The inequality that we can write is:
x - 2.45 ≥ 4.6
And the solution is x ≥ 7.05
How to write the inequality?Here we want to write in mathematic form the following sentence:
"2.45 less than a number x is greater than or equal to 4.6 "
First, "2.45 less than a number x...."
Is written as the difference:
x - 2.45
And that is greater or equal to 4.6, then we will have an inequality, and it will be:
x - 2.45 ≥ 4.6
We can solve that for x by adding 2.45 in both sides, so we will get:
x ≥ 4.6 + 2.45
x ≥ 7.05
That is the inequality solved.
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The inequality 2.45 less than a number x is greater than or equal to 4.6 as an equation is
[tex] x \: \geqslant 6.95[/tex]
What is inequality?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
The question can be expressed mathematically as:
x - 2.4
[tex] \geqslant [/tex]
4.5
By solving the above inequality,
We have x
[tex] \geqslant [/tex]
4.5 + 2.5
Hence, the inequality gives us
[tex]x \: \geqslant 6.95[/tex]
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Which of the following represents the strongest correlation?
A.) .00
B.) .34
C.) -.45
D.) -.28
Answer:
B. -0.45
Step-by-step explanation:
I'm assuming the values you have provided are pertaining to the correlation coefficient.
Correlation Coefficient:The correlation coefficient (r) is used to describe how strongly points are correlated and in which direction they are correlated. This correlation coefficient ranges between -1 and 1: [tex]-1\le r\le1[/tex]
If the correlation coefficient is negative, the correlation is down-sloped or in other words as the variable on the x-axis increases, the variable on the y-axis decreases.
If the correlation coefficient is positive, the correlation is upward-sloped or in other words as the variable on the x-axis increases, the variable on the y-axis also increases.
The strength of the correlation can be analyzed by the absolute value of the correlation coefficient (r). So if you want to compare two correlation coefficients and say which has a stronger correlation, you would first take the absolute value and then compare which is larger as such: [tex]|r|[/tex]
In this case the -0.45 is technically less than the 0.34, although the absolute value indicates it is a stronger correlation, just in a different direction. You can compare all the other options and -0.45 has the largest absolute value.
toddler triplets whose names are red, green and blue each have a coat whose colour is given by their name, but they aren't clear on which coat belongs to which of them. when they go out, red chooses a coat at random among the three coats, green chooses a coat at random among the remaining two coats and blue is left to take the remaining coat. how many ways are there for exactly one of the toddler triplets to end up with their coat?
Answer:
A way for one of the toddler triplets to end up with their coat is if the other two toddler triplets each get one another coat.
making it a 33% chance of one of the toddler triplets to end up with their own coat.
100% divided by 3 = 0.33
The area of the regular octagon is 10.15 cm².
1.45 cm
What is the measure of the apothem, rounded to the
nearest hundredth of a centimeter
The measure of the apothem is 1.75cm.
What is a regular octagon?
Eight equal sides and eight equal angles make up a normal octagon. Each side is the same length, and each angle is the same size. The total interior and external angles are 1080° and 360°, respectively. The inner angle at each vertex of a regular octagon is 135°.
Here, we have
Given: The area of the regular octagon is 10.15 cm².
We have to find the measure of the apothem.
The octagon can be divided into 8 congruent (identical) isosceles triangles. One of them is AOB.
Area (triangle AOB) = 10.15/8 = 1.27cm².
Area(triangle AOB) is also 1/2*MO*AB
1.27 = 1/2*MO*1.45
MO = 1.75cm
Hence, the measure of the apothem is 1.75cm.
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I need some help answering this question right here
The given expression can be as 2 + i as a complex number standard form.
Complex numbers:The combination of a number and an imaginary number is a complex number. Complex numbers are symbolized by the symbol z and have the form a + ib. a and b are said to be real numbers.
The imaginary portion of the complex number can be represented by the letter i called the iota.
