Answer:
Exact Form:
y = 31/6, −13/6
Decimal Form:
y = 5.16,−2.16
Mixed Number Form:
y = 5 1/6,−2 1/6
Evaluate.
7- 24 ÷ 8 × 4 + 6
Answer:
-35
Step-by-step explanation:
Question =7-24÷8×4+6
=7-192÷4+6
=7-49+6
=-41+6
=-35
Therefore,right answer is (-35)
PLEASE MARK ME AS THE BRAINIEST.
A teacher claims that the relationship between
number of hours studied for a test and test score can be
described by g(x) = 45 + 9x, where x represents the
number of hours studied. Graph this function
The graph representing the given function g(x) = 45 + 9x is as drawn in the attachment.
How to draw a Linear Equation Graph?
We are given the equation of line as;
g(x) = 45 + 9x
Where;
x represents the number of hours studied.
g(x) represents the test score
Thus, to plot this graph, we need to input some x values and find their corresponding g(x) values
At x = -10;
g(x) = 45 + 9(-10)
g(x) = -45
At x = -1;
g(x) = 45 + 9(-1)
g(x) = 35
At x = 0;
g(x) = 45 + 9(0)
g(x) = 45
At x = 1;
g(x) = 45 + 9(1)
g(x) = 54
At x = 2;
g(x) = 45 + 9(2)
g(x) = 63
At x = 3;
g(x) = 45 + 9(3)
g(x) = 72
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the desert temperature, h, oscillates daily between 40°f at 5am and 80°f at 5pm. write a possible formula for h, measured in hours from 5am, using the form h
The form of a periodic function is H(t) = 20cos(π/12(t+12))+ 60.
What do periodic functions mean?
A function that periodically returns to the same value. Despite the similarity in sound between periodic motion and oscillatory motion, not all periodic motions are oscillatory motion.
Since the values of H oscillates between two values, then the choices of the function are either sine or cosine. However, since the variable measures the time from 4 AM, and 4 AM represents the trough of the oscillation, then cosine is the more appropriate choice. Recall the form of a periodic function
y =A cos(B(x +C))+D
It is given that the peak of desert temperature is at 80F, and the lowest is 40F. Note that the distance between the two temperatures is
80F − 40F =40F
Since the amplitude is the distance from the middle line to either peak or trough, then it is half the distance from the trough to the peak. Hence
A = 40/2= 20
Notice that one full oscillation occurs after one day or 24 hours. Hence the period is
B =2π/24 = π/12
The graph of the cosine function begins at the peak, whereas the function needs to begin at the trough, since the variable t represents the number of hours after 4 AM. Thus, the graph must be shifted horizontally to the left one half-cycle, which is
C = 12
Since the original cosine function has the centerline at x= 0 the centerline of the function must be shifted by the number of units corresponding to the midway point of the peak and the trough. Hence
D= 80 + 40/2 = 120/2 = 60
ubstituting
A =20, B = π/12. C= 12 , and D= 60 into
The form of a periodic function
H(t) = 20cos(π/12(t+12))+ 60
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On the first day of class, a statistics professor asked her students to report their grade point averages (gpas) as part of a class survey. for those students who knew their gpas, the histogram was:______.
On the first day of class, a statistics professor asked her students to report their grade point averages (gpas) as part of a class survey. for those students who knew their gpas, the histogram was Left skewed.
The meaning of grade point averages?
You can determine your grade point average (GPA) by dividing the total number of high school credits you have earned by the total of all of your course grades. The majority of secondary and universities record grades on a 4.0 scale.What exactly does a 4.0 GPA mean?
High schools commonly report grade point averages (GPAs) on a 4.0 scale. A 4.0, or the highest grade, is awarded. You can get your total GPA by averaging your grades from all of your classes. This scale is regularly used in the majority of institutions and many secondary schools.Learn more about grade point averages
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Frankie plays 2/7 of a song on his guitar in 3/4 of a minute How long will it take him to play the entire song?
Answer:
1.25
Step-by-step explanation:
Mr McGee found that 6 students in his class have a sports practice today based on this result how many of the 300 students in the school have practice today
Answer: Number of students out of 300 who will attend sports class are 200.
Step-by-step explanation:
Let x be no. of students in 300 students who have sports practice;
Mr McGee found that 6 students out of 9 in his class have a sports practice today.
so according to ratio and proportions we have:
6/9=x/300
by cross multiplying 300 on left hand side we have ;
x=200 students
So
number of students out of 300 who will attend sports class are 200.
