The solution is, the value of x = 5+ 8√2, 5- 8√2
What is simplification?Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
here, we have,
given that,
(x - 5)² +15=143
we know, (a-b)^2 = a^2 -2ab + b^2
so, we get,
x^2 - 10x + 25+15 = 143
or, x^2 -10x -103 = 0
now, solving we get,
x = 5+ 8√2, 5- 8√2
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find the volume v of the described solid s. a pyramid with height h and base an equilateral triangle with side a (a tetrahedron)
The volume of the solid is equal to one third of the area of the base times the height. Therefore, the volume of the tetrahedron is equal to [tex](1/3)*(a^2)*h[/tex].
The volume of a pyramid (or tetrahedron) is equal to one third of the area of the base times the height. Therefore, if we were given a pyramid with a base that is an equilateral triangle with side a and a height of h, then the volume of the solid can be calculated by using the formula [tex](1/3)*(a^2)*h[/tex]. This is because an equilateral triangle has sides of equal length and all of its angles are equal to 60°. Since the area of an equilateral triangle is equal to [tex](a^2)*√3/4[/tex], then the volume of the solid can be calculated by multiplying the area of the base by one third and then multiplying it by the height of the pyramid, which is [tex](1/3)*(a^2)*√3/4*h[/tex]. The final result is the volume of the solid, which is [tex](1/3)*(a^2)*h[/tex].
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A metallurgist has one alloy containing 22% copper and another containing 53% copper. How many pounds of each alloy must he use to make 51 pounds of a third alloy containing 30% copper? (Round to two decimal places if necessary.)
Answer:
37.8387 pounds of the 22% alloy copper and 13.1612 pounds of the 53% alloy copper must be used.
Step-by-step explanation:
Let x represent the amount of 22% copper needed.
Therefore, 51-x represents the amount of 53% copper needed.
Therefore, we can write
(22% * x) + (53% * (51-x)) = 30% * (51)
⇒0.22x + 0.53(51-x) = 0.3(51)
⇒ x = 37.8387
Thus, x =37.8387 and 51-x = 13.1612
The t distribution is similar to the z distribution in all BUT one of the following characteristics. Which one is it? Explain
a. Continuous
b. Symmetrical
c. Bell-shaped
d. t distribution's mean=0 and standard deviation=1
d.) T distribution's mean=0 and standard deviation=1 is not true. Instead, the t distribution has a mean of 0 and a standard deviation that varies based on the sample size and degrees of freedom
The t distribution is not similar to the z distribution in terms of its standard deviation. Unlike the standard normal distribution (z distribution), which has a mean of 0 and a standard deviation of 1, the t distribution has a mean of 0, but its standard deviation varies depending on the sample size. Specifically, the t distribution has heavier tails than the z distribution, which means it has more spread in the distribution and more extreme values are more likely to occur.
The t distribution's mean=0 and standard deviation=1 is not true, hence the proper response is d. The t distribution, on the other hand, has a mean of zero and a standard deviation that varies according to the sample size and degrees of freedom.
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Question 4 pts (Lesson 2.11: Covariance and Correlation ) Suppose that the correlation between December snowfall and temperature in Siberacuse NY is -0.5. Further suppose that Var(S) =100 in2 and Var(T) = 25 (degrees F)2 . Find Cov(S,T) (in units of degree inches, whatever those are): a. -25 0 b. - 0 c 0 d. 25
The answer is (a) -25. The covariance is negative, indicating that the December snowfall and temperature in Syracuse NY have an inverse relationship. Snowfall, in particular, tends to decrease as temperatures rise. Covariance units are the product of the units of the two variables, which in this case are in2 and (degrees F)2, so covariance units are degree inches.
We are given the following details:
Correlation coefficient between December snowfall and temperature in Syracuse, New York: -0.5
December snowfall variation (S): 100 in2
Temperature variation in December (T): 25 (degrees F)2
We are asked to calculate the correlation between December snowfall and temperature in degrees inches.
Cov(S,T) can be calculated using the covariance formula:
Corr(S,T) = Cov(S,T) * sqrt(Var(S)) * sqrt(Var(T))
Plugging in the values from the problem yields:
Cov(S,T) = (-0.5) * sqrt(100 in2) * sqrt(25 (degrees F)2) = (-0.5) * 10 in * 5 degrees F = -25 degree inches
As a result, the answer is (a) -25. The covariance is negative, indicating that the December snowfall and temperature in Syracuse NY have an inverse relationship.