Here i² = -1
Here we have
[tex]\frac{4 +\sqrt{16 - 4(5)}}{2}[/tex]
The above expression can be simplified as follows
=> [tex]\frac{4 +\sqrt{16 - 20}}{2}[/tex]
=> [tex]\frac{4 +\sqrt{- 4}}{2}[/tex]
As we know, [tex]i^{2} = -1[/tex]
=> [tex]\frac{4 +\sqrt{i^{2} (2)^{2} }}{2}[/tex]
=> [tex]\frac{4+2i}{2}[/tex]
=> [tex]\frac{2(2+i)}{2}[/tex]
= 2 + i
Therefore,
The given expression can be as 2 + i as a complex number standard form.
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Solve for n. 7n - 2 = 5n + 6
Answer:
n = 4
Step-by-step explanation:
Pre-SolvingWe are given the equation 7n - 2 = 5n + 6, ans we want to solve it for n.
To do this, we need to isolate n one one side.
SolvingLet's start by adding 2 to both sides.
7n - 2 = 5n + 6
+2 +2
_______________
7n = 5n + 8
Now, subtract 5n from both sides.
7n = 5n + 8
-5n -5n
_______________
2n = 8
Divide both sides by 8 to get the value of n.
2n = 8
÷2 ÷2
________
n = 4
A human resource manager is researching the entry-level salary for a technician position. He determines that other companies in the area are paying $15.50, $16.85, $14.25 and $15.95 per hour. What is the average pay for an entry-level technician position?
The average pay for an entry-level technician position is $15.6375.
What is arithmetic mean?The arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean
The formula for the mean of a given set of data is as follows:
Average = Sum of Observations/Total number of observations
Σx = 15.50 + 16.85 + 14.25 + 15.95 = 62.55
Here n = 4
⇒ Average = Σx/n
⇒ Average = 62.55/4
Apply the division operation, and we get
⇒ Average = 15.6375
Thus, the average pay is $15.6375.
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u) A man working in a firm gets monthly Salary of Rs 65 000 Read the tax rates given below and answer the following question (Annual income 450,000 Cupto 450.000) 450,001 -5,50,000 5,50,001 - 7.50,000 7,50, 001-20, 00,000 Soln Tax rate 1% 10%. 20%. 30%
The annual salary of the man is Rs 780,000 and his total taxes is given by the relation T = Rs 9,000
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Since the man's monthly salary is Rs 65,000, his annual salary would be:
Annual salary = Monthly salary x 12
Annual salary = 65,000 x 12
Annual salary = 780,000
His annual salary of Rs 780,000 falls in the third tax bracket which is from 750,001 to 2,000,000.
So, the tax rate applicable to him would be 30%.
To calculate the amount of tax he would have to pay, we can use the formula:
Tax amount = Tax rate x Taxable income
where taxable income is the income above the lower limit of the tax bracket.
In this case, the taxable income would be:
Taxable income = Annual income - Lower limit of tax bracket
Taxable income = 780,000 - 750,001
Taxable income = 29,999
So, the amount of tax he would have to pay would be:
Tax amount = 30% x 29,999
Tax amount = 8,999.7
Rounding this to the nearest rupee gives us:
Tax amount = Rs 9,000
Hence , the man would have to pay Rs 9,000 in taxes on his annual salary of Rs 780,000.
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Sanjay is making two pumpkin pies for Thanksgiving, one to share with his family and one to share with his friends. He adds the same amount of cinnamon to both pies, but he adds more pumpkin puree to the pie he will share with his friends. Which pie will have a stronger cinnamon flavor?
Answer:
Step-by-step explanation:
Sanjay is making two pumpkin pies for Thanksgiving, one to share with his family and one to share with his friends. He adds the same amount of cinnamon to both pies, but he adds more pumpkin puree to the pie he will share with his friends. Which pie will have a stronger cinnamon flavor?
"The pie he will give to his parents"
More pumpkin flavor less cinnamon flavor
I need this fast so plese help
The simplified expression of -7(3z + 5t - 3g) is -21z - 35t + 21g.
How to simplify an expression?An algebraic expression consists of unknown variables, numbers and arithmetic operators such as addition, subtraction, multiplication etc.