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Answer:
Step-by-step explanation: Based on the given condition, formulate :
multiply total students with 6
6×300 =1800
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Victor wants to learn to snowboard. He went to Snowy Ridge Mountain and rented a snowboard for $35, then took 5 hours of group snowboarding lessons. Victor paid $175 in all.
Which equation can you use to find how much Snowy Ridge charges, x, for each hour of group snowboarding lessons?
Answer: They charge $28 per lesson the Equation is 35 + 5x = $175
Step-by-step explanation: He rented the snowboard for $35 and then took 5 hours of snowboarding lessons. Then the whole thing cost $175.
PLEASE HELP ASAP!
:))
Answer: The converse of this theorem is also true; that is, if two lines n and m are cut by a transversal so that the alternate interior angles are congruent, then n║m.
Step-by-step explanation:
What does it mean converse in geometry?
The converse of a statement is formed by switching the hypothesis and the conclusion. The converse of "If two lines don't intersect, then they are parallel" is "If two lines are parallel, then they don't intersect." The converse of "if p, then q" is "if q, then p."
So, in the figure below, if we can choose n║m, then ∠1≅∠2
Since n║m , by the corresponding Angles Postulate,
∠1≅∠2.
Therefore, by the definition of congruent angles,
m∠1=m∠2
Since ∠1 and ∠2 form a linear pair, they are supplementary, so
m∠1+m∠2=180°.
Therefore, the converse of this theorem is also true; that is, if two lines n and m are cut by a transversal so that the alternate interior angles are congruent, then n║m.
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what fractions are equivalent to 4.05 with a bar notation over the 0 and 5
Answer:
Part 1) The fractions in the list are not equal to the decimal number indicated
Part 2) The fractions 401/99 and 802/198 are equal to the decimal number indicated.
Part 1)
we have the decimal number
4.05 -----> is a terminating decimal ( t's a decimal with a finite number of digits)
Convert to fraction number
Multiply and divide by 100
Simplify
Divide by 5 both numerator and denominator
therefore
The fractions in the list are not equal to the decimal number indicated.
Part 2) we have
4.050505... ------> is a repeating decimal (is a decimal that has a digit, or a block of digits, that repeat without ever ending)
Let
x=4.050505...
we have that
Multiply by 2 both numerator and denominator
therefore
The fractions 401/99 and 802/198 are equal to the decimal number indicated.
Step-by-step explanation:
Labels for gender where 1=female and 2=male is an example of using ______ scale.
Labels for gender where 1=female and 2=male is an example of using a nominal variable scale.
What is a nominal variable?A categorical variable (also known as a nominal variable) has two or more categories but no inherent ordering of the categories. Because the categories (woman, man, transgender, non-binary, etc.) cannot be ordered from high to low, gender is an example of a nominal variable. Medal winners are an example of an ordinal variable because the categories (gold, silver, bronze) can be ordered from most valuable to least valuable. A categorical variable is a variable in statistics that can take on one of a restricted, and usually fixed, a number of possible values, assigning each individual or other unit of inspection to a specific group or nominal category based on some qualitative property. For example, a nominal variable scale is used to label gender, with 1 representing female and 2 representing male.Therefore, labels for gender where 1=female and 2=male is an example of using a nominal variable scale.
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I am not understanding
Justin is evaluating the expression 12.53.8x, when x is 7.9.
12.5+3.847.9)
16.3(7.9)
128.77
What was Justin's error?
Justin should have multiplied 12.5 and 7.9 first.
Justin should have added 12.5 and 7.9 first.
Justin should have multiplied 3.8 and 7.9 first.
O Justin should have added 3.8 and 7.9 first.
Justin should have multiplied 3.8 and 7.9 first
How to evaluate an expression?He is trying to evaluate the expression 12.5 + 3.8x, when x = 7.9.
This was Justin solution to the expression
12.5 + 3.8(7.9)
16.3(7.9)
128.77
Now let's do our own arithmetic,
12.5 + 3.8x
we have to substitute the value of x in the equation.
12.5 + 3.8(7.9)
Using PEMDAS principle, we have to multiply before addition.
Therefore,
12.5 + 3.8(7.9)
12.5 + 30.02
42.52
Hence, Justin should have multiplied 3.8 and 7.9 first
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Solve the compound inequality 6b < 36 or 2b + 12 > 6
A. b < 6 or b > 6
B. b < 6 or b > 3
C. b > 6 or b < −3
D. b < 6 or b > −3
Answer:
D.)
Step-by-step explanation:
x = 10 g y = 10 kg y + x =
a)10.1 kg
b)100.1 g
c)10.1 kg
d)10.01 g
The correct option is d)10.01 kg; y + x = 10.01 kg.
