The given statement can be translated into an algebraic expression as: s - 6.
What is an Algebraic Expression?Algebraic expression can be defined as a mathematical statement that expresses a given statement or word problem using numbers, variables, and operation signs.
How to Translate a Phrase or Statement into an Algebraic Expression?To translate a given statement into algebraic expression, the unknown number is usually represented by a letter or alphabet.
In the given statement, "the difference of a number s and 6", s is the unknown number. "Difference" means subtraction. Subtraction would then be represented by the operation sign, "-".
The statement would therefore be translated into an algebraic expression as: s - 6.
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In a certain chemical, the ratio of zinc to copper is 4 to 19 . A jar of the chemical contains of copper. How many 741 grams of zinc does it contain?
Based on the ratio of zinc to copper, and the grams of copper in the jar, the grams of zinc will be 156 grams of Zinc
How to find the grams?The ratio of zinc to copper is 4 to 19 which means that for every 4 grams of Zinc, the chemical will have 19 grams of copper.
The means that if there is 741 grams of copper, the grams of Zinc will be:
= (Grams of Copper x Ratio of Zinc) / Ratio of copper
Solving gives:
= (741 x 4) / 19
= 2,964 / 19
= 156 grams of Zinc
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simplify the following to surd:
√3 + 1/√3 - 1/√27
Answer: -√3
Step-by-step explanation:
√3 + 1√3 - 1√27
√3 + √3 - √(3^2 x 3)
2√3 - 3√3
(2 - 3)√3
-1√3
-√3
a nutrition label states that there are 36g of carbohidrates in each serving. accounts for 12% of daily value. how many grams recommended per day?
There are 36 grams of carbohydrates in each serving. The total number of grams of carbohydrates that should be consumed daily is 300.
Given that,
There are 36 grams of carbohydrates in each serving, according to the nutrition label is 12% of the daily value.
We have to find how many grams are advised each day.
We can write 12% as 0.12.
Let x be the total number of grams of carbohydrates that should be consumed daily.
We can write the equation as
0.12x=36
x=36/0.12
x=3600/12
x=300
Therefore, the total number of grams of carbohydrates that should be consumed daily is 300.
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Another formula for the volume of a right rectangular prism is V=______ where b is the ________ and h is the _______
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
volume of a rectangular prism
Step 02:
geometry:
1. volume of a rectangular prism
- One formula for the volume of a right rectangular prism is V = l w h , where l represents length , w represents width , and h represents height.
- Another formula for the volume of a right rectangular prism is V = Bh , where B is the base area and h is the height.
That is the solution.
Given the volume of storage boxes at 4,800 cubic feet and the cost of storage at 4.5 cents per cubic foot per month, what is the monthly cost of storage?$228$216$206$198None of these choices are correct
Given:
The volume of storage boxes at 4,800 cubic feet
And the cost of storage = 4.5 cents per cubic feet
so, to find the monthly cost of the storge, we will multiply the cost by the volume as follows:
[tex]4.5\cdot4800=21,600\text{ cents}[/tex]convert to dollars by divide by 100
So, the answer will be the monthly cost = $216
Let P be a polynomial function, and P(x)=x4−dx3+8x2−14x+16. If (x−2) is a factor of the polynomial, what is the value of d? Explain or show how you know.
The value of d is x - 2 is a factor of the polynomial function P(x) is 4.5
How to calculate the value of d?The polynomial function is given as
P(x) = x⁴ − dx³ + 8x² −14x + 16
Also, we have the factor of the polynomial to be
x - 2
Set the factor to 0
So, we have
x - 2 = 0
Solve for x
x = 2
If truly, the variable x - 2 is a factor of the polynomial, then the following must be true
P(2) = 0
Start by substituting 2 for x in the equation P(x) = x⁴ − dx³ + 8x² −14x + 16
So, we have
P(2) = (2)⁴ − d(2)³ + 8(2)² −14(2) + 16
Evaluate the exponents
P(2) = (16) − d(8) + 8(4) −14(2) + 16
Evaluate the sum of products
P(2) = −8d + 36
Set to 0
−8d + 36 = 0
So, we have
−8d = - 36
Divide
d = 4.5
Hence, the value of d is 4.5
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Express each of the following in simplest radical form, combining terms where possible.