To simplify an expression means to write an equivalent expression which contains no similar terms.
Therefore, let's simplify the expression as follows:
-7(3z + 5t - 3g)
Hence, open the brackets
-7(3z + 5t - 3g) = -21z - 35t + 21g
Therefore, the simplified expression is -21z - 35t + 21g.
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(PLEASE HELP!) Complete the following transactions and explain how they would appear in your register.
• Your beginning balance on October 1 is $542.89.
• You pay Land Electric $43.90 on October 7. (Check #400)
• You deposit your paycheck on October 23 ($7.25/hour for 40 hours/wk for 2 weeks with deductions of FICA (7.65%), federal withholding (12%), and state withholding (8.75%).
• You buy $78.54 plus 6% sales tax in clothes from FitRight on October 24 using your debit card.
Be sure to include in your response:
• the steps you followed to complete your computations.
• the balance as of October 24
•the process for entering the transaction in the registry
Answer:
To complete the transactions in your register:
Beginning balance on October 1: $542.89
On October 7, you pay Land Electric $43.90. This is a check transaction and the check number is 400. To record this in your register, you would subtract $43.90 from your current balance, which would bring your new balance to $498.99.
On October 23, you deposit your paycheck. To calculate your paycheck, you would multiply your hourly wage ($7.25) by the number of hours worked (40) by the number of weeks (2). This would give you a gross pay of $1140. Then, you would calculate the deductions: FICA (7.65%), federal withholding (12%), and state withholding (8.75%). To do this, you would multiply your gross pay by the percentage for each deduction and then subtract that amount from the gross pay. Your final paycheck would be $1140 - $87.41 (FICA) - $136.8 (federal withholding) - $100.65 (state withholding) = $815.34. To record this in your register, you would add $815.34 to your current balance, which would bring your new balance to $1314.33
On October 24, you buy $78.54 in clothes from FitRight and pay 6% sales tax. To calculate the sales tax, you would multiply $78.54 by 0.06 and add that amount to the total cost of the clothes. The total cost of the purchase including sales tax would be $78.54 + $4.71 = $83.25. To record this in your register, you would subtract $83.25 from your current balance, which would bring your new balance to $1231.08
The balance as of October 24 would be $1231.08
In the register
10/1 Beginning balance $542.89
10/7 Check #400 Land Electric -$43.90
10/23 Paycheck $815.34
10/24 Debit FitRight -$83.25
Ending balance $1231.08
Step-by-step explanation:
ABOVE
The quadrilateral DEFG,show. On the coordinate plane below is dilated from the origin by a space factor r= 2/3. Identify the coordinates of the dilated figure D^1 E^1 F^1 G^1 and the draw and label on the coordinate plane
Resizing or changing an object is the process of dilation. Through the use of the specified scale factor, it is a transformation that reduces or enlarges the objects.
What is Dilation Geometry?The pre-image refers to the original figure and the new figure that results from dilation is known as the image. Two forms of dilation exist:An object's size expands when it undergoes expansion.When an object gets smaller, the process is called contraction.The following illustration, which depicts a square dilating, should be noted. However, the square's shape doesn't change; rather, its size is raised.In mathematics, dilation is the process of modifying an object's or shape's size without altering its shape. The form could be a point, a section of a line, a polygon, etc. It should be noted that while the shape can be altered in size, the proportions of its various dimensions and angles never change.The angles are the same when PQR is increased to P'Q'R. After dilatation, the vertices of the PQR have new coordinates.P(1,3) → P' (3,9) (3,9)
Q(3,1) → Q' (9,3) (9,3)
R(1,1) → R' (3,3) (3,3).
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If 7 more than twice a number is 5 less than three times the same number, what is the number?
Answer:
12
SolutionLet X be the unknown number we are supposed to find.
Given information from the question, we can form up an equation:
2X + 7 = 3X - 5
3X - 2X = 7 + 5
X = 12
Therefore the unknown number is 12
what is 36 percent of 128
Answer:
Step-by-step explanation:
36 percent can be written as 36/100. So now the question is 36/100 x 28.