What is referred as the unit conversion?When converting units, you are generally given one measure but instead asked to convert it to another.
For example, you may be given a volume in "gallons" but also asked to convert it to "fluid ounces." They will have given you (or you will be able to quickly find) the conversion units which are appropriate for the task. In order to complete the conversion, you will be required to multiply or divide by one of the following unit equivalences.For the given values in the question;
x = 10 g and y = 10 kg
As, both the values are of mass.
For adding both values, the unit must be same.
So, convert the value of x in kg from g.
1 kg = 1000 g
Thus, 1 g = 1/1000 kg
10 g = 10/1000 kg
10 g = 0.01 kg
Now add both;
x + y = 0.01 + 10
x + y = 10.01 kg
Thus, the value of x + y is found as 10.01 kg.
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The correct question is-
a)10.1 kg
b)100.1 g
c)10.1 kg
d)10.01 kg
Let , which represents the set of points on and inside an in the xy-plane. find two specific examples two vectors, and a vector and a scalar to show that h is not a subspace of .
The two vectors and a vector and a scalar which shows that H is not a subspace of [tex]R^2[/tex] are [tex]\bold{\left[\begin{array}{c}\frac{1}{5} \\\frac{1}{4} \end{array}\right]}[/tex] , [tex]\bold{\left[\begin{array}{c}\frac{1}{6} \\\frac{1}{7} \end{array}\right]}[/tex] and [tex]\left[\begin{array}{c}\frac{1}{6} \\\frac{1}{3} \end{array}\right][/tex] and 6.
Given the set, [tex]H=\{\left[\begin{array}{c}x\\y\end{array}\right] :8x^2+5y^2\leq 1\}[/tex] which represents the set of points on and inside an ellipse in the xy-plane.
We have to show that H is not a subspace.
We can show that this set is not closed under vector addition of two vectors by finding those vectors.
[tex]\left[\begin{array}{c}\frac{1}{5} \\\frac{1}{4} \end{array}\right][/tex] and [tex]\left[\begin{array}{c}\frac{1}{6} \\\frac{1}{7} \end{array}\right][/tex] are two vectors in H, since it satisfies the given condition, [tex]8x^2+5y^2\leq 1[/tex].
i.e., [tex]8\times(\frac{1}{5})^2 + 5\times (\frac{1}{4})^2 = 0.6325\leq 1[/tex] and [tex]8\times(\frac{1}{6})^2 + 5\times (\frac{1}{7})^2 = 0.3242\leq 1[/tex]
[tex]\left[\begin{array}{c}\frac{1}{5} \\\frac{1}{4} \end{array}\right][/tex] + [tex]\left[\begin{array}{c}\frac{1}{6} \\\frac{1}{7} \end{array}\right][/tex] = [tex]\left[\begin{array}{c}\frac{11}{30} \\\frac{11}{28} \end{array}\right][/tex]
But [tex]8\times(\frac{11}{30})^2 + 5\times (\frac{11}{28})^2 =1.847 \geq 1[/tex]
So the vector [tex]\left[\begin{array}{c}\frac{11}{30} \\\frac{11}{28} \end{array}\right][/tex] does not belongs to H.
So It is not closed under addition.
Now we will prove that H is not closed under scalar multiplication of a vector and a scalar either.
[tex]\left[\begin{array}{c}\frac{1}{6} \\\frac{1}{3} \end{array}\right][/tex] is a vector in H. But [tex]6\left[\begin{array}{c}\frac{1}{6} \\\frac{1}{3} \end{array}\right][/tex] does not belongs to H, where 6 is a scalar.
This is because [tex]6\left[\begin{array}{c}\frac{1}{6} \\\frac{1}{3} \end{array}\right][/tex] = [tex]\left[\begin{array}{c}1 \\2 \end{array}\right][/tex] and [tex]8\times1^2 + 5\times 2^2 =28 \geq 1[/tex].
So the two vectors are [tex]\bold{\left[\begin{array}{c}\frac{1}{5} \\\frac{1}{4} \end{array}\right]}[/tex] and [tex]\bold{\left[\begin{array}{c}\frac{1}{6} \\\frac{1}{7} \end{array}\right]}[/tex] and one vector and a scalar are [tex]\left[\begin{array}{c}\frac{1}{6} \\\frac{1}{3} \end{array}\right][/tex] and 6.
The question is incomplete. Find the complete question below:
Let [tex]H=\{\left[\begin{array}{c}x\\y\end{array}\right] :8x^2+5y^2\leq 1\}[/tex], which represents the set of points on and inside an in the xy-plane. Find two specific examples two vectors, and a vector and a scalar to show that H is not a subspace of [tex]R^2[/tex].