√25+√45-√20
5√2 is the solution of surd .
What does a math surd mean?
When a square root, cube root, or other root symbol is used in an expression, it is known as a surd. Irrational numbers cannot be stated accurately in decimal form because their decimals do not finish or recur. Surds are used to write irrational numbers precisely.In mathematics, an index is an exponent or power applied to a number or a variable. For instance, the index of 2 in the number 24 is 4.= √25+√45-√20
= √70 - √20
= √50
= 5√2
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Find the exact value of sim,cos, and ya for the angle below. Simply all roots.
Hello!
The angle of 30º is one of the remarkable angles (the others are 45º and 60º).
These angles are the most used in trigonometry, so it's good to memorize it.
Below, I'll explain to you one way to memorize it as a table:
For the sine and cosine, let's fill these spaces with 1 2 3 on the first line, and 3 2 1 on the second line. Then we're going to divide all of that by 2.
When the numerator is 2 or 3 we will put a square root in it.
For the tangent, it will be a little different:
• Tangent of ,30º ,is √3/3
,• Tangent of ,45º ,is 1
,• Tangent of ,60º ,is √3
So, the final answers for your exercise are:Sin 30º: 1/2 or 0.5
Cos 30º: √3/2
Tan 30º: √3/3
find the area of the triangle
Answer:
a=4, b=5, c=3
=4+5+3/2
=12/2
=s=6
Now,
we have,
√s(s-a)(s-b)(s-c)
√6(6-4)(6-5)(6-3)
√6×2×1×3
√36
=6
Proof if the triangle is a right angled triangle or not
To proof if a triangle is a right angled triangle, Pythagoras theorems must be obeyed
Pythagoras theorem states that
[tex]\begin{gathered} c^2=a^2+b^2\text{ where c = hypotenus, i.e the longest sides} \\ a,\text{ and b are the other two sides} \\ \end{gathered}[/tex]nows, lets test the triangle with pythagoras theorem
longest side, c = 97, a = 65, b = 72
[tex]undefined[/tex]Keandra is taking a trip to visit her extended family and makes a stop somewhere during her trip. The distance between Cincinnati, where Keandra started, and Dayton, where Keandra made the stop is 54 miles. The distance between Dayton and Toledo, where Kendra’s family lives is 150.2 miles. How far did Keandra travel on her trip? Round to the correct number of significant figures.
Kendra travel a total of 204.2 miles
What is addition?
Addition is a basic arithmetic process in which we bring 2 or more number to get a new total. it is denoted by '+'
We are given that Kendra is going from Cincinnati to Toledo and she takes a halt at Dayton
Now the distance between Cincinnati and Dayton is 54 miles.
and the she has to travel 150.2 miles more
Hence the distance between Dayton and Toledo is 150.2 miles
To find out total distance travel add the two distances
We get 54+150.2 = 154.2 miles
Hence the total distance traveled by Kendra is 204.2 miles
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find the correct area
The figure consist of triangle, rectangle and semi circle.
Determine the area of figure.
[tex]\begin{gathered} A=\frac{1}{2}\cdot4\cdot8+2\cdot4+\frac{\pi}{8}(4)^2 \\ =16+8+6.28 \\ =30.28 \\ \approx30.3 \end{gathered}[/tex]Thus area of figure is 30.3 meter square.
an auto dealer would like to determine if there is a difference in the braking distance (the number of feet required to go from 60mph to 0mph) of two different models of a high-end sedan. six drivers are randomly selected and asked to drive both models and brake once they have reached exactly 60mph. the distance required to come to a complete halt is then measured in feet. the results of the test are as follows. can the auto dealer conclude that there is a significant difference in the braking distances of the two models? use α
According to the information, it can be concluded that there is no significant difference in the braking distances of the two models.
How to check if there is a wide difference in braking distances?To check if there is a wide difference between the braking distances of the two models we can use several alternatives. One of them is to add all the braking distance results of each car and take the average as shown below:
Model A: 150 + 145 + 160 + 155 + 152 + 153 = 915 / 6 = 152.5Model B: 152 + 146 + 160 + 157 + 154 + 155 = 924 / 6 = 154According to the above, it can be concluded that the braking distance of both models only varies by 2 feet, so it is considered that there is not a great difference in braking distances.
