The order from least to greatest to satisfy the inequality t < -3 is (-∞, -2).
What is called the inequality?Inequality is just a mathematical statement which uses the inequality symbol to show the relationship between two expressions. Both sides of the an inequality sign have different expressions. It implies that expression on the left should be greater or smaller than expression on the right, or vice versa.For the given question,
The inequality is given as;
t < -3
For the inequality to be true the value of 't' must be less than -3.
Thus, the values will range between.
(-∞, -2)
Where, -∞ represents the least value and -2 shows the greatest value for 't'.
Thus, the order from least to greatest to satisfy the inequality t < -3 is (-∞, -2).
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Solve (t+2)3/4 =2 where t is a real number.t=
Solution:
Given the equation:
[tex]\begin{gathered} (t+2)^{\frac{3}{4}}=2 \\ \text{where t is a real number} \end{gathered}[/tex]step 1: Take both sides of the equation to the power of 4.
Thus,
[tex]\begin{gathered} ((t+2)^{\frac{3}{4}})^4=(2)^4 \\ \Rightarrow(t+2)^3=16 \end{gathered}[/tex]step 2: Take the cube root of both sides of the equation.
Thus,
[tex]\begin{gathered} \sqrt[3]{(t+2)^3}=\sqrt[3]{16} \\ \Rightarrow(t+2)=16^{\frac{1}{3}} \\ \end{gathered}[/tex]step 3: Solve for t.
[tex]\begin{gathered} 16^{\frac{1}{3}}^{} \\ \text{can be rewritten as} \\ (2^4)^{\frac{1}{3}}=2^{\frac{4}{3}} \\ \text{thus, we have} \\ t+2=2^{\frac{4}{3}} \\ \text{subtract 2 from both sides of the equation} \\ t+2-2=2^{\frac{4}{3}}-2 \\ \Rightarrow t=2(2^{\frac{1}{3}}-1) \\ =2(1.25992-1) \\ \Rightarrow t=2(0.25992) \\ \therefore t=0.51984 \end{gathered}[/tex]Hence, the value of t in the equation is evaluated to be 0.51984.
PLEASE SOLVE SOON
Solve for x and explain each step you take as you solve the problem. Verify your answer is correct.
-7 over 6 times x - 6 equals -48
The value of x for the given algebraic expression is 36.
Linear ExpressionA linear expression can be represented by a line. The standard form for this equation is: y=mx+b , for example, y=9x+1.
The question gives the linear expression in text format. Therefore, you should convert the text in algebraic expression. See some tips:
the word over in math can be represented by division (÷ or / )the word times in math can be represented by product ( x or · )the word equals in math can be represented by equality ( = )Converting the text into algebraic expression, you have:
[tex]\frac{-7}{6}[/tex] * x - 6 = -48
-7x -6*6= -48*6 ( Multiply both sides by 6)
-7x -36 = -288
-7x = -288 +36
-7x = -252
x= -252 / -7
x=36
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A population of values has a normal distribution with μ=126.7 and σ=78.3. You intend to draw a random sample of size n=242.
In a population of values having a normal distribution with (μ = 126.7) and (σ = 78.3), and we intend to draw a random sample of size (n = 242),
(i) The probability that a single randomly selected value is greater is than 119.2 is 0.54
(ii) The probability that a sample of size (n = 242) is randomly selected with a mean greater than 119.2 is 0.932
As per the question statement, a population of values has a normal distribution with (μ = 126.7) and (σ = 78.3) and we intend to draw a random sample of size (n = 242).
We are required to calculate:
(i) The probability that a single randomly selected value is greater is than 119.2
(ii) The probability that a sample of size (n = 242) is randomly selected with a mean greater than 119.2
Let us assume that, a random variable "X" follows normal distribution with mean (μ = 126.7), standard deviation (σ = 78.3) and a sample size of (n = 242).