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How to find the missing variable and /or the side length ?.please help this is geometry
The missing variables of the line transversal using similarity ratio are;
x = 10
MT = 14
UP = 23
How to find the proportion of similar sides?When two parallel lines crossed by a transversal, they formed same-side interior angles and their sum is equal to 180 degrees. As the sum of the same side interior angles is 180 degrees therefore the angles are supplementary.
Now, from the diagram, using the concept of similarity ratio, we can say that;
2/3 = (x + 2)/(x + 8)
Cross multiply to get;
2(x + 8) = 3(x + 2)
2x + 16 = 3x + 6
x = 10
Thus;
MT = (10 + 2) + 2
MT = 14
UP = (12 + 8) + 3
UP = 23
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there are 20 oranges in the basket.if Ayo picks two oranges how many is left
Answer: 18
Step-by-step explanation: 20 - 2 = 18
Priyas's cat Wright y
5 and 1/2 pounds and her dog weights 8 and 1/4 pounds
Their combineta weight id pounds
Answer:
13 3/4
Step-by-step explanation:
5+8 = 13
1/2 = 2/4
2/4+1/4 = 3/4
1
A red die is tossed and then a green. die is tossed.
What is the probability that the red die shows a
number larger than 4 or the green die shows a
number less than 2?
The two events are not mutually exclusive. So to find the
probability of the union, use:
P(A or B) = P(A) + P(B) - P(A and B)
[?]
P(A or B)
=
8
P(B)
Green die
What is the probability of the red die rolling a
P(A)
Red die
+
-
8)
P(B)
P(A)
Red die Green die
number greater than 4?
Enter your answer in simplest form.
Enter
On solving the provided question, we can say that the probability of the red die rolling is 16.67% probability = 0.1667
What is probability?A branch of mathematics called probability theory determines the chance that an event will occur or that a statement is true. A probability is a number between 0 and 1, where 1 denotes certainty and about 0 denotes how probable an event is to occur. The possibility or likelihood that a specific event will occur is expressed numerically as a probability. Probabilities can also be expressed as percentages from 0% to 100% or as numbers between 0 and 1. the proportion of occurrences among all equally likely alternatives that lead to a certain event relative to all possible outcomes.
red die, there are 3 numbers greater than 3 out of 6 numbers
Probability (A) = 3/6 = 1/2.
green die, there are 2 numbers less than 3 out of 6 numbers
Probability (B) = 2/6 = 1/3.
events are independent
P(A and B) = [tex]P(A)P(B) = 1/2 X 1/3 = 1/6 = 0.1667[/tex][tex]P(A)P(B) = 1/2 X 1/3 = 1/6 = 0.1667.[/tex]
16.67% probability = 0.1667
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Solve the following equation
Answer:
x=
Step-by-step explanation:
⅔x= 7x-1
2/3x=6
multiply both sides by 3/2
(3/2)(2/3x)= 6×3/2
x=
EASY POINTS!
Which is the BEST definition of the term mirror line?
A mirror line is the line over which an object in the coordinate plane is reflected.
A mirror line is a line in the plane that is units away from the y-axis.
A mirror line is another name for the line of translation.
A mirror line is always a diagonal line in the plane that divides it into eight sections.
The best definition of the term mirror line is "A mirror line is the line over which an object in the coordinate plane is reflected". So option A is correct.
What is mirror line ?A form or item is divided into two equal and symmetrical portions by a line of symmetry. Because it divides the figure symmetrically and the separated portions resemble mirror images of one another, we also refer to this line as the axis of symmetry or the mirror line.
Given options,
A. A mirror line is the line over which an object in the coordinate plane is reflected.
Yes this statement is according to definition of mirror line.
B. A mirror line is a line in the plane that is units away from the y-axis.
no its is not like that so it is incorrect option.
C. A mirror line is another name for the line of translation. no translation is a different concept so it also incorrect.
D. A mirror line is always a diagonal line in the plane that divides it into eight sections. it is also not correct.
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The graph on the right shows the remaining life expectancy, E, in years for females of age x.
Find the average rate of change between the ages of 50 and 60. Describe what the average rate of
change means in this situation.
The average rate of change of life expectancy between the ages of 50 and 60 is
(Type an integer or a decimal.)
The average rate of change of life expectancy between the ages of 50 and 60 will be 0.88.
What is the average rate change?It is the average amount by which the function varied per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph depicting the function.
Average rate = [f(x₂) - f(x₁)] / [x₂ - x₁]
The graph on the right shows the remaining life expectancy, E, in years for females of age x.