Note: This question is incomplete because there is some information missing. Here is the complete information:
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View the attached image to answer.
The inequality that can be used with the squeeze theorem to calculate the limit of f(x) is [tex]-x^{2} \leq x^{2} cos\frac{1}{x^{2} } \leq x^{2} or -x^{2} \leq f(x)\leq x^{2}[/tex]
Squeeze Theorem,
If f(x)g(x)h(x) for all numbers and at some point x=k we get f(k)=h(k), then g(k) must also be equal to them, according to the squeeze (or sandwich) theorem. Theorem: By "squeezing" sin(x)/x between two better functions and using them to discover the limit at x=0, we can utilize them to obtain tricky limits like sin(x)/x at x=0.
The given function is [tex]f(x) = x^{2} cos(\frac{1}{x} )[/tex]
The range of the cos function is from -1 and 1.
We have,
[tex]-1\leq cos\frac{1}{x^{2} } \leq 1\\[/tex]
Multiplying the above inequality by x^2, we get :
[tex]-x^{2} \leq x^{2} cos\frac{1}{x^{2} } \leq x^{2}[/tex]
The above equation can be rewritten as,
[tex]-x^{2} \leq f(x)\leq x^{2}[/tex]
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Which function is increasing?
A.f(x)=(0.5)^x
B.f(x)=5*x
C.f(x)=(1/15)^x
D.f(x)=(1/5)^x
The answer will be f(x) = 5*. If f′(x)>0 on an open interval, then f is increasing on the interval and If f′(x)<0 on an open interval, then f is decreasing on the interval.
Which function is making f X larger?For a given function, y = F(x), the function is known as an increasing function if the value of y increases as the value of x increases, and the function is known as a decreasing function if the value of y decreases as the value of x increases.The order of the numbers is said to be growing if they are written from smallest to largest, but decreasing order is used when the numbers are written from largest to smallest.You must first compute the derivative, then make it equal to 0, and then determine which zero values the function is negative between in order to determine whether a function is decreasing. In order to determine when the function is negative and, consequently, decreasing, test values on all sides of these.Hence, The answer will be f(x) = 5*. If f′(x)>0 on an open interval, then f is increasing on the interval and If f′(x)<0 on an open interval, then f is decreasing on the interval.
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Please answer this math question below
The probability that at least 1 American will say that they have been decapitated is (C) 0.15.
What do we mean by probability?Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates that the event is impossible and 1 indicates certainty.The likelihood that something will happen can be summed up as probability.We can talk about the likelihood or likelihood of different outcomes when we don't know how an event will turn out.Events that follow a probability distribution are the subject of statistics.So, the probability that at least 1 person will say yes:
We know that 15% will say yes, then:
20/100 × 15 = 3Probability formula: P(E) = favorable events/ Total events
Now, put values and solve as follows:
P(E) = favorable events/ Total eventsP(E) = 3/20P(E) = 0.15Therefore, the probability that at least 1 American will say that they have been decapitated is (C) 0.15.
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An amusement park charges $32 for admission and $6 to park your car. Write an inequality that represents the possible number of people that could go for $166. Solve the inequality. What is the maximum number of people that could go?
The maximum number of people that could go will be 5.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
For the inequality, we have to apply the arithmetic operation in which we do the multiplication of x and apply the inequality for the given data.
It is given that,
An amusement park charges $32 for admission and $6 to park your car.
To ascertain the maximum or lowest values of a scenario with many restrictions, a system of linear inequalities is frequently utilized. Inequalities reflect a limit of what is permitted or achievable rather than a precise quantity.
Suppose that everyone is going in one car and x is the number of persons in the car. The inequality represents the possible number of people that could go for $166 is,
32x+6≤166
32x≤160
x≤160/32
x≤5
Thus, the maximum number of people that could go will be 5.
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Camilla is making fruit punch for a school function. she finds a recipe that calls for 2 parts orange sherbet, 3 parts ginger ale, 4 parts unsweetened pineapple juice, and 4 parts fruit juice. she has 1 1 2 gallons of orange sherbet on hand. how many fluid ounces of the other ingredients will she need to make fruit punch with the same ratio of ingredients as the recipe? (hint: 1 gallon = 128 fluid ounces)
Answer:
8 3/8 gallons
Step-by-step explanation:
What is the equation of g(x)?