Its easier if you simplify 100 and 28 by a common factor, which im going to use 4 for. So instead you get 36/25 x 7.
36x7=252
252/25=10.08
Answer:
46.08
Step-by-step explanation:
Remember that a percent is always a fraction out of 100, in this case 36/100, so it can also be written as a decimal number, in this case 0.36. Now all you need to do is multiply 128*0.36
Anne has opened up a systematic savings account into which she deposits $500 per month compounded monthly at a rate of 7.8%. How long will it take her to reach $500,000? Round your answer to the nearest tenth of a year.
Help, please!! I need a step-by-step tutorial. Or just the formula and how is set up. Thank you <33
Answer:
Step-by-step explanation:
The formula for calculating the time it takes to reach a target amount with a constant periodic deposit is given by
Time = ln(Target Amount / (Periodic Deposit x (1 + Interest Rate)^0)) / ln(1 + Interest Rate)
In this case, we have Target Amount = 500,000, Periodic Deposit = 500, and Interest rate = 7.8%. Plugging the values into the formula gives
Time = ln(500,000 / (500 x (1 + 0.078)^0)) / ln(1 + 0.078)
Time = ln(500,000 / 500) / ln(1.078)
Time = ln(1,000) / ln(1.078)
Time = 8.98 years
Rounding to the nearest tenth of a year, the answer is 8.9 years.
pls help. I've been stuck on this question and I just cannot find the answer. Pls help
Answer:
(g+f)(x/4) = x^2/16 + 3x/4
Step-by-step explanation:
To find (g+f)(x/4), we must first find the expressions for g(x) and f(x) and then add them together.
g(x) = x^2 + 4
f(x) = 3x - 4
So (g+f)(x) = g(x) + f(x) = x^2 + 4 + 3x - 4 = x^2 + 3x + 0
Now we can substitute x/4 for x in the expression:
(g+f)(x/4) = (x/4)^2 + 3(x/4) + 0
Multiplying it out
(g+f)(x/4) = (x^2/16) + (3x/4) + 0
so (g+f)(x/4) = x^2/16 + 3x/4
A landscaping business is purchasing plants from a nursery to finish a project. It will
cost $14 each to buy each tree and $7 each to buy each bush. The landscaper wishes to
keep the spending to no more than $870. Let t be the number of trees and b be the
number of bushes.
Select the inequality that describes the situation.
14t+7b> 870
O 14t+ 76 2 870
O 14t+7b < 870
O 14t+7b ≤ 870
I think it is the third answer.
Because your problem says 'no more than' so it can't be the fourth one,because it has '≤' which means that the number is lower or equal.
So it is the third one.
Hope I helped you!
Suppose Kristen is researching failures in the restaurants business
The standard deviation of the number of restaurants that failed within a year is 3.46.
What is Normal Distribution?The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.
Given that the probability that an independent restaurant will fail in the first year is 48%. Therefore, the probability can be written as,
p = 48% = 0.48
q = 1-p = 1-0.48 = 0.52
Also, Kristen obtains a random sample of 66 independent restaurants that opened in her city more than one year ago and determines if each one had closed within a year. Therefore, the sample size is 53.
n = 53
Now, the standard deviation can be calculated as,
Standard deviation, σ = √(npq)
= √(53 × 0.48 × 0.52)
= √11.9808
= 3.46
Hence, the standard deviation is 3.46.
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pleasr help me out with this
Answer:
3π - π√2/2 or 7.2 cm-------------------------
According to the given we can state:
AD = BC = AB = 2AO = 2,EO is the perpendicular bisector of AB,Arc AC and arc BD are of equal length.Find arc AB, it is a semicircle of 1 cm radius:
arc(AB) = 1/2 × 2πr = πr = π cmΔAEO and ΔBEO are both isosceles, hence ∠A and ∠B are both 45°.
Find arcs ABD and BAC:
arc(ABD) + arc(BAC) = 2 × 45/360 × 2πr = 1/2 × πr = π cm∠AEB is a right angle since ∠AEO and ∠BEO are both 45°.