Then the average rate of change is given as,
Average rate = (32.8 - 24) / (60 - 50)
Average rate = 8.8 / 10
Average rate = 0.88
The average rate of change of life expectancy between the ages of 50 and 60 will be 0.88.
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Question 4(Multiple Choice Worth 2 points)
(Linear Functions MC)
Which statement best explains whether the data in the following table represents a linear or nonlinear function?
X y
-4 3
-1 1.5
01
4 -1
O The table represents a nonlinear function because the graph does not show a constant rate of change.
The table represents a linear function because the graph shows a constant rate of change.
O The table represents a nonlinear function because the graph shows a rate of change that is decreasing.
O The table represents a linear function because the graph shows a rate of change that is increasing.
Answer: B
Step-by-step explanation: The table represents a linear function because the graph shows a constant rate of change.
At 6.pm the temperature in phoenix is the same at the temperature in Tucson.By 9.pm the temperature in phoenix has dropped 2 degrees in Tucson it has dropped 4 degrees by 11.pm the temperature in phoenix has dropped another 3 degress represent each city temperature at 11 pm with an algebraic expression and bar model
Answer: 58 degrees
Step-by-step explanation:
construct a scatter plot for the data.label your y-axis in increments of 50
After the graph is labeled and titled, it is complete and ready to be used to represent the relationship between the two variables.
What is data?Data is the collection of data term that is organized and formatted in a specific way it's typically contains fact observation or statistics that are collected through a process of measurement or research data set can be used to answer question and help make informed decision they can be used in a variety of ways such as to identify trends on cover patterns and make prediction.
A scatter plot is used to represent the relationship between two variables using data points. In this case, the x-axis would represent the data points, while the y-axis would be labeled in increments of 50. To construct a scatter plot, one must first gather the data points and then plot them on a graph. The data points should be connected with a line or points to form the scatter plot.
To begin, the data points must be collected and organized. This can be done by organizing the data points in a table, using two columns to represent the x-axis and y-axis values. Once the data is organized, the x-axis and y-axis values can then be plotted on a graph. The y-axis should then be labeled in increments of 50. Once the data points are plotted, a line or points should be used to connect the data points, forming the scatter plot.
Finally, the scatter plot should be labeled and given a title, if applicable. The x-axis should be labeled with the data points, while the y-axis should be labeled in increments of 50. The title should provide a brief description of what the scatter plot is depicting. After the graph is labeled and titled, it is complete and ready to be used to represent the relationship between the two variables.
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Which of the following best describes the equation below? y = -5x^2 - 14 A. linear B. both linear and nonlinear C. neither linear nor nonlinear D. nonlinear
Answer:
D. Nonlinear
Step-by-step explanation:
y = -5x^2 - 14 is a parabola.
Linear lines are straight lines.
A parabola is not a straight line.
You flip a coin, spin the spinner, and flip a coin again. Find the probability of flipping heads, spinning an odd number, and then flipping tails.
The probability of flipping heads, spinning an odd number, and then flipping tails is 1/8.
How to find the probabilityThe probability of flipping heads, spinning an odd number, and then flipping tails is given by the product of the individual probabilities of each event.
The probability of flipping heads is 1/2,
the probability of spinning an odd number is 2/4 or 1/2, and
the probability of flipping tails is 1/2.
So, the probability of flipping heads, spinning an odd number, and then flipping tails is:
1/2 * 1/2 * 1/2 = 1/8
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select the expression that is equivalent to (x + 6)^2 A. x^2 + 12x^2 + 36 B x^2 + 12x + 36 C 2x + 12x + 12 D x^2 + 6x + 36
3x
x equals ur mom so udhdhddhehehrhrhrhrrruur mom is ur mome
The company president thought that type of music listened to (country vs. classical) could predict production line output. For one week the entire plant listened to country music, then for the next week the entire plant listened to classical music. He then compared the production line output between the country and classical music production line outputs.
(a) What type of research hypothesis is tested in this study?
associative RH
causal RH
(b) What type of design is being used in this study?
true experiment
non-experiment
(c) What type of design is being used in this study (mark all that apply)
cross-sectional design
within-group design
between subjects design
repeated measures design
longitudinal design
within-subjects design
between groups design
(d) Will the design used in this study provide an appropriate test of the research hypothesis?
Yes, this design can be used to test this research hypothesis
No, this design can not be used to test this research hypothesis
a) Type of research hypothesis is tested in this study is causal RH
b) Type of design is being used in this study is non-experiment
c) Type of design is being used in this study is within-subjects design
d) No, the design used in this study cannot provide an appropriate test of the research hypothesis.