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explain why 8 < x < 2 has no solution? need the answer quick
Answer:
8 < x < 2 has no solution because there is no number greater than 8 (8 < x), yet less than 2 (x < 2). It's impossible, so there is no solution.
If the inequality was something like 8 < x < 10, then it will work because 8 can be less than x and x can be less than 10.
Hope this helps and have a great rest of your day! :)
A random sample of 100 diabetics undergoes genotyping and it was found that 23 of them have the gene. compute the z test statistic needed for this hypothesis test.
The z test statistic needed for this hypothesis test is 0.75 .
Z test is a statistical test that is conducted on data that approximately follows a normal distribution. The z test can be performed on one sample, two samples, or on proportions for hypothesis testing. It checks if the means of two large samples are different or not when the population variance is known.
NOW,
sample proportion = p = x / n = 0.23
Test statistics
z = ( p - p0 ) / [tex]\sqrt{ p0*(1-p0)}[/tex] / n
= ( 0.23 - 0.20) / [tex]\sqrt{ (0.20*0.80) / 100}[/tex]
= 0.75
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select the correct answer. what is the slope of the line that goes through the points (-4,2) and (8,5)?
A. "-4"
B. "-1/4"
C. 1/4
D. 4
Answer: The slope of the line that goes through the points is = ¼
Step-by-step explanation:
Define Slope:
The slope is a numerical value that describes the steepness of a line and is usually determined by calculating the ratio of the vertical distance to the horizontal distance (rise over run) between two points.
The slope of the line that goes through the points (-4,2) and (8,5).
Let, X1=-4
Y1=2
X2=8
Y2=5
We can use m=(y2-y1) / (x2-x1)
replace with x1, y1 and x2, y2 values in this equation
We can write: m=[(5-2) / (8-(-4))]
Solve it: M= 3/12
M=1/4
So, the slope of the line that goes through the points is = ¼.
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Orville is thinking of a number. The product of the number and 39 is 156. Find Orville's number. 46
Answer:
I believe the multiplied number would be 4.
39 × 4 = 156
The number is = 4
Step-by-step explanation:
I'm not sure what is 46 at the end of the question.
Travis wrote five checks to the employees of his business, each for $225. if the original balance in his checking account was $890, what is his new balance?
Travis's checking account new balance, after wrote five checks to the employees of his business is - $235
To solve this problem, we have to state the equation using the information of the problem
Information about the problem:
Original balance= $890Check amount of each employer= $225No. of checks= 5Final balance = ?Calculating the checks total amount Travis wrote to the employees of his business:
Total amount for his employers = Check amount of each employer * No. of checks
Total amount for his employers = $225 * 5
Total amount for his employers = $1125
Calculating the final balance, we have:
Final balance = Original balance - Total amount for his employers
Final balance = $890 - $1125
Final balance = - $235
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
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(-2,-4) and (3,-9)?
What we answering with these 2 points ?
Where's the question?
Determine whether each of the following functions is a solution of laplace's equation uxx uyy = 0.
Both functions are the solution to the given Laplace solution.
Given Laplace's equation: [tex]u_{x x}+u_{y y}=0[/tex]
We must determine whether a given function is the solution to a given Laplace equation.If a function is a solution to a given Laplace's equation, it satisfies the solution.(1) [tex]u=e^{-x} \cos y-e^{-y} \cos x[/tex]
Differentiate with respect to x as follows:
[tex]u_x=-e^{-x} \cos y+e^{-y} \sin x\\u_{x x}=e^{-x} \cos y+e^{-y} \cos x[/tex]
Differentiate with respect to y as follows:
[tex]u_{x x}=e^{-x} \cos y+e^{-y} \cos x\\u_{y y}=-e^{-x} \cos y-e^{-y} \cos x[/tex]
Supplement the values in the given Laplace equation.
[tex]e^{-x} \cos y+e^{-y} \cos x-e^{-x} \cos y-e^{-y} \cos x=0[/tex]
The given function in this case is the solution to the given Laplace equation.
(2) [tex]u=\sin x \cosh y+\cos x \sinh y[/tex]
Differentiate with respect to x as follows:
[tex]u_x=\cos x \cosh y-\sin x \sinh y\\u_{x x}=-\sin x \cosh y-\cos x \sinh y[/tex]
Differentiate with respect to y as follows:
[tex]u_y=\sin x \sinh y+\cos x \cosh y\\u_{y y}=\sin x \cosh y+\cos x \sinh y[/tex]
Substitute the values to obtain:
[tex]-\sin x \cosh y-\cos x \sinh y+\sin x \cosh y+\cos x \sinh y=0[/tex]
The given function in this case is the solution to the given Laplace equation.