(i) The probability that a single randomly selected value is greater is than 119.2 is,
P (X > 119.2) = [1 - P(X < 119.2)]
= [1 - P{(X - μ)/σ < (119.2 - 126.7)/78.3}]
= [1 - P{Z < (-0.096)}]
= (1 - 0.462)...[Using Excel Function "NORMSDIST (-0.096)]
= 0.538
≈ 0.54
(ii) The probability that a sample of size (n = 242) is randomly selected with a mean greater than 119.2 is.
P(X bar > 119.2) = [1 - P( < 119.2)]
= [1 - P{(X bar - μ)/(σ/√n) < (119.2 - 126.7)/(78.3/√242)}]
= [1 - P{(X bar - μ)/(σ/√n) < (119.2 - 126.7)/5.033}]
= [1 - P{Z < (-1.49)}]
= (1 - 0.068)...[Using Excel Function "NORMSDIST (-1.49)]
= 0.932
Probability: Probability is the branch of mathematics concerning numerical descriptions about the extent to which an event is likely to occur, or how likely it is that, a proposition is true, and is measured by the ratio of the favorable cases to the whole number of cases possible.Sample: In statistics, quality assurance, and survey methodology, sampling is a logical selection of a subset (a statistical sample) of individuals from within a larger statistical population to estimate characteristics of the whole population.To learn more about Samples and Probability, click on the link below.
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Could please get help with this math. I need help weather each of the triangles can be the HL congruence property?
In order to use the HL congruence property, the triangles must have the hypotenuses and one pair of corresponding legs with the same length.
(a)
These are right triangles and have only one pair of legs with the same length, therefore the answer is NO.
(b)
These right triangles have one pair of legs with the same length and a common hypotenuse, therefore the answer is YES.
(c)
These triangles are not right triangles, therefore the answer is NO.
(d)
These right triangles have one pair of legs with the same length and the hypotenuses also have the same length, therefore the answer is YES.
i am working on an assignment and it just says canceling fractions like 1. 14 over 28 = not sure what to do here?
SOLUTION
This is
[tex]\frac{14}{28}[/tex]Now, both 14 and 28 are divisible by 2. So, 2 will cut 14 to give 7, and 2 will cut 28 to give 14 so you have
[tex]\begin{gathered} \frac{14}{28} \\ \text{cutting each by 2 you have } \\ \frac{7}{14} \end{gathered}[/tex]Now, only 7 can cut 7 and 14. 7 will cut 7 to get 1 and, 7 will cut 14 to get 2. So we have
[tex]\begin{gathered} \frac{7}{14} \\ \text{cutting each by 2 we have } \\ \frac{1}{2} \end{gathered}[/tex]Hence the answer is
[tex]\frac{1}{2}[/tex]Six tickets to a movie cost $76.50. What constant of proportionality relates the number of tickets and total cost?
A: 6.00
B: 6.25
C: 12.00
D: 12.75
The relationship has a constant of proportionality of 12.75
How to determine the constant of proportionality?From the question, the given parameters are
Number of tickets = 6Cost of the tickets = $76.50The above parameters can be represented as the following points
(x, y) = (6, 76.50)
The constant of proportionality of the points is then calculated as
k = y/x
Substitute the known values in the above equation
So, we have the following equation
k = 76.50/6
Evaluate the quotient
So, we have
k = 12.75
Hence, the constant of proportionality is 12.75
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HELP ASAP!!!!!
Point P is shown on the number line below. The distance between point Q and point P is 6 ½ units.
P
-12-10-8-6-4-2 0 2 4 6 8 10 12
a. Which number could represent point Q?
b. Explain how you determined your answer.
a: The number which could represent point Q are +2.5 or -10.5.
b. For determining the point Q add and subtract 6.5 units from point P.
What is meant by the term number line?A number line is a graphical portrayal of numbers on such a straight line in mathematics. A number line has numbers that are sequentially placed at equal distances across its length. It can be extended in any direction indefinitely and is generally denoted horizontally.A number line's numbers increase when moving from left to right as well as decrease when moving from right to left.A number line can represent any type of number, including fractions, decimals, integers, and so on.For the given question;
The distance between point Q and point P is 6 ½ units.
