log (2x) = -1 => x = 0.05, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Given: log (2x) = -1
Raising both sides to 10, in order to remove the logarithm:
=> [tex]10^{log_{10}(2x)} = 10^{-1}[/tex]
=> 2x = [tex]\frac{1}{10}[/tex] ( as [tex]a^{log_a(x)} = x[/tex])
=> x = [tex]\frac{1}{20} =[/tex] 0.05
Hence, log (2x) = -1 => x = 0.05, by properties of logarithm.
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Please helpppppp hurry
60 points only if right
The coordinates of four points on each of the lines are:
6. (1, 4), (2, 9), (3, 14), (4, 19)
7. (1, 7), (2, 6), (3, 5), (4, 4)
8. (1, 0.5), (2, 0.7), (3, 0.9), (4, 1.1)
9. (1, -1.5), (2, 0), (3, 1.5), (4, 3)
10. (1, 4.5), (2, 5), (3, 5.5), (4, 6)
11. (0, -5), (3, -3), (6, -1), (9, 1)
12. (0.1, 34), (0.2, 38), (0.3, 42), (0.4, 46)
How to Determine the Coordinates that Lie on a Line?The equation of a line in slope-intercept form where m = slope and b = y-intercept is written as:
y = mx + b.
To find the coordinates, plug in x-values to find the corresponding y-values the equation of the line would give.
6. Slope (m) = 5
y-intercept (b) = -1
Equation of the line: y = 5x - 1
Substitute x = 1, 2, 3, and 4, into the equation to find their corresponding y-values:
y = 5(1) - 1
y = 4
y = 5(2) - 1
y = 9
y = 5(3) - 1
y = 14
y = 5(4) - 1
y = 19
The coordinates of four points on the line are:
(1, 4), (2, 9), (3, 14), (4, 19)
7. Slope (m) = -1
y-intercept (b) = 8
Equation of the line: y = -x + 8
Substitute x = 1, 2, 3, and 4, into the equation to find their corresponding y-values:
y = -(1) + 8
y = 7
y = -2 + 8
y = 6
y = -3 + 8
y = 5
y = -4 + 8
y = 4
The coordinates of four points on the line are:
(1, 7), (2, 6), (3, 5), (4, 4)
8. Slope (m) = 0.2
y-intercept (b) = 0.3
Equation of the line: y = 0.2x + 0.3
Substitute x = 1, 2, 3, and 4, into the equation to find their corresponding y-values:
y = 0.2(1) + 0.3
y = 0.5
y = 0.2(2) + 0.3
y = 0.7
y = 0.2(3) + 0.3
y = 0.9
y = 0.2(4) + 0.3
y = 1.1
The coordinates of four points on the line are:
(1, 0.5), (2, 0.7), (3, 0.9), (4, 1.1)
9. Slope (m) = 1.5
y-intercept (b) = -3
Equation of the line: y = 1.5x - 3
Substitute x = 1, 2, 3, and 4, into the equation to find their corresponding y-values:
y = 1.5(1) - 3
y = -1.5
y = 1.5(2) - 3
y = 0
y = 1.5(3) - 3
y = 1.5
y = 1.5(4) - 3
y = 3
The coordinates of four points on the line are:
(1, -1.5), (2, 0), (3, 1.5), (4, 3)
10. Slope (m) = 1/2
y-intercept (b) = 4
Equation of the line: y = 1/2x + 4
Substitute x = 1, 2, 3, and 4, into the equation to find their corresponding y-values:
y = 1/2(1) + 4
y = 4.5
y = 1/2(2) + 4
y = 5
y = 1/2(3) + 4
y = 5.5
y = 1/2(4) + 4
y = 6
The coordinates of four points on the line are:
(1, 4.5), (2, 5), (3, 5.5), (4, 6)
11. Slope (m) = 2/3
y-intercept (b) = -5
Equation of the line: y = 2/3x - 5
Substitute x = 0, 3, 6, and 9, into the equation to find their corresponding y-values:
y = 2/3(0) - 5
y = -5
y = 2/3(3) - 5
y = -3
y = 2/3(6) - 5
y = -1
y = 2/3(9) - 5
y = 1
The coordinates of four points on the line are:
(0, -5), (3, -3), (6, -1), (9, 1)
12. Equation of the line: y = 40x + 30
Substitute x = 0.1, 0.2, 0.3, and 0.4, into the equation to find their corresponding y-values:
y = 40(0.1) + 30
y = 34
y = 40(0.2) + 30
y = 38
y = 40(0.3) + 30
y = 42
y = 40(0.4) + 30
y = 46
The coordinates of four points on the line are:
(0.1, 34), (0.2, 38), (0.3, 42), (0.4, 46)
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Dan will begin advertising his video production business online using a pay-per-click method, which charges $ 30 as an initial fee, plus a fixed amount each time the ad is clicked. Dan estimates that with the cost of 8 cents per click, his ad will be clicked about 150 times per day. Which expression represents Dan's total estimated cost of advertising, in dollars, after x days?