Hence ∠CED is also right angle as vertical angle with ∠AEB.
Find the length of EC and ED.
We know AD = BC = 2 cm and ΔAEO is 45° right triangle.
It gives us:
AE = √2Then:
ED = AD - AE = 2 - √2Find arc ECD:
arc(ECD) = 1/4 × 2πr = 1/2 × π(2 - √2) = π - π√2/2 cmThe perimeter is the sum of all the arc measures:
P = π + π + π - π√2/2 = 3π - π√2/2 or 7.2 cm (rounded)Answer:
[tex]\textsf{Perimeter}=3\pi-\dfrac{\pi}{\sqrt{2}}=7.20333649...\; \sf cm[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.4 cm}\underline{Arc length}\\\\Arc length $=r \theta$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in radians.\\\end{minipage}}[/tex]
To convert degrees to radians, multiply the angle in degrees by π/180°.
Arc AB
As arc AB has center O, the radius of arc AB is OA = 1 cm.
As AB is a straight line, ∠AOB is 180° = π.
Therefore, the length of arc AB is:
[tex]\implies AB=r \:\theta=1 \cdot \pi = \pi[/tex]
Arc AC
Triangle BOE is a right triangle with base of 1 cm and height of 1 cm.
Therefore, ∠OBE is 45° = π/4
If arc AC has center B, then the radius is AB = 2 cm.
Therefore, the length of arc AC is:
[tex]\implies AC=r \:\theta=2 \cdot \dfrac{\pi}{4} = \dfrac{\pi}{2}[/tex]
Arc BD
Arc BD is the same as arc AC.
[tex]\implies BC= \dfrac{\pi}{2}[/tex]
Arc CD
As triangle BOE is a right triangle with base of 1 cm and height of 1 cm, the length of its hypotenuse BE is:
[tex]\implies BE=\sqrt{1^2+1^2}=\sqrt{2}[/tex]
As arc AC has center B and radius of AB = 2 cm, then BC is also its radius and therefore BC = 2 cm
Therefore:
[tex]\implies CE=BC-BE[/tex]
[tex]\implies CE=2-\sqrt{2}[/tex]
The arc CD has center E so its radius is CE = 2-√2.
As ∠BEO and ∠AEO are both 45° then ∠AEB is 90°.
According to the vertical angle theorem, ∠CED is also 90° = π/2.
Therefore, the length of arc CD is:
[tex]\implies CD=r \:\theta=(2-\sqrt{2}) \cdot \dfrac{\pi}{2} = \dfrac{(2-\sqrt{2})\pi}{2}[/tex]
Perimeter of the egg
The perimeter of the egg is the sum of the found arcs:
[tex]\implies \textsf{Perimeter}=AB+AC+BD+CD[/tex]
[tex]\implies \textsf{Perimeter}=\pi+\dfrac{\pi}{2}+\dfrac{\pi}{2}+\dfrac{(2-\sqrt{2})\pi}{2}[/tex]
[tex]\implies \textsf{Perimeter}=2\pi+\dfrac{(2-\sqrt{2})\pi}{2}[/tex]
[tex]\implies \textsf{Perimeter}=2\pi+\dfrac{2 \pi}{2}-\dfrac{\sqrt{2}\:\pi}{2}[/tex]
[tex]\implies \textsf{Perimeter}=3\pi-\dfrac{\sqrt{2}\:\pi}{2}[/tex]
[tex]\implies \textsf{Perimeter}=3\pi-\dfrac{\pi}{\sqrt{2}}[/tex]
[tex]\implies \textsf{Perimeter}=7.20333649...\; \sf cm[/tex]
Pls help solve asap!!!!! I don’t understand
-2а + 3 ≥ 6а - 1 > 3а - 10
Answer:
00088n886668hb76u8y687440
A function f(x)=^3√x is transformed into the function g (x) = 2^3√x-4+5. Name and explain in
complete sentences the transformations that occurred to the parent cube root function.
The required transformations are
f(x) is shifted 5 units to the right andf(x) is shifted 5 units upWhat is function?A function is a mathematical equation which shows the relationship between two variables.