O g(x) = 10x - 3
Og(x) = 10x +3
O g(x) = 10x - 3
Og(x) = 10 + 3
The function g(x) of graph has the following equation: g(x) = (10)ˣ⁻³
In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.
Two functions' graphs, f(x) and g, are provided to us (x).
The exponential function f(x) is defined as follows: f(x) = (10)ˣ
Finding the equation for the converted function g is now required of us (x).
The graph of the function g(x) may be shown to travel through the points (3,1), (4,10), (5,100), and so forth.
This indicates that the following is the equation or expression for the function g(x):
g(x) = (10)ˣ⁻³
Given that we have g(x) for x=3 , (10) ³⁻³
When x=4, we obtain g(x) = (10) ⁴⁻³
g(x) = (10)¹
g(x) = 10
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The atrium was built in the shape shown. Find the area and perimeter of the atrium. Round to the nearest whole unit. (Dimensions are in m.)
Total area
A = semi circle + triangle.
1. Area of the semi circle:
[tex]A\text{ = }\frac{\pi\times r^2}{2}=\text{ }\frac{\pi\times3^2}{2}=\text{ 14.14 }[/tex]2. Area of the triangle:
[tex]A\text{ = }\frac{b\times h}{2}[/tex]h = 6; to find base we use the Pythagoras theorem, as follows:
[tex]b=\sqrt[]{10^2-6^2}=\text{ 8}[/tex]Then,
[tex]A\text{ = }\frac{8\text{ x 6}}{2}\text{ = 24}[/tex]Total area = 14 + 24 = 38 m²
Perimeter =
6 (π + 2) + 10 + 8 = 49 m
Solve for x.
2(5x+4) = 7(2)
5x + 4 = 14
What is our next step in solving for x?
A. multiply both sides by 4
C. subtract 4 from both sides
B. add 4 to both sides
D. divide both sides by 4
It's answer option c i.e, subtract 4 from both sides
It's a linear equation 5x + 4 = 7
What is linear equation ?
An equation between two variables that gives a straight line when plotted on a graph or say first degree equation is also known as linear equation.
The equation of first steps is
=> 2(5x+4) = 7(2)
=> 5x + 4 = 14
Now, subtract 4 from 14
=> 5x = 14 - 4
=> 5x = 10
=> x = 10/5
=> x = 5 (Ans.)
It's a final answer for x, but here in question we need to find next step.
Therefore, It's answer option c i.e, subtract 4 from both sides.
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The recipe for a homemade glass cleaner indicates to use a ratio of 1 part vinegar to 4 parts water. Autumn used 2.25 ounces of vinegar and 9 ounces of water. Is the relationship between vinegar and water in the recipe and vinegar and water in Autumn's cleaning solution a proportional relationship?
Combine 1 part distilled vinegar and 10 parts warm water in a spray bottle. Wipe the window down with a gentle, clean, lint-free microfiber cloth or paper towel to remove any dust before applying your solution. Spray the entire surface after that.
How does a proportionate relationship work?Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant.If a table displays a proportional relationship, the ratio of each pair of values can be determined. The table depicts a proportionate relationship if all of those ratios are the same.The equation y = kx represents a proportionate relationship between two quantities y and x that have the same proportionality constant, k.A linear relationship between two amounts or variables is referred to as proportionality in mathematics. Both quantities increase in size when one doubles, and both decrease in size when one drops to a tenth of its original value.To know more about proportional relationship refer to:
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QUICK its the middle one
Answer:
25000000 should be the answer
Step-by-step explanation:
...
Suppose another tire is rolled 100 revolutions and travels about 7,540 inches, what is the radius of this tire?
The radius of the tire given the inches travelled in 100 revolution is 12 inches.
What is the radius?A tire has the shape of a circle. A circle is a bounded object which points from its center is equidistant to its circumference. One revolution is equal to the circumference of the tire. The circumference of a circle is the distance round the circle.
