)/(-3)×11 = 11:
Answer: x = 11
Answer:3x-4=2x+7
Step-by-step explanation:
first, 4-2x+10=x-19
14+19 =x+2x
33=3x
x=11
A. 2x+10=8
2x= -18
x=-9
B. 3x-9=9
3x=18
x=6
C. x+2=2x-3
3x = 5
x = 5/3
D. 3x-4 = 2x+7
3x-2x=7+4
x=11
the cruising speed of the bullet train will be in excess of 150 miles per hour. use s to represent the train's cruising speed (in miles per hour).
The necessary phrase will be s≥150 because the bullet train's cruising speed will be greater than 150 mph.
What is 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. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases. A group of numbers that have been written together using the arithmetic operations addition, subtraction, multiplication, and division is known as a numerical expression in mathematics. The number can be stated in a variety of ways, including verbally and numerically.
Here,
No less than" means "greater than or equal to" (≥).
So you want s to be greater than or equal to 150 mph.
s≥150
The required expression will be s≥150 as the cruising speed of the bullet train will be in excess of 150 miles per hour.
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What is 2 divided by 3? Explain the steps pleas.
The value of 2 divided by 3 is 0.67
How to evaluate the quotient expression?From the question, we have the following parameters that can be used in our computation:
2 divided by 3
To start with, we need to represent the expression properly as a quotient
So, we have the following representation
2 divided by 3 = 2/3
Evaluate the quotient expression using a calculator
This gives
2 divided by 3 = 0.67
Hence, the solution to 2 divided by 3 is 0.67
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8) if 2 to the power (x + 2) = k, what is the value of x in terms of k ?
and how
if (x+2)² = k , making x the subject is x = √k - 2
What is subject of formula?The subject of a formula is the variable that is being worked out. It can be recognised as the letter on its own on one side of the equals sign.
For example, if V = πr²h and we want to make r the subject of the formula, we make r in place of V.
Therefore r² = V/πh
r = √ (V/πh)
Similarly
(x+2)² = k
when we square root both sides
x+2 = √k
Collecting like terms
x = √k - 2
therefore making x the subject in the formula (x+2)² = k in terms of k is x = √k - 2
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At what annual percent rate would you need to invest $12,000 and make $2,880 in interest after 8 years?
PLEASE HELP ME WITH THESE 2 QUESTIONS
y=-2/7x-7 in standard form
Answer:
Write in standard form.
2x+7y=−49
Step-by-step explanation:
Part A what is the equation that can be used to solve for x
Part b what is the value of x
lost-time accidents occur in a company at a mean rate of 0.3 per day. what is the probability that the number of lost-time accidents occurring over a period of 7 days will be exactly 3? assume poisson situation. p(x
The probability that the number of lost-time accidents occurring over a period of 7 days will be exactly 3 is 0.7295
Binomial Distribution
The binomial distribution is the sum of a series of multiple independent and identically distributed Bernoulli trials. In a Bernoulli trial, the experiment is said to be random and can only have two possible outcomes- success or failure.
In a binomial distribution the probability of getting success must remain the same for the trials we are investigating. For example, when tossing a coin, the probability of flipping a coin is ½ or 0.5 for every trial we conduct, since there are only two possible outcomes.
Mean rate of lost time accident = 0.3 per day
probability that the number of lost-time accidents occurring over a period of 7 days will be no more than 3.
n = 7
Using binomial distribution formula :
P(x ≤3)
Probability of success (p) = 0.3
1 - p = 1- 0.3 = 0.7
nCx * p^x * (1 - p)^(n-x)
Using the binomial probability distribution calculator to save computation time :
P(x ≤3) = P(x = 0) + p(x = 1) + p(x = 2) + p(x = 3)
P(x ≤3) = 0.0403 + 0.1556 + 0.2668 + 0.2668
P(x ≤3) = 0.7295
0.7295
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On a recent survey, students were asked if they like to fly and if they can drive. The partial results are given in the relative frequency table.
Complete the relative frequency table, showing all necessary calculations.
By using the tabular data given , the complete relative frequency table has been shown below
What is tabular data?
Data given in the form of rows and columns is known as tabular data.
The relative frequency table has been shown below
Frequency of students who like to like to fly and can drive = 0.32
Total frequency of students who like to fly = 0.70
Frequency of students who like to like to fly cannot drive = 0.70 - 0.32 = 0.38
Frequency of students who can drive = 0.45
Frequency of students who cannot drive = 0.55
Frequency of students who do not like to fly can drive = 0.45 - 0.32 = 0.13
Frequency of students who do not like to fly cannot drive = 0.55 - 0.38 = 0.17
Total frequency of students who do not like to fly = 0.13 + 0.17 = 0.30
The complete relative frequency table is
Can drive Cannot drive Row totals
Like to fly 0.32 0.38 0.70
Do not like to fly 0.13 0.17 0.30
Column totals 0.45 0.55 1
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There are 7 gloves in the lost & found box. There are 2 blue gloves, 3 green gloves,
1 black glove, and 1 brown glove. What fraction of the gloves are black?
