Explanation:
We have to find 5% of the original cost first:
[tex]21.99\times\frac{5}{100}=21.99\times0.05=1.0995[/tex]And then add it to the original price:
[tex]21.99+1.0995=23.0895[/tex]Since it's a price, we have to round this result to the nearest hundredth
Answer:
The new price is $23.09
I need help with question 4-8, can you please help me?Use f(X) as g(X) for question 5 and 6
Question 4
The x values for which g(x) = 3
From the graph, we have this value to be:
[tex]0\text{ }\leq\text{ x }\leq\text{ 2}[/tex]Question 5
f(x) = 6, What is x?
From the graph, we can determine the value of x corresponding to f(x)= 6:
[tex]x\text{ = }4[/tex]Question 6:
f(x)= 0, What is x?
From the graph, we can determine the value of x corresponding to f(x) = 0
[tex]x\text{ = 7}[/tex]Question 7
The domain of the function:
The domain is the set of allowable inputs.
[tex]\lbrack0,\text{ 12\rbrack}[/tex]Question 8
The range is the set outputs
[tex]\lbrack0,\text{ 6\rbrack}[/tex]Don’t get part b of the question. Very confusing any chance you may help me with this please.
To solve this problem, first, we will solve the given equation for y:
[tex]\begin{gathered} x=3\tan 2y, \\ \tan 2y=\frac{x}{3}, \\ 2y=\arctan (\frac{x}{3}), \\ y=\frac{\arctan(\frac{x}{3})}{2}=\frac{1}{2}\arctan (\frac{x}{3})\text{.} \end{gathered}[/tex]Once we have the above equation, now we compute the derivative. To compute the derivative we will use the following properties of derivatives:
[tex]\begin{gathered} \frac{d}{dx}\arctan (x)=\frac{1}{x^2+1}, \\ \frac{dkf(x)}{dx}=k\frac{df(x)}{dx}. \end{gathered}[/tex]Where k is a constant.
First, we use the second property above, and get that:
[tex]\frac{d\frac{\arctan(\frac{x}{3})}{2}}{dx}=\frac{d\arctan (\frac{x}{3})\times\frac{1}{2}}{dx}=\frac{1}{2}\frac{d\arctan (\frac{x}{3})}{dx}\text{.}[/tex]Now, from the chain rule, we get:
[tex]\frac{dy}{dx}=\frac{1}{2}\frac{d\text{ arctan(}\frac{x}{3})}{dx}=\frac{1}{2}\frac{d\arctan (\frac{x}{3})}{dx}|_{\frac{x}{3}}\frac{d\frac{x}{3}}{dx}\text{.}[/tex]Finally, computing the above derivatives (using the rule for the arctan), we get:
[tex]\frac{dy}{dx}=\frac{1}{2}\frac{\frac{1}{3}}{\frac{x^2}{9}+1}=\frac{1}{6}(\frac{1}{\frac{x^2}{9}+1})=\frac{3}{2(x^2+9)}.[/tex]Answer:
[tex]\frac{3}{2(x^2+9)}.[/tex]the mean salary offered to students who are graduating from coastal state university this year is $24,215, with a standard deviation of $3712. A random sample of 80 coastal state students graduating this year has been selected. What is the probability that the mean salary offer for these 80 students is $24,250 or more?
Given that the mean and standard deviation of the population are $24,215 and $3712 respectively,
[tex]\begin{gathered} \mu=24215 \\ \sigma=3712 \end{gathered}[/tex]The sample size taken is 80,
[tex]n=80[/tex]Consider that the salary of students in the sample is assumed to follow Normal Distribution with mean and standard deviation as follows,
[tex]\begin{gathered} \mu_x=\mu\Rightarrow\mu_x=24215 \\ \sigma_x=\frac{\sigma}{\sqrt[]{n}}=\frac{3712}{\sqrt[]{80}}\approx415 \end{gathered}[/tex]So the probability that the mean salary (X) is $24250 or more, is calculated as,
[tex]\begin{gathered} P(X\ge24250)=P(z\ge\frac{24250-24215}{415}) \\ P(X\ge24250)=P(z\ge0.084) \\ P(X\ge24250)=P(z\ge0)-P(0From the Standard Normal Distribution Table,[tex]\begin{gathered} \emptyset(0.08)=0.0319 \\ \emptyset(0.09)=0.0359 \end{gathered}[/tex]So the approximate value for z=0.084 is,
[tex]\emptyset(0.084)=\frac{0.0319+0.0359}{2}=0.0339[/tex]Substitute the value in the expression,
[tex]\begin{gathered} P(X\ge24250)=0.5-0.0339 \\ P(X\ge24250)=0.4661 \end{gathered}[/tex]Thus, there is a 0.4661 probability that the mean salary offer for these 80 students is $24,250 or more.