Therefore, both functions are the solution to the given Laplace solution.
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The correct question is given below:
Determine whether each of the following functions is a solution of Laplace's equation uxx + uyy = 0. (Select all that apply.) u = e^(−x) cos(y) − e^(−y) cos(x) u = sin(x) cosh(y) + cos(x) sinh(y)
Consider the expression 4a + (-3b), where bis a negative number and a < b. Is the sum positive or negative?
The sum will be negative.
The product of two negative numbers is always positive and if we add two numbers, the sign of the greater number is used in the result.
Here, we are given an expression 4a + (-3b)
Also we are told that a < b and b is a negative number
Mow, since b is a negative number, (-3b) will always be positive. This is because the product of two negative numbers, here -3 and b, will always be positive.
Now, a can be positive or negative. If a is positive, the sum will always be positive. However, if it is negative, the sum can be either positive or negative.
Here, in fact, since a < b, a will always be negative only
Let us take an example, say a = -3 and b = -2
Then the sum becomes 4(-3) + (-3)(-2)
= -12 + 6
= -6
If we observe closely since a and be are both negative and a < b, in absolute terms a will always be greater than b since for negative numbers higher the value, smaller is the number.
Thus, we can conclude that 4a > (-3b) for all values of a and b
and since 4a will always be negative, the sum will also be negative.
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PLS HELP
This is the one thing I need to do for my assignment and I don't know it
Answer:
Step-by-step explanation:
the square root of 74 is 8.60
Even if you round it should be 8.7 but 8.5 is only one digit down from 8.60 if that makes sense so 8.6 is only one digit from 8.5 with is a comparable value
Complete the table of values for f(x) = -3|x+1|-4 using the table of values for g(x) = |x|
f(x)>=-7
Functions:
Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are ubiquitous in mathematics.
If a variable y is so related to a variable x that whenever a numerical value is assigned to x, there is a rule according to which a unique value of f(x)is determined, then f(x) is said to be a function of the independent variable x
Given :
f(x) = -3|x+1|-4
using the table of values for g(x) = |x|
Solution :
f(x) = -3|x+1|-4
f(x) = -3|g(x)+1|-4
f(x) = -3||x|+1|-4
which means |x| is always positive |x|>0
f(x) = -3||x|+1|-4
f(x) = -3x-3-4
f(x) = -3x-7
f(x)>=-7
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Each side of a square is lengthened by 2 inches. The area of
this new, larger square is 36 square inches. Find the length of
a side of the original square.
Please help using systems of equations!!
Answer:
4 inches.
Step-by-step explanation:
Since the shape is a square, each side length will be the same. This mean that you must find the square root of 36 to find the length of each side of the new square.
√36=6
Each side of the new square is 6. It says it was lengthened by 2 inches. Subtract 2 from 6.
6-2=4
Each side of the original square is 4 inches.
Hope this helps!
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2
You can also use scientific notation for very small numbers. The
thickness of a dollar bill is about 0.0043 inches. Write this quantity in
scientific notation.
A. First move the decimal point to the right to get a number that is
greater than or equal to 1 but less than 10.
0.0043 The decimal point moves 3
places to the right.
Remove the extra zeros to get the first factor:
B. Since 0.0043 is less than 1, you moved the decimal point to the right,
so the exponent in the power of 10 will be negative.
-3
0.0043 = 4.3
X 10
the thickness in scientific notation is:
4.3* 10⁻³ inches
How to write the thickness in scientific notation?
Here we know that the thickness of a dollar bill is 0.0043 inches.
Now, scientific notation refers to the notation where we have a single digit at the left of the decimal point, and the order of the number is defined by a factor of a power of 10.
To write our number in scientific notation we need to count the number of zeros that we have before the first non-zero decimal, and we can see that it is equal to 3.
Then we can move all the digits 3 units to the left, and add a factor 10⁻³ to correct that, then we will get:
0.0043 = 4.3* 10⁻³
From this, we conclude that the thickness in scientific notation is:
4.3* 10⁻³ inches
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Filip is inviting 6 friends to a party. Each friend wants 5 cookies and each box has 8 cookies. How many boxes should Filip get?
Can someone find the measure of angle b
After executing the following statement, the value of x is ________. double x = 5 4 * 3 / 2 ;
The value of x is 81 . double x = 5 4 * 3 / 2 .
What is a linear equation?
An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."x = 54 * 3/2
x = 27 * 3
x = 81
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