(F) (30+0.08 x) 150
(G) 360 x
(H) 30+1200 x
(I) 30+12 x
Total estimated cost for advertising= 30 +12x
The initial fees for ad is given= $30
And the fixed amount per click = 8 cents
Total number of click ad per day= 150
We know that,
$1= 100 cents
So 8 cents= $0.08
Now we will find the total estimated cost of advertising in dollars for x days.
Total estimated cost= The initial fees + charge per click ×total clicks ×total days
⇒ $30 + 0.08×150×x
⇒ 30+ 12x
Hence the answer is option( I) 30+12x.
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Please Help ASAP! I'll Mark You Brainliest If You're the Best. ;D
Write the function rule g(x) after the given transformations of the graph of f(x) = 9x.
reflection in the x-axis; vertical compression by a factor of 1/3
g(x) = []
The function rule after the given transformation is g(x) = -3x
What is a function?A function is defined as a relation between a set of inputs having one output each.
We have,
f(x) = 9x
Vertical compression = 1/3
Reflection in x-axis.
We know that when we compress a function f(x) by scale factor m
The new compress function is represented:
F(x) = m(f(x))
Reflection across the x-axis changes the sign of the new function.
Now,
With the vertical compression:
F(x) = 1/3 (f(x))
F(x) = 1/3(9x) = 3x
With the reflection in the x-axis:
g(x) = - F(x)
g(x) = -3x
Thus the function rule after the given transformation is g(x) = -3x
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A 42-inch string is to be cut so that one piece is 7 inches longer than the other. what is the length of the shorter piece? the shorter piece has a length of __ inches.
If a 42-inch string is to be cut so that one piece is 7 inches longer than the other, then the shorter piece has a length of 17.5 inches
The length of the shorter piece can be determined by using an algebraic expression.
Any expression consisting of both numbers and letters is considered to be an algebraic expression.
Considering, x to be the length of the shorter piece
As the longer piece is 7 inches longer than the shorter piece, an algebraic expression can be given as,
x + (x + 7) = 42
x + x + 7 = 42
2x + 7 = 42
2x = 42 - 7
2x = 35
x = 35 ÷ 2
x = 17.5
Hence, the length of the shorter piece is calculated to be 17.5 inches.
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Which proportion is a representation of "The number x is 15% of 60?"
Answer:
Im pretty sure its A
Step-by-step explanation:
Solve each inequality using a table.
(Hint: For more accurate results, set ΔTbl=0.001 . )
log x+log (x+1)<3
After solving the given inequality the answer is logx+log₁₀(x+1)<3.
What exactly do we mean by inequality?Inequality is a connection in mathematics that makes a non-equal comparison between two numbers or even other mathematical expressions.It is most commonly used on a number line to compare the size and shape of two numbers.So,
Given: logx+log(x+1)<3Then,
logx+log(x+1)<3 ⇒ logx+log₁₀(x+1)<3Therefore, after solving the given inequality the answer is logx+log₁₀(x+1)<3.
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CF = FB and AE = EB, CB = 33, AB = 22, DE =
Answer:
Im letting yall know rn that the answer actually 19 other guys wildn with 14
Step-by-step explanation:
Colin Edmond has a $60,000 term life policy. The annual premium is $1,060. Colin pays $96.28 monthly.
(Use a thousands comma where applicable.)