i am stuck on this question. any help would be greatly appreciated
step 1
determine the slope of the given line
y=(3/5)x-17
The slope is m=3/5
Remember that
If two lines are parallel, then their slopes are equal
that means
The slope of the parallel line to the given line is m=3/5 too
step 2
Find out the equation of the line parallel to the given line
y=mx+b
we have
m=3/5
point (-5,15)
substitute and solve for b
15=(3/5)(-5)+b
15=-3+b
b=18
therefore
The equation of the line is
y=(3/5)x+18helpppppppppp!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
(f o g)(x) = 8x³ + 2x - 6
(g o f)(x) = 2x³ + 2x - 12
Step-by-step explanation:
f(x) = x³ + x - 6; g(x) = 2x
(f o g)(x) = f(g(x))
f(g(x)) = (2x)³ + (2x) - 6
f(g(x)) = 8x³ + 2x - 6
(g o f) = g(f(x))
g(f(x)) = 2(x³ + x - 6)
g(f(x)) = 2x³ + 2x - 12
I hope this helps!
How many different lineups can Coach Lay create using 10 girls to fill 5 spots on the basketball court. Positions do not matter.
This is the formula for combinations
In this case, n = 10 and k = 5
C = 10!/(10-5)!(5)! = 3628800/(120)(120) = 3628800/14400 = 252
Answer:
252 different line u
The difference of 4R and 108
The expression of the mathematical statement given as the difference of 4R and 108 is |4R - 108|
How to rewrite the mathematical statement as an expression?From the question, the mathematical statement is given as
The difference of 4R and 108
In mathematics, the difference of numbers or expressions implies that we subtract one of the numbers from the other number or expression
This in other words means that difference means subtraction
So, we have the following representation
The difference of 4R and 108 ⇒ 4R - 108
However, we do not know the bigger number.
So, the expression can be rewritten as
The difference of 4R and 108 ⇒ 108 - 4R
So, we have two options
4R - 108 and 108 - 4R
When both expressions are combined, we introduce the absolute value symbol i.e. |.....|
|4R - 108|
Hence, the expression represented by the statement is |4R - 108|
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A teacher gets snacks for the class for $50 and also purchases 6 boxes of pencils. The teacher spent a total of $62. Write an equation that models the situation with x, the cost of one box of pencils.
Answer:
50 + 6x = 62
Explanation:
If x represents the cost of one box of pencils and the teacher got snacks for $50, purchased 6 boxes of pencils, and spent a total of $62, we can write the equation that models the above situation as shown below;
[tex]50+6x=62[/tex]Which of the following shapes is the cross-section for a cylinder?A. SquareB. TriangleC. CircleD. Pentagon
Solution:
Concept:
The vertical cross-section of a cylinder is a rectangle, and the horizontal cross-section is a circle.
From the explanation above,
The final answer is CIRCLE
OPTION C is the right answer
gabrielle opened a savings account and deposited $800.00 . the account earns 2% interest compounded annually.
We need the actual question. I can write the compounded interest accrued value equation for this, but if no question about number of years the deposit is kept, there is no question to be solved. Please continue the formulation of the question. What is it we need to find? what amount of money she needs to collect?
The formula for accrued value with compounded interest would be written as:
[tex]A=P(1+r)^t[/tex]with the information on the account, we can write it as:
[tex]A=800(1+0.02)^t[/tex]but we cannot do anything with it unless you give:
1) the time to keep the account collecting interest,
OR
2) the total amount of money she needs to obtain.