(a) The research hypothesis being tested in this study is a causal hypothesis. The company president believes that the type of music listened to can predict production line output.
(b) The type of design being used in this study is a non-experiment. The researcher is not manipulating the type of music listened to; instead, the plant is naturally exposed to either country or classical music.
(c) The design being used in this study is within-subjects design, as the same group of individuals is exposed to both types of music. It is also a repeated measures design, as the same individuals are measured twice (once under country music and once under classical music).
(d) No, the design used in this study cannot provide an appropriate test of the research hypothesis. Since the researcher is not manipulating the type of music listened to, it is possible that other variables could be affecting the production line output, such as different environmental conditions on each week, or different levels of motivation.
Therefore, it is difficult to determine if any differences in production line output are actually due to the type of music listened to. A true experiment with random assignment of workers to the two music conditions would provide a better test of the research hypothesis.
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If 16 out of 20 vegetables are carrots, how many carrots vegetables will there be per 100 vegetables total?
Answer:
80
Step-by-step explanation:
16/20 —> 80/100
or
16/20 = 8/10 = 80%
Which equation will solve the following word problem? Sarah spends an average of $64.11 per week at the grocery store. She spent $53.22 last week, and $64.11 this week. How much did Sarah spend two weeks ago?
Sarah spend $161.24 before two weeks.
What is Average?In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.
Given:
Sarah spends an average of $64.11 per week.
She spent $53.22 last week, and $64.11 this week.
As, 1 month = 4.34524 weeks
So, before two weeks she spends
64.11 = (64.11 + 53.22 +x )/ 4.34524
278.5733364 = 117.33 + x
x= 161.24
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The ratio of fish to birds at a pet store is 8 to 3. Which combination of fish and birds could the pet store have?
A.
32 fish and 12 birds
B.
28 fish and 8 birds
C.
32 fish and 8 birds
D.
28 fish and 12 birds
Answer: A. 32 fish and 12 birds
Step-by-step explanation:
Since their greatest common factor is [tex]4[/tex], [tex]32\div 4= 8[/tex] and [tex]12\div 4 =3[/tex]. This satisfies the ration [tex]8:3[/tex].
(a) Determine the ratio of the volume of a (right circular) cone to the volume of a cylinder with the same height and base radius:
First you will need to determine the equation of the line which rotates to generate the cone.)
(a) Ratio of the volume of a right circular cone to the volume of a cylinder with same height and base radius= 1/3
(b)Ratio of the volume of a paraboloid to the volume of a cylinder= 1/2
(c)Ratio of the volume of a sphere and cylinder= 4/6
(a)Let r be the radius and h be the height of the right circular cylinder and right circular cone.
Volume of the right circular cylinder= πr²h
Volume of the right circular cone= 1/3 πr²h
Ratio of volume of a cone to the volume of a cylinder
= 1/3
Therefore, Ratio of the volume of a right circular cone to the volume of a cylinder with same height and base radius= 1/3
(b) Volume of the paraboloid = π/2r²h
Ratio of volume of a paraboloid to the ratio of volume of a cylinder
=1/2 πr²h/ πr²h
= 1/2
Therefore, Ratio of the volume of a paraboloid to the volume of a cylinder= 1/2
(c)Volume of a sphere= 4/3πr³
Given: Height of a cylinder h=2r (the diameter of the sphere)
Volume of a cylinder = 2πr³
Ratio of volume of a sphere to the volume of a cylinder
= 4/3πr³/ 2πr³
= 4/6
Therefore, Ratio of the volume of a sphere and cylinder= 4/6
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Complete question:
(a) Determine the ratio of the volume of a (right circular) cone to the volume of a cylinder with the same height and base radius:
First you will need to determine the equation of the line which rotates to generate the cone.)
b) Determine the ratio of the volume of a paraboloid (a parabola rotated about the y axis) to the volume of a cylinder with the same height and base radius:
(c) Archimedes was particularly pleased when he determined the ratio of the volumes of a sphere and cylinder. Determine the ratio of the volume of a sphere to the volume of a cylinder having the same radius, and having height the same as the diameter of the sphere:
what is the product of these bionomials? (x - 6)(x + 2) =
Answer:
Step-by-step explanation:
Multiply x*x, then X*2, then -6*2, lastly -6*x. So in other words multiply all of the factors. pay close attention to the + and - negative signs.