The location of point P is (-4) (seen from the number line).
a. The number could represent point Q are either +2.5 or -10.5.
b. Determine the number;
Add 6 ½ units = 6.5 units to (-4)
= -4 + 6.5
= + 2.5
Thus, point Q = + 2.5
Now, subtract 6 ½ units = 6.5 units to (-4).
= -4 - 6.5
= -10.5
Thus, point Q = + 2.5.-10.5.
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integrate 1∫^-1 (2-x/3) dx
Answer:
Step-by-step explanation:
[tex]\int~x^{-1}(2-x/3) dx \\\int\frac{2-x/3}{x} dx\\=\int\frac{2}{x} dx-\int~x^{-2/3}~dx\\=2 ln ~x-\frac{x^(-2/3+1)}{-2/3+1} +c\\=lnx^2-3x^{1/3}+c[/tex]
19. 6x + 1 = 6x-8
Tell weather the equation is and identity or has no solution
Answer:
No solutions
Step-by-step explanation:
the x's cancel out
An ion has a charge of +7. How far is it from being neutral? a. -0.07b. -7c. 7d. 70e. 0.7
If the ion has a charge of +7, in irder to get to neutral (charge zero), one needs to subtract 7 charges from it. Therefore it is -7 far from being neutral.
Then the correct answer is option "b" in the list.
18-?=32
Find the ?
Thank you so much for the help
Answer:
-14
Step-by-step explanation:
[tex]18-?=32 \\ \\ -?=14 \\ \\ ?=-14[/tex]
Shannon went to the book store. She bought a book for $7.00, a magazine for $4.25 and a bookmark for $1.99. Her purchase was 15% off. She handed the cashier a $20 bill. How much change did she
Show work?
Answer:
8.74$
Step-by-step explanation:
so first what you want to do is that you want to add $7 with 4.25 dollars plus 1.99 dollars the next thing you want to do is take 85% of this number you will get 0.85 times that sum
that sum is 13.24. now because she is getting 15% off of her purchase that means you want to take 85% of that 13.24 number . so you will get 1 1.254 you will need to round this because it is in dollars . so you will get 11.25 as her purchase price . now because she gave a $20 bill you need to subtract that number from 20 and you will get 8.746 which is rounded to 8.74 because it is in dollars that is the answer that is her change
PLEASE HELP IM SICK AND I DONT UNDERSTAND.DO IN 30 MINS!!!!!!
Answer:
x = 7Step-by-step explanation:
The given angles are corresponding angles and as such have same measure.
Set equation and solve for x:
14x + 12 = 16x - 216x - 14x = 12 + 22x = 14x = 7Suppose 2x + 6y= 12. Find y if:x = −4y = ?
Given the equation:
[tex]2x+6y=12[/tex]If we know that x = -4, then:
[tex]2\cdot(-4)+6y=12[/tex]Solving for y:
[tex]\begin{gathered} -8+6y=12 \\ 6y=12+8 \\ 6y=20 \\ y=\frac{20}{6} \\ \therefore y=\frac{10}{3} \end{gathered}[/tex]In September, there were 16 members in the music club. In October, the number of members was 24. What was the percent increase from September to October?20 out of 22 students passed the quiz. What percentage of students passed the quiz?A real estate agent sold a house for $178,000. He makes 5.5% commission. How much did he make?The original price of a shirt is $23. It is 20% off. What is the sale price?
Percentage increase from September to October = 50%
Explanations:Number of members in the music club in September = 16
Number of members in the music club in October = 24
Increase in members from September to October = 24 - 16
Increase in members from September to October = 8
Percent increase from September to October = (8/16) x 100
Percentage increase from September to October = 100/2
Percentage increase from September to October = 50%
“Please help me I’ll mark u brainly please don’t do this for the points”
The measure of angle x in each of the triangles is:
1) 20°
2) - 49°
3) 8°
4) 33.33°
5) 10°
6) 3°
7) 1°
8) 2°
9) 6°
1) The measure of the inner angles in the triangle are 100°, 40°, and 2x°.
The sum of all angles in the triangle is equal to 180°.
Therefore,
100° + 40° + 2x = 180°
140° + 2x = 180°
2x = 40°
x = 20°
2) The measure of the inner angles in the triangle are 99°, 37°, and (- x - 5)°.