What is transformation?Transformation is the performing of the mathematical operations of dilation, translation, relection and rotation on a function.
How to describe the transformation?Given the function [tex]f(x) = 2^{3\sqrt{x} }[/tex] which is transformed into the function [tex]g(x) = 2^{3\sqrt{x - 4}} + 5[/tex], we describe the transformations as follows.
First Since we have x - 4, [tex]f(x) = 2^{3\sqrt{x} }[/tex] is shifted four units to the right. So, we have , [tex]g(x) = 2^{3\sqrt{x - 4}}[/tex].
Also, since 5 is added to [tex]g(x) = 2^{3\sqrt{x - 4}}[/tex]. [tex]g(x) = 2^{3\sqrt{x - 4}}[/tex]. is shifted 5 units up to get [tex]g(x) = 2^{3\sqrt{x - 4}} + 5[/tex],
So, the required transformations are
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how do find the factors of a fraction Example 3 1/2 (unit rate, proportionality)
The factors of a fraction 3 1/2 is 3/2.
What are the factors?Generally, A divisor of an integer n, also known as a factor of n, is an integer m that can be multiplied by another number to generate n. Another name for this concept is a factor of n. One may also state that n is a multiple of m in this particular scenario.
Since 3/2 is a fraction, it does not have any factors since factors are integers that may evenly divide a number. Since 3/2 is a fraction, it does not have any factors. Only integers are capable of having factors; fractions are unable to do so.
To find the factors of a fraction, you can factor the numerator and denominator separately.
In the case of 3 1/2, the numerator 3 is a prime number and cannot be factored further.
However, the denominator 2 can be factored as 2 x 1.
Therefore, the factors of 3 1/2 are: (3 x 1) / (2 x 1),
which can be simplified to 3/2.
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Sea level is defined as having an elevation of 0. A dolphin is 7 meters below sea level.
How should the value 2(-7) be interpreted in this context?
A. a location that is twice as far below sea level as the dolphin
B. a location that is twice as far above sea level as the dolphin
C. a location that is 2 meters closer to sea level than the dolphin
D. a location that is 2 meters farther from sea level than the dolphin
Help…
The value 2(-7) is interpreted that a location that is twice as far below sea level as the dolphin. Option A is the correct option.
What is the meaning of interpretation?
Elucidate, explain, explicate, and expound are some synonyms for interpret. While all of these words mean "to make something clear or understandable," interpretation adds to explain why dealing with something requires imagination, sympathy, or special knowledge.
Given that sea level is defined as having an elevation of 0. A dolphin is 7 meters below sea level.
If the level is below sea level, then it can represent by a negative number.
The statement "A dolphin is 7 meters below sea level." can be written as:
A dolphin is -7 meters far from sea level.
Thus 2(-7) represents a location that is 7 meters below the dolphin's position.
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Solve for x. -2x + 1 = 3x + 16
Answer:
x=-3
Step-by-step explanation:
I showed my work in the picture
Answer:
[tex]\boxed{\sf x=-3}[/tex]
Step-by-step explanation:
[tex]\sf -2x+1=3x+16[/tex]
Subtract 3x from both sides:-
[tex]\sf -2x+1-3x=3x+16-3x[/tex]
[tex]\sf -5x+1=16[/tex]
Subtract 1 from both sides:-
[tex]\sf -5x+1-1=16-1[/tex]
[tex]\sf -5x=15[/tex]
Divide both sides by -5:-
[tex]\sf \cfrac{-5x}{-5}=\cfrac{15}{-5}[/tex]
[tex]\sf x=-3[/tex]
Therefore, x = -3!
______________________
Hope this helps!
Have a great day!
Mick's zoo offers a promotional deal: get a free $3 cotton candy and a free
$2 soda with the purchase of five $12 admission tickets. A group of 20
students will each purchase a ticket. If half of them want cotton candy and
1/4 of them want soda, how many dollars would they save by using the
promotional deal?