Paying monthly, at the end of 12 months Colin pays $___
Colin pays $___ more monthly than he would annually.
Colin pays (to the nearest percent) ___% more by paying monthly than he would paying annually.
Paying monthly premium, at the end of 12 months Colin pays $1,155.36
Colin pays $95.36 more monthly than he would annually.
Colin pays (to the nearest percent) 8.99 % more by paying monthly premium than he would paying annually.
What is monthly and annual premium?Premium is the amount of money one has to pay to insurance companies so that they provide us coverage at the time of need.
If we make payments monthly, the the premium is monthly.
If we pay the amount at the end of the year, then the premium is annual.
Given that Edmond has a $60,000 term life policy. The annual premium is $1,060. Colin pays $96.28 monthly.
Monthly premium of Edmond = $96.28
If he pays monthly, then total payment at the end of 12 months
= 12 *$96.28 = $1155.36
Then total payment at the end of 12 months is greater than the annual premium by = 1,156.36 - 1,060 = 95.36
Percentage of extra amount paid when colin paid monthly
= (extra payment made/ annual payment ) *100 = (95.36/1,060)*100 =8.99 %
Therefore, Colin pays 8.99 % more by paying monthly than he would paying annually.
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The midpoint of AB is M(0, 6). If the coordinates of A are (2, 5), what are the
coordinates of B?
can someone please explain to me how to solve this question
According to the given figure, option (A) and option (F) are correct options which better shows ∠4 ≅ ∠6 respectively.
Let's procced to solve this question.
∠4 ≅ ∠8 by the corresponding angle postulate because two parallel lines is cut by a transversal and ∠4 ≅ ∠8 by the corresponding angle postulate. It's true.
∠6 ≅ ∠8 by the definition of vertical angles. It's true.
and by using the transitive property of congruence that ∠A ≅ ∠B and ∠B ≅ ∠C then ∠A ≅ ∠C.
⇒ ∠4 ≅ ∠6 by the transitive property of congruence.
Hence, option (A) is correct.
Now,
∠2 ≅ ∠6 by the corresponding angle postulate because two parallel lines is cut by a transversal and ∠2 ≅ ∠6 by the corresponding angle postulate. It's true.
∠2 ≅ ∠4 by the definition of vertical angles. It's true.
and by using the transitive property of congruence that ∠A ≅ ∠B and ∠B ≅ ∠C then ∠A ≅ ∠C.
⇒ ∠4 ≅ ∠6 by the transitive property of congruence.
Hence, option (F) is correct.
Therefore, option (A) and option (F) are correct option.
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On the first day of June, there were about 16.81 h of daylight in a city. Five months later, there were about 8.10 h of daylight. What was the
percent decrease?
After five months, the percentage decrease in the daylight is 51.815%
As per the question, On the first day of June, there was 16.81 hours of daylight in a city and five months later, there was 8.10 hours of daylight. We are supposed to find the percent decrease in the daylight.
Percentage increases or decreases are calculated by setting the problem up proportionally.
We are trying to calculate at what percentage of 16.81 is 8.10 first
Let "x" be the percentage required percentage
therefore [tex]\frac{x}{100} =\frac{8.10}{16.81}[/tex]
[tex]x = \frac{8.10*100}{16.81} \\x=\frac{810}{16.81} \\x=48.185%[/tex]
8.10 is approximately 48.185% of 16.81.
So the percentage decrease is [tex]100 - 48.185=51.815[/tex]%
Hence the percentage decrease is 51.815%
Percentage: A ratio or figure stated as a fraction of 100 is called a percentage. It is frequently indicated with the percent sign ("%)").To learn more about percentage, click on the link given below:
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Suppose that a classroom has 8 light bulbs. The probability that each individual light bulb works is 0. 8. Suppose that each light bulb works independently of the other light bulbs. What is the probability that all eight of the light bulbs work?.
0.1678 is the probability that all the light bulbs work
Define probability?
Probability is a branch of mathematics and can be defined as the one which deals with the explanation of the possibility of an event to occur or take place. Probability has a range between 0 to 1. In probability, 0 indicates the impossibility of an event to occur and 1 indicates the certainty of that event to occur or take place.