The sum of all angles in the triangle is equal to 180°.
Therefore,
99° + 37° + ( - x - 5 )° = 180°
136° + (- x - 5)° = 180°
( - x - 5 )° = 44°
x = - 49°
3) The measure of the inner angles in the triangle are 60°, 60°, and ( - 12 + 9x)°.
The sum of all angles in the triangle is equal to 180°.
Therefore,
60° + 60° - 12 + 9x = 180°
120° - 12° + 9x = 180°
108° + 9x = 180°
9x = 72°
x = 8°
4) The measure of the inner angles in the triangle are 36°, 46°, and ( 2 - 3x)°.
The sum of all angles in the triangle is equal to 180°.
Therefore,
36° + 46° - 2° + 3x° = 180°
82° - 2° + 3x° = 180°
80° + 3x° = 180°
3x = 100°
x = 33.33°
5) The measure of the inner angles in the triangle are 71°, 50°, and ( 6x - 1 )°.
The sum of all angles in the triangle is equal to 180°.
Therefore,
71° + 50° - 1° + 6x° = 180°
121° - 1° + 6x° = 180°
120° + 6x° = 180°
6x = 60°
x = 10°
6) The measure of the inner angles in the triangle are 45°, 90°, and ( 8x + 21 )°.
The sum of all angles in the triangle is equal to 180°.
Therefore,
45° + 90° + 21° + 8x° = 180°
156° + 8x° = 180°
8x = 24°
x = 3°
7) The measure of the inner angles in the triangle are 85°, 64°, and ( 4x + 27 )°.
The sum of all angles in the triangle is equal to 180°.
Therefore,
85° + 64° + 27° + 4x° = 180°
176° + 4x° = 180°
4x = 4°
x = 1°
8) The measure of the inner angles in the triangle are 44°, 104°, and ( 7x + 18 )°.
The sum of all angles in the triangle is equal to 180°.
Therefore,
44° + 104° + 18° + 7x° = 180°
166° + 7x° = 180°
7x = 14°
x = 2°
9) The measure of the inner angles in the triangle are 125°, 25°, and ( - 5x )°.
The sum of all angles in the triangle is equal to 180°.
Therefore,
125° + 25° - 5x° = 180°
150° + 5x° = 180°
5x = 30°
x = 6°
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Find the equation of the linear function represented by the table below in slope-intercept form. XY-153-117-2711-43
First, we have to find the slope, using the following formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Let's use the points (-1,5) and (7, -27). Where,
[tex]\begin{gathered} x_1=-1 \\ x_2=7 \\ y_1=5 \\ y_2=-27 \end{gathered}[/tex]Then, we use these values to find the slope.
[tex]m=\frac{-27-5}{7-(-1)}=\frac{-32}{8}=-4[/tex]Now we use the point-slope formula.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-5=-4(x-(-1)) \\ y-5=-4(x+1) \\ y-5=-4x-4 \\ y=-4x-4+5_{} \\ y=-4x+1 \end{gathered}[/tex]Therefore, the slope-intercept form is y = -4x+1.Consider the following algebraic expression:4x - 6Step 1 of 2: Identify the first term of the algebraic expression. Indicate whether the term is a variable term or a constant term. For avariable term, identify the variable and the coefficient of the term.
ANSWER and EXPLANATION
We want to identify the first term of the algebraic expression given:
[tex]4x-6[/tex]The first term of the expression is:
[tex]4x[/tex]The variable in the expression is the algebraic term. The algebraic term is:
[tex]x[/tex]Therefore, the coefficient of the first term is:
[tex]4[/tex]Question 36 of 50
Which of the following choices is the correct range for the function h(x) = -3x2 if the domain is (0, -2, 1)?
(0, -6, -3)
(0, -12, 3)
None of these choices are correct.
(0, 6, -3)
(0, 12, 3)
The range of the function, h(x) = - 3x² with domain of (0, -2, 1) are (0, -12, -3). Therefore, non of the options is correct.
How to find range of a function?The domain of a function is the set of all possible inputs for the function.