Answer: [tex]x^{2}[/tex]+2x-6x+2x
Simplify: [tex]x^{2}[/tex]-4x+2x
What kind of problem is "What number multiplied by the expression of 5 x 10^3 is equivalent to the expression 5 x 10^6?"
The problem is the multiplication with exponent or scientific notation kind of problem.
What is meant by Scientific Notation?Scientific notation is a way of writing a large number or small number with many digits in a simpler form using the power of 10.
For example, 30,000 can be written as 3 × 10⁴.
Here, the problem is defined as multiplying the expression 5 × 10³ with some number to get the expression 5 × 10⁶.
Let x be the number that is multiplied.
(5 × 10³) x = 5 × 10⁶
x = (5 × 10⁶) / (5 × 10³)
x = 10⁶ / 10³
x = 10⁶⁻³ = 10³
So here we are using the scientific notation to solve the whole problem and the answer itself is in the scientific notation.
Hence the given problem is a Multiplication of numbers in scientific notation kind of problem.
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The square root of a number will always have two outcomes One is positive and the other is negative.
true or false
The square root of zero is a counterexample of the statement, so it is false.
Is the statement true or false?Here we have the following statement about square roots:
"the square root of a number will always have two outcomes One is positive and the other is negative."
This seems to be true because:
-2*-2 = 2*2 = 4
So √4 = 2 and -2
But, particularly the square root of zero is:
√0 = 0
So here we have only one outcome that is neither positive nor negative, then the statement is false.
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Find the quotient. 2/5÷ 3 2/3 ?
Answer:
6/55
Step-by-step explanation:
2/5 ÷ 3 2/3
3 2/3 = 11/3
2/5 ÷ 11/3
= 2/5 x 3/11
= 6/55
So, the answer is 6/55
The sides of a triangle are 44, 73, and 86. Use the Pythagorean Theorem to determine
if the triangle is right, acute, or obtuse.
The triangle is
of the squares of the other two sides.
because the square of the largest side
Submit Answer
the sum
at
The triangle with sides 44, 73, and 86 is an obtuse triangle.
The Pythagorean Theorem states that the square of the length of the hypotenuse (the side opposite the right angle) in a right triangle is equal to the sum of the squares of the lengths of the other two sides, can be used to determine whether the triangle is right, acute, or obtuse.
In an acute triangle, the square of the hypotenuse length is less than the sum of the squares of the other two sides; in an obtuse triangle, the square of the hypotenuse length is greater than the sum of the squares of the other two sides.
Begin by calculating the square of each side:
[tex]44^2 = 1936[/tex]
[tex]73^2 = 5329[/tex]
[tex]86^2 = 7396[/tex]
Let us now see if the triangle fulfils the Pythagorean Theorem:
1936 + 5329 = 7265
We know the triangle is not obtuse because 7265 is less than 7396.
1936 + 7396 = 9332
We know the triangle is not acute because 9332 is greater than 5329.
5329 + 7396 = 12725
We know the triangle is obtuse because 12725 is greater than 7265 but less than 9332.
As a result, the triangle with sides 44, 73, and 86 is obtuse.
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The weight of 3 identical containers holding a total of 9 gallons of fertilizer is 70.8 pounds. The weight of 5 of the containers holding a total of 15 gallons of fertilizer is 118.0 pounds. Can you determine the weight of each container?
Answer:
Step-by-step explanation:
Let's call the weight of each container "w". We can set up two equations based on the information given:
Equation 1: 3w = 70.8 (the weight of 3 containers holding 9 gallons)
Equation 2: 5w = 118.0 (the weight of 5 containers holding 15 gallons)
To solve for "w", we can first solve Equation 1 for "w":
3w = 70.8
w = 70.8/3
w = 23.6
Now we can substitute this value of "w" into Equation 2 and solve for the total weight of 5 containers:
5w = 118.0
5(23.6) = 118.0
So each container weighs 23.6 pounds.
Which graph represents the equation y = −12 x + 3 ?
Graph 2
It is the graph with the line on the positive Y-Axis as the equation is ended with +3
Tyler gets his hair cut at the barber
shop once every 4 weeks. How many
trips will he make to the barber shop
in 2 years? You may use the table to
help, if needed. Note: There are
52 weeks in one year.
Answer:
he would go to the barber shop 21 times in 2 years
Step-by-step explanation:
divide 4 by 52 and then multiply by 2
Answer:
26
Step-by-step explanation:
52÷4 = 13 times a year
therefore, for two years
13 × 2 = 26