Circumference of a circle = 2πr
Where:
π = pi = 22/ 7r = radiusCircumference = total distance / number of revolutions
7540 / 100 = 75.40 inches
75.40 inches = 22/7 x r x 2
75.40 = 44/7 x r
r = 75.40 x 7/44 = 12 inches
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PLEASE HELP ASAP WILL GIVE 61 POINTS AND BRAINLEST
write an equation in slope intercept form for the lines through points (-2 6) (7 -1)
Y= (-7/9)x + 40/9
Y= (7/9)x + 9/40
Y= (7/9)x + 40/9
Y= (-7/9)x + 9/40
Answer:
[tex]y = - \frac{7}{9} x + \frac{40}{9} [/tex]
Step-by-step explanation:
[tex]m = \frac{ - 1 - 6}{7 - ( - 2)} = - \frac{7}{9} [/tex]
[tex] - 1 = - \frac{7}{9} (7) + b[/tex]
[tex] - \frac{9}{9} = - \frac{49}{9} + b[/tex]
[tex]b = \frac{40}{9} [/tex]
[tex]y = - \frac{7}{9} x + \frac{40}{9} [/tex]
A jewelry store offers Chuck a job paying 40 thousand dollars per year plus 2% of every sale that he makes. The equation models the money Chuck makes if he sells x dollars of jewelry. y= 40000 +0.02x Or Chuck can take the job and make 60 thousand dollars per year. How much jewelry does Chuck need to sell so that the first option is more profitable? Construct a viable argument to support your solution.
Chuck needs to sell more than 1000000 dollars of Jewelry.
In this question, a jewelry store offers Chuck a job paying 40 thousand dollars per year plus 2% of every sale that he makes.
We have been given the equation models the money Chuck makes if he sells x dollars of jewelry y= 40000 +0.02x
Also, he has second option that he can take the job and make 60000 dollars per year.
We need to find the amount of jewelry Chuck needs to sell so that the first option is more profitable.
We need to find the value of x for which y > 60000
so we get an inequality.
i.e., 40000 +0.02x > 60000
0.02 x > 60000 - 40000
0.02x > 20000
x > 1000000
Therefore, Chuck needs to sell more than 1000000 dollars of Jewelry.
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Melissa has two chickens. Chicken A produces 3 eggs every 2 days. Chicken B produces 5 eggs every 3 days. In each case, the number of eggs produced is proportional to the number of days. What is the constant of proportionality for each chicken? Round your answers to the nearest hundredth if necessary.
Proportionality constant for chicken B is greater. The proportionality constant for chicken A is 1.5 and that of chicken B is 1.67.
Chicken A produces 3 eggs every 2 days.
Chicken B produces 5 eggs every 3 days.
Let k₁ and k₂ be the constant of proportionality for chicken A and chicken B respectively.
According to question,
For chicken A, 3 eggs in 2 days
3 = k₁ 2
k₁ = 1.5
For chicken B, 5 eggs in 3 days
5 = k₂ 3
k₂ = 5/3 = 1.66
Thus, Proportionality constant for chicken B is greater. The proportionality constant for chicken A is 1.5 and that of chicken B is 1.67.
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17+ 20 ÷ 4-5 = [?].
Answer:
Step-by-step explanation:
17+20/4-5
17+5-5
17-10
17
ramel borrows $4,000 from his local credit union, to be repaired with3.75% annual interest over 5 years, How Much money will ramel have paid back after 5 years
assuming is simple interest
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$4000\\ r=rate\to 3.75\%\to \frac{3.75}{100}\dotfill &0.0375\\ t=years\dotfill &5 \end{cases} \\\\\\ A=4000[1+(0.0375)(5)] \implies A=4000(1.1875)\implies A = 4750[/tex]
80% of a number is equal to two-thirds of a second number.
The whole number ratio of the first number to the second number in its lowest terms is x:y
What is the value of x−y
?
Answer:
-1
Step-by-step explanation:
Let's assume 100 as the number. 80% of that number is 80. That's A. And since 80 is two-thirds of that number, the second number has to be 120. Simplifying that would give 5/6. 5-6 = -1
Answer: 1:1.2
1-1.2= -0.2
Step-by-step explanation:
x = first number
y = second number
80/100*x (80 percent of one number)
2/3*y (two thirds of the second number)
equating
80/100*x=2/3*y
= 1.2=y
substituting:
80/100*x = 2/3 * 1.2
= x=1
substituting the value of x in the original equation
80/100 * 1 = 2/3 * y
= y=1.2
so, x=1, y=1.2
x:y
=1:1.2
x-y= 1 - 1.2 = -0.2