In other words, the domain of a function are the independent values of the function.
Domain are usually represented by the x value.
The range of a function refers to all the possible values y could be.
Therefore, the function is as follows:
h(x) = - 3x²
Therefore, the domain are (0, -2, 1).
The range that represents the domain can be computed as follows:
h(0) = - 3(0)² = 0
h(-2) = - 3(-2)² = -12
h(1) = - 3(1)² = -3
Therefore, non of the choices are correct. The range of those domain are (0, -12, -3)
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The number of hits to a website follows a Poisson process. Hits occur at the rate of1.4 per minute between 7:00 P.M. and 10:00 P.M. Given below are three scenarios for thenumber of hits to the website. Compute the probability of each scenario between 9:30 PM and9:35 P.M. Interpret each result.(a) exactly four(b) fewer than four(c) at least four
Given that:
Rate at which the hits occur between 7 PM and 10 PM = 1.4 per minute
Then:
Number of hits between 9:30 AM and 9:35 AM
[tex]\begin{gathered} =5\cdot(1.4) \\ =7 \end{gathered}[/tex]The probability distribution function of Poisson distribution is
[tex]P(X=x)=\frac{e^{-\lambda}\lambda^x}{x!}[/tex](a) P(x=4)
[tex]\begin{gathered} =\frac{e^{-7}7^4}{4!} \\ =0.0912 \end{gathered}[/tex](b) P(x < 4) = P(x=0)+P(x=1)+P(x=2)+P(x=3)
[tex]\begin{gathered} =\frac{e^{-7}7^0}{0!}+\frac{e^{-7}7^1}{1!}+\frac{e^{-7}7^2}{2!}+\frac{e^{-7}7^3}{3!} \\ =e^{-7}+7e^{-7}+\frac{49e^{-7}}{2}+\frac{343e^{-7}}{6} \\ =0.0818 \end{gathered}[/tex](c) To find
[tex]\begin{gathered} P(x\ge4)=1-P(x<4) \\ =1-0.0818 \\ =0.9182 \end{gathered}[/tex]Check whether the sequence is arithmetic. If so, find the common difference d.
1, 10, 19, 28,37
Answer: 9
Step-by-step explanation: 1+9 =10
10+9=19
19+9=28
28+9=37
3x+2y=10 and 2x+3y=-4parallel perpendicular or neither
Solve using substitution:2x + 3y - 4z = 9 4y – 6z = 16z = 2
ANSWER
x = -2, y = 7, z = 2
EXPLANATION
We are given a system of three equations:
2x + 3y - 4z = 9 ________(1)
4y - 6z = 16 ___________(2)
z = 2 ________________(3)
Since we have been given the value of z, from (3) we have that (2) becomes:
4y - 6(2) = 16
4y - 12 = 16
4y = 12 + 16 = 28
y = 28 / 4
y = 7
Put the values of y and z in (1):
=> 2x + 3(7) - 4(2) = 9
2x + 21 - 8 = 9
2x + 13 = 9
Collect like terms:
2x = 9 - 13 = -4
x = -4 / 2
x = -2
So, x = -2 and y = 7 and z = 2
Pls complete fast and be sure of ur answer 
The number of students which are either in algebra or physics are 23 which is the second option.
Given that:-
Total number of students = 30
Number of students both in physics and algebra = 4
Total number of students in Physics = 12
Total number of students in Algebra = 19
We have to find the number of students which are either in algebra or physics.
Number of students in physics but not in algebra = 12 - 4 = 8
Number of students in algebra but not in physics = 19 - 4 = 15
We know that:-
Number of students which are either in algebra or physics = Number of students in physics but not in algebra + Number of students in algebra but not in physics
Hence, we can write,
Number of students which are either in algebra or physics = 8 +15 = 23.
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Solve- (-8/5)x - 6 = -54and explain
Giveb data:
The given expression is (-8/5)x-6=-54.
The given expression can be written as,,
[tex]\begin{gathered} (-\frac{8}{5})x-6=-54 \\ -\frac{8}{5}x=-48 \\ x=\frac{5\times48}{8} \\ =30 \end{gathered}[/tex]Thus, the value of x is 30.