What is the value of that new bicycle she wants?
Well, you have the equation needed. If you don't give me more info on what is needed, I cannot help you solve the equation. We need an extra piece of information.
The information now provided is that the person wants to keep the savings account for 2 years. So we use t = 2 in the equation above to obtain the answer:
[tex]A=800(1.02)^2=832.32[/tex]At the end of the two years she will have a total of $832.32
the lettuce i have is 25 calories per serving. serving size is 85 grams. i had 27 grams . how many calories would this be? if you don’t know , don’t respond
There would be 91.8 calories in 27 grams.
Define unitary method.The unitary approach involves determining the value of a single unit, from which we can calculate the values of the necessary number of units. We must first determine the number of objects at the unit level in order to answer questions based on the unitary technique, after which we must determine it for higher values. For instance, if the price of 5 chocolates is $10, it is preferable to first determine the price of 1 chocolate in order to get the price of 6 chocolates. Once we get the price for 6 chocolates, we multiply it by 6.
Given,
Calories per serving = 25
Serving size = 85 grams
Calories per serving using unitary method:
Dividing,
[tex]\frac{85}{25}[/tex]
3.4
Calories per serving using unitary method is 3.4 calories.
Now, we have 27 grams,
Multiplying:
27 (3.4)
91.8
There would be 91.8 calories in 27 grams.
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Jordan owns a house painting service. For each house, they charge $95 plus $60 per hour of work. A linear equation that expresses the total amount of money Jordan earns per house is y=60x+95. What are the independent and dependent variables? What is the y-intercept and the slope?
Answer:
The slope is 60
The y intercept is 95
The independent variable is x (the number of hours)
The dependent variable is y (The amount earned.)
Step-by-step explanation:
How do I solve:7/8+y= -1/8
We are given the following equation
[tex]\frac{7}{8}+y=-\frac{1}{8}[/tex]Let us solve the equation for variable y
Our goal is to separate out the variable y
Subtract 7/8 from both sides of the equation.
[tex]\begin{gathered} \frac{7}{8}-\frac{7}{8}+y=-\frac{1}{8}-\frac{7}{8} \\ y=-\frac{1}{8}-\frac{7}{8} \end{gathered}[/tex]Since the denominators of the two fractions are the same, simply add the numerators.
[tex]\begin{gathered} y=-\frac{1}{8}-\frac{7}{8} \\ y=\frac{-1-7}{8} \\ y=\frac{-8}{8} \\ y=-1 \end{gathered}[/tex]Therefore, the value of y is -1
find the value of n in each equation the name the property that is used
14.
n=11+0
Add numbers ( 11+ 0 = 11)
n=11
Addition property
May I please get help with this. I have tried multiple times but still could not get the correct or at least accurate answers
step 1
Find out the value of y
we have that
y+75=180 degrees ------> by same side ineterior angle
g(x)= x^2 + 2hx) = 3x - 2Find (g+ h)(-3)
Given the following functions;
f(x) = x^2 + 2
g(x) = 3x - 2
(g+h)(x) = g(x)+h(x)
(g+h) = x^2 + 2 + 3x - 2
(g+h) = x^2+3x + 2-2
(g+h) = x^2 + 3x
To get (g+h) (-3), we will subtitute x = -3 into the resulting function as shown;
(g+h) (-3) = (-3)^2+3(-3)
(g+h) (-3) = 9 - 9
(g+h) (-3) = 0
Hence the value of the expression (g+h) (-3) is 0
What is the y-intercept of 4x + 8y = 12?