As the light bulbs are not dependent on each other and work independently, the probability that all eight of the light bulbs will work can be calculated by multiplying the probability of each of the eight light bulbs.
As the probability of each of the eight light bulbs to work = 0.8
probability all the eight light bulbs work = 0.8^8
probability all the eight light bulbs work = 0.1678
Hence, 0.1678 is the probability that all the light bulbs work.
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The perimeter of a rectangular pool is 160 meters. The length of the pool is 20 meters more than its width. What is the length?
The length of the rectangular pool is 50 meters
How to determine the value
The formula for perimeter of a rectangle is expressed as;
Perimeter = 2 ( l + w)
Where:
l is the lengthw is the widthFrom the information given, we have;
Perimeter = 160 meters
Length = 20 + w
Substitute into the formula
160 = 2( 20 + w+ w)
expand the bracket
160 = 2(20 + 2w )
160 = 40 + 4w
collect like terms
160 - 40 = 4w
4w = 120
w = 120/ 4
w = 30 meters
But length = 20 + w = 20 + 30 = 50 meters
Thus, the length of the rectangular pool is 50 meters
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in jacobs neighborhood, 1/4 of the houses are blue, 5/8 of the houses are red and the rest are gray. what fraction of the houses are gray?
Step-by-step explanation:
the common number of 4 and 8 is 8. You multiply 1/4 by 2 and it is equal to 2/8. 2/8+ 5/8= 7/8. 8-7=1. 1/8 of the houses are gray.
Phoebe, Andy and Polly share £270
Phoebe gets three times as much as Andy who gets twice as much as Polly.
Work out how much they each get.
The appropriate choice of ratio will be given by
Polly got £30, Andy got £60, Phoebe got £180
What is ratio?
Ratio determines the comparision among many quantities with the same unit.
Here,
Let Polly got £x
So Andy got £2x and Phoebe got £3(2x) = £6x
Total Amount = £(x + 2x + 6x)
= £9x
By the problem,
9x = 270
x = [tex]\frac{270}{9}[/tex]
x = 30
So Polly got £30,
Andy got £(2 * 30) = £60
Phoebe got £(6 * 30) = £180
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Write each expression as a single natural logarithm. -2 ln 2
Expression as a single natural logarithm of -2 ln 2 is -1.386.
What is natural logarithm?
-2 ln 2
[tex]ln 2^{-2}[/tex] = - 1.386
The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.
The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).
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Evaluate each expression for the given value of the variable.
(x²-x ; x=2)
After evaluating the expression we get 2.
Given, x² ₋ x
Finding the value of an algebraic expression when a specified number is used to replace the variable is known as evaluating the expression. In order to evaluate an expression, we first replace the expression's variable with the given number, then we streamline the expression using the order of operations.
A procedure called evaluation involves analyzing a program critically. It entails gathering and studying data regarding a program's operations, features, and effects. Its objective is to assess a program, enhance its effectiveness, and/or provide information to help with programming decisions.
substitute the value of x =2
2² ₋ 2
= 4 ₋ 2
= 2
hence we get the answer as 12.
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PLEASE HELP
PLEASE SHOW HOW U CHECKED UR WORK
Answer: 2= -8+x
Step-by-step explanation:
Add eight to both sides to get
10=x
CHECK
then plug it in to get
2=-8+10
simplify
2=2
When x = 2 and y = 4 what is the vaule of 7x - y?
Answer: 10
Step-by-step explanation:
x = 2
y = 4
equation :
7x - y
after putting the values to the equation :
7(2x) - (4)
7*2 = 14
14 - 4 = 10
The answer is 10.
Find the amount in a continuously compounded account for the given conditions.
principal: $ 500 ; annual interest rate: 4.9 % ; time: 2.5 years
The amount in a continuously compounded account is $ 565.2 .
If compound interest is calculated and reinvested into the balance of an account across an essentially unlimited number of periods, continuous compounding is the mathematical limit that compound interest can reach.
The amount in the continuously compounded account is given as:
[tex]A=Pe^{rt}[/tex]
Where P is the principal amount, r is the interest rate, and t is the time period in years.