What should the side length be, to the nearest hundredth, for each petit four?
Cube is a 3D closed structure in which each adjacent side is perpendicular to each other and every side is equal to each other. Let the side of cube be 's'cm.
The formula for the Volume(V) of a cube is,
[tex]V=s^3[/tex]Given
[tex]V=67cm^3[/tex]Therefore,
[tex]67=s^3[/tex]Evaluate for s
[tex]\therefore s=\sqrt[3]{67}=4.06154\approx4.06cm[/tex]Hence, the value for the side length of each petit four is 4.06cm.
Answer:
4.06 cm
Step-by-step explanation:
since it is a cube it is the cube root of 67 and I popped it in the calculator and got 4.06 of the answer rounded from the 100th place
what does x-4>-8 equal
We need to solve the following inequality:
[tex]x-4>-8[/tex]To do that we have to isolate the variable on the left side. The first step is to add "4" on both sides.
[tex]\begin{gathered} x-4+4>-8+4 \\ x>-4 \end{gathered}[/tex]The value of x must be greater than -4 for this inequality bo be valid.
To graph this result we need to draw a line at the point that x = -4, then we collor the side that is greater than that.
A better drawing can be seen below:
To graph it at the line we need to go to the point that solves the equation, in this case is -4 and if the signal is ">" we collor the right part of the line.
I need help with "E" and "F" :)
Derivative of the given function
E. f(x) = [1 + sin ³(x^5)]² = sin ⁶(x⁵) +2 sin ³(x^5) + 1
F. f(x) = arcsin√sinx = cos x / 2sinx^1/2√ 1- sinx .
According to the chain rule, the derivative of a composite function is equal to the inner function derivative with respect to x times the inner function derivative with respect to each individual composite function.
E) f(x) = [1 + sin ³(x^5)]²
Rearrange terms
[sin ³(x^5) + 1]²
Expand the square
[sin ³(x⁵) + 1]²
[sin ³(x^5) + 1] [sin ³(x^5) + 1]
Distribute
(sin ³(x⁵) + 1) sin ³(x^5) + 1 (sin ³(x^5) + 1)
(sin ⁶(x⁵) + 1) (sin ³(x^5) + 1) (sin ³(x^5) + 1)
Multiply by 1
sin ⁶(x⁵) + 1 sin ³(x^5) + 1 sin ³(x^5) + 1
Combine the terms
sin ⁶(x⁵) + sin ³(x^5) + sin ³(x^5) + 1
sin ⁶(x⁵) +2 sin ³(x^5) + 1
Hence, the solution of the derivative
f(x) = [1 + sin ³(x^5)]² = sin ⁶(x⁵) +2 sin ³(x^5) + 1
Hence, E. f(x) = [1 + sin ³(x^5)]² = sin ⁶(x⁵) +2 sin ³(x^5) + 1
F. f(x) = arcsin√sinx = cos x / 2sinx^1/2√ 1- sinx . is the derivative of the functions .
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Events in a sample space that are equally likely to occur. what is the method called??
These events are called "Equally likely Events" and it useful to use when the outcomes of an experiment are equally likely to happen.
Find the monthly interest payment in the situation below.Vic bought a new plasma TV for $2400. He made a down payment of $100 and then financed the balance through the store. Unfortunately, he was unable to make the first monthly payment and now pays 4% interest per month on the balance (while he watches his TV).What is Vic's monthly interest payment? $ enter your response here (Round to the nearest dollar as needed.)
Given:
Vic bought a new plasma TV for $2400.
He made a down payment of $100 and then financed the balance through the store.
The interest per month is 4% on the balance.
To find:
Vic's monthly interest payment.
Explanation:
The cost of a plasma Tv is $2400.
The down payment made is $100.
Balance amount for financing is $2400 - $100 = $2,300.
Since the interest rate is 4% per month
So, the monthly interest payments will be,
[tex]2300\times\frac{4}{100}=92[/tex]The monthly interest payments will be $92.
Final answer:
The monthly interest payments will be $92.