Answer: 1/7
Step-by-step explanation:
There are total of 7 gloves
There is 1 black glove
So take 1 divided by 7
The Fraction is 1/7
a sample of 50 drills had a mean lifetime of 12.68 holes drilled when drilling a low-carbon steel. assume the population standard deviation is 6.83. what sample size (i.e., how many) would you need to have so that a 95% confidence interval will have a margin of error of 1.0?
Using the z-distribution, it is found that the 95% confidence interval for the mean lifetime of this type of drill, in holes drilled, is (10.4, 13.94).
We are given the standard deviation for the population, hence, the z-distribution is used. The parameters for the interval is:
Sample mean of [tex]x = 12.7[/tex]
Population standard deviation of [tex]\sigma = 6.37[/tex]
Sample size of .n = 50
The margin of error is:
[tex]M = z \frac{\sigma }{\sqrt{n} }[/tex]
In which z is the critical value.
We have to find the critical value, which is z with a p-value of [tex]\frac{1+\alpha }{2}[/tex] , in which [tex]\alpha[/tex] is the confidence level.
In this problem, , thus, z with a p-value of , which means that it is z = 1.96.
Then:
[tex]M= 1.96\frac{6.37}{\sqrt{50} } = 1.77[/tex]
The confidence interval is the sample mean plus/minutes the margin of error, hence:
x- M = 12.17 - 1.77 =10.4
x+M = 12.17 + 1.77 = 13.94
The 95% confidence interval for the mean lifetime of this type of drill, in holes drilled, is (10.4, 13.94).
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if we alternately flip a balanced coin and a coin that is loaded so that the probability of getting heads is 0.45, what are the mean and the standard deviation of the number of heads that we obtain in 10 flips of these coins?
Probability of getting head = 0.45
Probability of getting tail = 1- 0.45
= 0.55
No of flip flops = 10
8 men make 10 cars in a day. How many cars do 20 men complete in day?
Answer: 25 cars
Step-by-step explanation:
Take 10 divided by 8 = 1.25 car per men
Then take 1.25 times 20 = 25 cars
which logarithm bases can you use to solve for in the exponential equation ? (select all that apply.) log base x log base 25 log base 4 log base 10
The exponential equation may be solved using log base x and log base 10 logarithm bases. The right answer is D.
Finding the base of the logarithm that may be used to determine the value of x is necessary in order to solve an exponential equation with the form log base x (y) = z.
The equation log base x (y) = z applies here. Let's explore each possible logarithm base:
Log base x: The problem may be solved directly using this logarithm base. The value of x that the equation requires may be discovered using the logarithm base x.
Log base 25: The problem cannot be properly solved using this logarithm base. It does not work with the provided equation.
Log base 4: The equation cannot be properly solved using this logarithm base. It does not work with the provided equation.
Log base 10: The problem may be readily solved using this logarithm basis. To determine the value of x that the equation requires, use the logarithm base 10 function.
The logarithm bases that may be utilised to solve the exponential equation based on the provided parameters are log base x and log base 10.
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Which of the following are the factors of 6x²+5x-6 *?
Answer:There are no choices but i do this type of work on edge so i could proably do it without the choices.
Step-by-step explanation:Answer would be (3x-2)(2x+3)
3x times 2x would be 6x squared 3x times 3 is 9x -2 times 2x is -4x
9x-4x is 5x and -2 times 3 is -6
Hope this helps:)
HAPPY NEW YEARS
in adult men ages 18 years and older, we are interested in what happens to testosterone levels as the men age. in this experimental design which variable is the y variable? testosterone age gender male
In this experimental design, the y variable is the testosterone levels.
A variable is defined as any symbol or letter that is used to express an unknown quantity. There are two types of variables: the dependent variable (y variable) and the independent variable ( x variable).
An independent variable (x variable) is the variable which causes the change in another variable.
A dependent variable (y variable) is the result or effect of that change in the dependent variable.
If we are interested in what happens to testosterone levels as the men age in adult men ages 18 years and older, then the x variable is the age and the y variable is the testosterone levels.
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1.45×4
2.65x5
3.77x6
4.89x7
5.52x3
whats are the answers of theses equations
Answer:
1. 45*4 = 180
2. 65*5= 325
3. 77*6=462
4. 89*7= 623
5. 52*3= 156
Answer:
5.8
13.25
22.62
34.23
16.56
Step-by-step explanation:
using the points 0, 5 and -2, 2 make an equation in slope intercept form
Please help soon! Thank you!
Answer:
8
Step-by-step explanation:
x=-4 perfectly suits x<=-1 since -4<=-1
Hence, when calculating g(-4), you need to apply the expression -x+4
Hence:
g(-4)=
-x+4=
-(-4)+4= ==> plug in -4 for x
4 + 4 = 8 ==> Negating a negative number is equaled to taking the
positive number.
7x +y = 33
3x + y = 17
The value of x = 4
The value of y = 3
7x + y = 33 ......eq(1)
3x + y = 17 .....eq(2)
Here subtract eq(2) from eq(1), we get
4x = 16
therefore x = 16/4
x = 4.
Now to get the 'y' value, substitute the 'x' value in eq(2)...
3(4) +y = 17
y = 5
Therefore,
x = 4
y = 3
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