Now, we have
The principal amount, P = $500
Annual interest rate, r = 4.9 % = 4.9 / 100 = 0.049
Time = 2.5 years
Therefore, the amount in a continuously compounded account is:
[tex]\[A=Pe^{rt}\][/tex]
[tex]A = $500 \times e^{0.049 \times 2.5}[/tex]
[tex]A = $500 \times e^{0.049 \times 2.5}[/tex]
[tex]A = $500 \times e^{0.1225}[/tex]
A = $500 × 1.13031912007
A = $ 565.159
A = $ 565.2
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Solve the equation −14 + x = −19 for x.
33
5
−5
−33
Answer:
X=-5 :)
Step-by-step explanation:
Answer:
-5
Step-by-step explanation:
14+5=19, so -14+ -5= -19
Which is an equivalent expression for 4 times d raised to the negative third power all over quantity 22 times d raised to the ninth power end quantity?
whoever gets it right gets a crown
please helppp
Answer:
An equivalent expression for 4 times d raised to the negative third power all over quantity 22 times d raised to the ninth power is 2d⁻³/11d⁻⁹
What is an expression?
An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
What is an exponent?
An exponent can be defined as a mathematical operation that is used to raise a quantity to the power of another and it is generally written as bⁿ.
Translating the word problem into an algebraic expression, we have;
4 times d raised to the negative third power = (4 × d)⁻³ = 4d⁻³
22 times d raised to the ninth power = (22 × d)⁻⁹ = 22d⁻⁹
Next, we would write the equation as a quotient:
Expression = 4d⁻³/22d⁻⁹
Expression = 2d⁻³/11d⁻⁹
Every counting number is a rational number true or false
Reason:
The counting numbers, aka the set of natural numbers, is the set {1, 2, 3, 4, 5, ...} which is the set of positive integers
A value like 5 is the same as 5/1, which shows it is rational.
A rational number is any fraction of two whole numbers (eg: 2/3 and 4/7). The denominator cannot be zero.
Since we can rewrite the 5 as 5/1, it can be done with any counting number to show the natural numbers is a subset of the rational numbers.
Any counting number is rational, but not the other way around.
What is the quotient of 4 over 5 divided by 3 over 4?
Answer:
Step-by-step explanation:
flip 3/4 since we are dividing so we get 4/5 times 4/3 to get 16/15
So we get 1 1/15
Let me know if this was helpful
A prism and two nets are shown below:
Image of a right triangular prism and 2 nets. The triangle bases have base 4, height 3, and diagonal side 5. The length of the prism from the bases is 8.6. Net A has 3 rectangles in a row. The middle one has sides AC and CD. This middle one has triangle ABC on top and identical triangle below. Net B is the same except that the triangle base ABC is on top of the last rectangle which has sides AC and CD. Units are in inches.
Part A: Which is the correct net for the prism? Explain your answer.
Part B: Write the measurements of Sides AB, BC, and CD of the correct net.
Part C: What is the surface area of the prism? Show your work.
Step-by-step explanation:
a) Imagine folding the net into the shape. In this case, Net A can have both triangles fold up, and both rectangles fold in to make the above shape.
b) Side AB on this net is the height of the triangle, 3 inches.
Side BC is the same as the hypotenuse (diagonal) on the triangle, which . is 5 inches.
Side CD is the same as the length of the shape, which is 8.6 inches.
c) Surface area = area of all sides
Triangle = 1/2 bh
= 2*3
= 6 inches squared
There are two triangles, so that adds to 12 inches squared.
Now all of the rectangles:
Left most = 3*8.6
= 25.8 inches squared
Middle = 4*8.6
= 34.4
Right most = 5*8.6
= 43
Now we can add all of this:
43 + 34.4 + 25.8 + 12
= 115.2 inches squared.
This is the surface area of the prism.
A recipe calls for cup of four and teaspoons of cooking oil. At this rate, how many teaspoon
of cooking oil are needed if 1 cup of flour is used? Give your answer in fraction form
Based on the number of cups of flour and the number of teaspoons of cooking oil, if 1 cup of flour is used, the number of teaspoons of cooking oil needed is 2 / 5 teaspoons of cooking oil
How to find the quantity of oil needed?When 5 cups of flour are used, then 2 teaspoons of cooking oil are needed by the recipe.