(I typed it wrong last time) ✋
Answer: $34.25
Step-by-step explanation:
A Pupil got to school by 7:30 am and left by 2:20pm. How many minutes did he spend in the school? Leave your answer in minutes.
Answer: Timespan is 410 minute(s).
Step-by-step explanation:
Understanding the meanings of words and phrases helps translate into algebraic expressions.
Example: 6 multiplied by the absolute value of 7 less than the cube of a number
6 · |n³ – 7|
? Question
What algebraic expression belongs with each verbal description?
the square root of the ____
of the ____ of a ____ and 11 → √x2² - 11 the ____ of __ times a number and -11 → -2x/11
the __ of the ____ ___ of two times a number and 11 → √2x + 11
Answer:
the square root of difference of the square of a number and 11the quotient of two times a number and -11the sum of the square root of two times a number and 11Step-by-step explanation:
A newspaper article headline reads "One in Five Believe the Path to Riches is the Lottery". A survey was done to test the claim that 20% of adult Americans believe that the lottery is the path to riches. The hypothesis test of H0: p=.2 versus Ha: p>.2 resulted in 0.79 for a right-tailed test. Calculate the p-value and write the correct conclusion in context.
The p-value for right tailed test based on the information will be 0.2147.
What is the p-value?The p-value, under the assumption that the null hypothesis is true, is the likelihood of obtaining results from a statistical hypothesis test that are at least as extreme as the observed results. The p-value provides the smallest level of significance at which the null hypothesis would be rejected as an alternative to rejection points. The alternative hypothesis is more likely to be supported by stronger evidence when the p-value is lower.
In this case, the survey was done to test the claim that 20% of adult Americans believe that the lottery is the path to riches. The hypothesis test of H0: p=.2 versus Ha: p>.2 resulted in 0.79 for a right-tailed test
The Z statistic given to be =0.79 for a right tailed test. Here, by looking aththe distribution table, the p value for Z=0.79 for one tail test is 0.2147.
So, we do not reject null hypothesis and then conclude that data does not provide sufficient evidence that the proportion of Americans who believe path to riches is the lottery is greater than 0.2
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national honors society is selling tickets to a winter wonderland fundraiser. the auditorium holds 300 people. tickets cost 10$ at the door and $7.50 if purchased in advance. the drama club has a goal of selling at least $1,200 worth of tickets to saturdays show write a system of inequalities that can be used to model the scenerio
A system of inequalities that can be used to model the scenario is d + a ≤ 300 and 10d ≥ 1,200.
What is a system of inequalities?A system of inequalities is two or more inequalities that must be proved simultaneously.
A system of inequalities contains at least two linear inequalities in the same variables.
Systems of inequalities are applied when there are a range of solutions and more than one constraint.
Inequalities may include greater than, less than, not equal to, equal to but less than, and equal to but greater than.
The total capacity of people the auditorium can hold = 300
The cost per ticket at the door = $10
The cost per ticket in advance = $7.50
Constraints:Tickets cannot exceed 300
Door tickets must generate at least $1,200
Inequalities:Let the number of tickets sold at the door = d
Let the number of tickets sold in advance = a
10d + 7.5a ≤ 300
10d ≥ 1,200
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Nicole cycled 9 laps on a bicycle path around the lake. If each lap was 9540ft long, what was the total distance she cycled? Write your answers in miles.
Answer:
162 miles.
Step-by-step explanation:
To find the total distance Nicole cycled, we can multiply the number of laps by the length of each lap.
The total distance Nicole cycled is:
9 laps * 9540 ft/lap = 858,600 ft
To convert this distance to miles, we can use the conversion factor that there are 5280 feet in a mile.
858,600 ft / 5280 ft/mile = 162 miles
So the total distance Nicole cycled is 162 miles.
A student says the expression 4+3(2x+2) is equivalent to the expression 6x+10 . As your answer, explain/show why the student is correct. Name each property that you use as you simplify the longer expression.
if im not wrong
4+3(2x+2) multiply since its in parenthesis first
property of mulitplication i think
4+6x+6
property of addition
6x+10
(this should be right)