Find the measure of all the angles if m<2 = 76°
By opposite angles we know that:
[tex]\begin{gathered} m1\measuredangle=m3\measuredangle \\ m2\measuredangle=m4\measuredangle \\ m5\measuredangle=m7\measuredangle \\ m8\measuredangle=m6\measuredangle \end{gathered}[/tex]By corresponding angles we know that
[tex]\begin{gathered} m5\measuredangle=m1\measuredangle \\ m2\measuredangle=m6\measuredangle \\ m4\measuredangle=m8\measuredangle \\ m7\measuredangle=m3\measuredangle \end{gathered}[/tex]by complementary angles we know that
[tex]\begin{gathered} m1\measuredangle+m2\measuredangle=180º \\ m1\measuredangle+76º=180º \\ m1\measuredangle=104º \end{gathered}[/tex]Using the correspondence and opposite angles:
[tex]\begin{gathered} m1\measuredangle=m3\measuredangle=m5\measuredangle=m7\measuredangle=104º \\ m2\measuredangle=m4\measuredangle=m6\measuredangle=m8\measuredangle=76º \end{gathered}[/tex]what is 234,181 rounded to the nearest thousand
The figure 234,181 has the digit 4 in the thousands place.
Rounding to the nearest thouand would therefore be
234,000
This is because, the digit 1 that follows is not up to 5 and therefore is insignificant. So the digit 1 and the others after it are all rounded up to zeros.
Lisa's rectangular living room is 15 feet wide. If the length is 7 feet less than twice the width, what is the area of her living room?
345ft²
1) Since we have the following data then we can write it down:
width: 15 ft
length: 2w-7
2) And we can write out the following equation regarding that the area of a rectangle is given by:
[tex]S=l\cdot w[/tex]We can plug into that the given data:
[tex]\begin{gathered} S=15(2(15)-7)) \\ S=15(30-7) \\ S=15\cdot23 \\ S=345 \end{gathered}[/tex]Notice we have used the FOIL acronym. And the PEMDAS order of operations prioritizing the inner parentheses.
3) So we can state that the area of her living room is 345ft²
Which equation shows a proportional relationship? options: O y = x O y + 1 = 7x O y - 2 = x + 8 O x = y + 5
A proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if:
y = kx
for some constant k , called the constant of proportionality . This means that as x increases, y increases and as x decreases, y decreases-and that the ratio between them always stays the same.
From the given options, the baove property is satisfied by,
[tex]y=\frac{2}{3}x[/tex]Thus, the correct option is A.
I need to use substitution to solve each system of equations then use ordered pairs
From the given question
There are given that the equation
[tex]\begin{gathered} 2x+5y=38\ldots(1) \\ x-3y=-3\ldots(2) \end{gathered}[/tex]Now,
From the equation (1)
[tex]\begin{gathered} 2x+5y=38 \\ 2x=38-5y \\ x=\frac{38}{2}-\frac{5}{2}y \\ x=19-\frac{5}{2}y\ldots(3) \end{gathered}[/tex]Then,
Put the equation (3) into the equation (2)
So,
[tex]\begin{gathered} x-3y=-3 \\ 19-\frac{5}{2}y-3y=-3 \\ 38-5y-6y=-6 \\ 38-11y=-6 \\ -11y=-6-38 \\ -11y=-44 \\ y=4 \end{gathered}[/tex]Then,
Put the value of y into the equation (3)
So,
[tex]\begin{gathered} x=19-\frac{5}{2}y \\ x=19-\frac{5}{2}(4) \\ x=19-\frac{20}{2} \\ x=19-10 \\ x=9 \end{gathered}[/tex]Hence, the value of x is 9 and y is 4.
Comment on the similarities and differences for the graph of every polynomial function.
There are different graphs of polynomial functions. In terms of shape, it can go from a straight line, slanting line, parabola, to curvy graphs especially when we are graphing polynomial functions with degrees 3 or higher.
See examples below:
However, what is similar to these graphs is that each graph is continuous or has no breaks and the domain of every polynomial function is the set of all real numbers.
Find the missing number so that the equation has infinitely many solutions.
we have the equation
-2x-9=-2x-?
Remember that
If in a system of two linear equations, we have two identical lines
then
The system has infinite solutions
therefore
the missing number is 9
-2x-9=-2x-9Find the solution(s) to the system of equations represented in the graph.0, −2) and (2, 0) (0, −2) and (−2, 0) (0, 2) and (2, 0) (0, 2) and (−2, 0)
Solution
The solution is the point of intersection.