If there is only 1 cup of flour being used therefore, the number of teaspoons of cooking oil needed will be:
= Number of teaspoons needed for 5 cups / Number of cups of flour needed
= 2 / 5 teaspoons of cooking oil
First part of question is:
A recipe calls for 5 cups of four and 2 teaspoons of cooking oil.
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5
An ant is 10 mm underground and
climbs up 0.25 mm per minute. A
i second ant is 15 mm underground and
climbs up 0.5 mm per minute. After
how many minutes will the first ant be
lower than the second ant?
d
S
Answer:
After 4 minutes
Step-by-step explanation:
After 1 min: Ant 1 is 9.75 mm underground. Ant 2 is 14.5 mm underground.
After 2 min: Ant 1 is 9.5 mm under. Ant 2 is at 14 mm under.
After 3 min: Ant 1 is 9.25 mm under.
After 4 min: Ant 1 is 9 mm under. Ant 2 is 13.5 mm under.
Ant 2 is now closer to the surface than Ant 1.
V.15 Solve a system of equations using any method: word problems GDQ
Write a system of equations to describe the situation below, solve using any method, and fill
in the blanks.
Scouting troops in Webster County are putting on a crab feed to raise money for camp. They
offer a complete crab dinner as well as a vegetarian option. One troop member sold tickets
for 23 crab meals and 34 vegetarian meals, with total receipts of $1,930. Another sold tickets
for 20 crab meals and 38 vegetarian meals, bringing in a total of $1,906. How much do the
two types of tickets cost?
A ticket for a crab meal costs $
and a ticket for a vegetarian meal costs $
The ticket for a crab meal costs $44 and a ticket for a vegetarian meal costs $27
From the question, we are to solve the system of equations.
First, we will form the system of equations
Let x represent the ticket for a crab meal and y represent the ticket for a vegetarian meal
From the given information,
"One troop member sold tickets for 23 crab meals and 34 vegetarian meals, with total receipts of $1,930"
That is,
23x + 34y = 1930 -------------- (1)
Also,
"Another sold tickets for 20 crab meals and 38 vegetarian meals, bringing in a total of $1,906"
20x + 38y = 1906 -------------- (2)
Now, solve the equations simultaneously
Multiply equation (1) 20 and equation (2) by 23
20 × [23x + 34y = 1930
23 × [20x + 38y = 1906
460x + 680y = 38600
460x + 874y = 43838
Subtracting the resulting equations, we get
-194y = -5238
y = -5238/-194
y = 27
Substitute the value of y into equation (1)
23x + 34y = 1930
23x + 34(27) = 1930
23x + 918 = 1930
23x = 1930 - 918
23x = 1012
x = 1012/23
x = 44
Hence, the ticket for a crab meal costs $44 and a ticket for a vegetarian meal costs $27
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Cara has 3 1/4 pounds of ham. If Timothy has 4/5 as much ham as Cara, how many pounds of ham does Timothy have?
Answer: 2.6 or 2 2/3
Step-by-step explanation:
3 1/4 = 3.25
3.25/5 = 0.65
0.65 x 4 = 2.6 or 2 2/3
for heights of full-grown men in a country, state whether you would expect a histogram of the data to be bell-shaped, uniform, skewed left, or skewed right.
Left-Skewed is the answer.
Histograms are a very common method of visualizing data, and that means that understanding how to interpret histograms is a valuable and important skill in virtually any career. There are a number of things to pay particular attention to when reading a histogram.
Bell-Shaped: A histogram with a prominent ‘mound’ in the center and similar tapering to the left and right. One indication of this shape is that the data is unimodal – meaning that the data has a single mode, identified by the ‘peak’ of the curve.
Uniform: A uniform-shaped histogram indicates data that is very consistent; the frequency of each class is very similar to that of the others.
Right-Skewed: A right-skewed histogram has a peak that is left of the center and a more gradual tapering to the right side of the graph.
Left-Skewed: A left-skewed histogram has a peak to the right of the center, more gradually tapering to the left side. It is unimodal, with the mode closer to the right and greater than either mean or median.
Undefined Bimodal: This shape is not specifically defined, but we can note regardless that it is bi-modal, having two separate classes or intervals equally representing the maximum frequency of the distribution.
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