Therefore, the answer is
[tex](0,2)\text{ and }(-2,0)[/tex]The measure of angle c below is(Hint: Slide 2)95/640
we know that
The sum of the interior angles in any triangle must be equal to 180 degrees
In the right triangle of the figure
we have
c+d+64=180
we have that
d=90 degrees (right angle)
substitute
c+90+64=180
c+154=180
c=180-154
c=26 degrees
check the image I got y=-xsqrt3/3 but I want to double check
Answer:
To convert the polar equation to a rectangular equation .
Given polar equation is,
[tex]\theta=\frac{11\pi}{6}[/tex]we know the convertion of polar coordinates (r,theta) to rectangular equation as,
[tex]\begin{gathered} x=r\cos \theta \\ y=r\sin \theta \end{gathered}[/tex]we get,
[tex]\theta=\frac{11\pi}{6}=(2\pi-\frac{\pi}{6})[/tex]Substitute this in the above equation we get,
[tex]\begin{gathered} x=r\cos (2\pi-\frac{\pi}{6}) \\ \\ y=r\sin (2\pi-\frac{\pi}{6}) \end{gathered}[/tex]Solving we get,
[tex]\begin{gathered} x=r\cos (\frac{\pi}{6}) \\ \\ y=-r\sin (\frac{\pi}{6}) \end{gathered}[/tex]we get,
[tex]x=r(\frac{\sqrt[]{3}}{2})[/tex][tex]y=-r(\frac{1}{2})[/tex]Substitute r=-2y in x we get,
[tex]x=-2y(\frac{\sqrt[]{3}}{2})[/tex][tex]y=-\frac{x}{\sqrt[]{3}}[/tex][tex]y=-\frac{\sqrt[]{3}x}{3}[/tex]The required rectangular form of the given plar equation is,
[tex]y=-\frac{\sqrt[]{3}x}{3}[/tex]Is 5/6 equivalent to 0.832
Answer: No
Step-by-step explanation:
1 divided by 6 would be 16 and 4/6. So you would have to multiply 16 and 4/6 by 5, add them together, and then divide by 10 to get the decimal. 16 * 5 = 80. 4/6 * 5 = 20/6. 80/10 = 8. 20/6 divided by 10 = 10/6. 8+10/6 is not equal to .832
Adding mixed fractions (A)1 1/14 + 3 1/14 =
Explanation:
To add mixed fractions we have to follow these steps:
[tex]1\frac{1}{14}+3\frac{1}{14}=[/tex]1. Add the whole numbers together
[tex]1+3=4[/tex]2. Add the fractions
[tex]\frac{1}{14}+\frac{1}{14}=\frac{2}{14}=\frac{1}{7}[/tex]3. If the sum of the fractions is an improper fraction then we change it to a mixed number and add the whole part to the whole number we got in step 1.
In this case the sum of the fractions results in a proper fraction, so we can skip this step.
Answer:
The result is:
[tex]4\frac{1}{7}[/tex]
how do I use a right triangle to write the following expression as an algebraic expression?
So, we want to express the following:
[tex]\sec (\sin ^{-1}(\frac{x}{\sqrt[]{x^2+81}}))[/tex]As an algebraic expression.
If:
[tex]\begin{gathered} \sin ^{-1}(\frac{x}{\sqrt[]{x^2+81}})=\theta \\ \text{Then,} \\ \sin (\theta)=\frac{x}{\sqrt[]{x^2+81}} \end{gathered}[/tex]We could draw the following triangle:
Remember that the secant function relations the hypotenuse of the triangle and the adjacent side of the triangle. So first, we should find the adjacent side using the pythagorean theorem:
[tex]\begin{gathered} a^2=(\sqrt[]{x^2+81})^2-x^2 \\ a^2=x^2+81-x^2 \\ a^2=81\to a=9 \end{gathered}[/tex]Therefore, the adjacent side is 81. And, the value of:
[tex]\sec (\sin ^{-1}(\frac{x}{\sqrt[]{x^2+81}}))[/tex]Is:
[tex]\sec (\sin ^{-1}(\frac{x}{\sqrt[]{x^2+81}}))=\frac{\sqrt[]{x^2+81}}{9}[/tex]