Answers
Using a system of equations, it is found that her normal week is of €285.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: Her normal hours.Variable y: Her time and a half hours.The first equation, considering the first sentence, is given by:
x + 8y = 375.
The second equation, considering the second sentence, is given by:
x + 4y = 330.
Then the system is:
x + 8y = 375.x + 4y = 330.Multiplying the second equation by -2, the system is:
x + 8y = 375.-2x - 8y = -660.Adding the equations, we have that her normal week is given by:
x = 660 - 375 = €285.
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Related Questions
Which algebraic expression is equivalent to the expression below 5(5x + 7) - 6 (4- 2x)
Answers
The algebraic expression equivalent to the expression 5(5x + 7) - 6 (4- 2x) is 37x + 11.
What is the equivalent of the expression?Given the expression; 5(5x + 7) - 6 (4- 2x)
We expand and collect like terms.
5(5x + 7) - 6 (4- 2x)
25x + 35 -24 + 12x
We collect like terms
25x + 12x + 35 - 24
37x + 11
Therefore, the algebraic expression equivalent to the expression 5(5x + 7) - 6 (4- 2x) is 37x + 11.
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Find the z-scores for the two normally distributed random variables, measured using different units of length.
a) x = 22 in, where X comes from N (15, 2.5)
b) y = 55.88 cm, where Y comes from N (38.1, 6.35)
Answers
Using the normal distribution, the z-scores are given as follows:
a) Z = 2.8.
b) Z = 2.8.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.Item a:
The parameters are:
[tex]\mu = 15, \sigma = 2.5[/tex]
Hence the z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{22 - 15}{2.5}[/tex]
Z = 2.8.
Item b:
The parameters are:
[tex]\mu = 38.1, \sigma = 6.35[/tex]
Hence the z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{55.88 - 38.1}{6.35}[/tex]
Z = 2.8.
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ped
Complete question :
Juan is rewriting the expression 12 d minus 26 c as a product. Which statements about the expression are accurate and relevant to his rewriting the expression? Select two options. The GCF of the numbers in each term in the expression is 2. The GCF of the numbers in each term in th
Answers
So the correct statement is:
" The GCF of the numbers in each term in the expression is 2"
How to rewrite the expression as a product?Here we have the expression:
12d - 26c
To rewrite ti as a product, we need to find the greatest common factor between 12 and 26.
The decomposition of these two numbers is:
12 = 2*2*3
26 = 2*13
The greatest common factor between the two numbers is 2, then we can rewrite:
12d - 26c = 2*(6d - 13c)
So the correct statement is:
" The GCF of the numbers in each term in the expression is 2"
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A bank gives an interest of 12% per annum.How long will it take to double one's interest?
Answers
Divide 72 by your rate and you get the amount of years.
A bag contains 240 marbles that are either red, blue, or green. The ratio of red to blue to green marbles is 5:2:1. If one-third of the red marbles and two-thirds of the green marbles are removed, what fraction of the remaining marbles in the bag will be blue?
A. 6/17
B. 1/2
C. 6/13
D. 7/18
Answers
The fraction of the remaining marbles in the bag will be blue is 6/17.
What fraction of the remaining marbles in the bag will be blue?The first step is to determine the initial number of marbles in the bag:
Initial number of red marbles in the bag : (5/8) x 240 = 150
Initial number of blue marbles in the bag : (2/8) x 240 = 60
Initial number of green marbles in the bag : 240 - 150 - 60 = 30
Number of red marbles remaining after 1/3 is removed = (1 - 1/3) x 150
2/3 x 150 = 100
Number of green marbles remaining after 2/3 is removed = (1 - 2/3) x 30
1/3 x 30 = 10
Total number of marbles now in the bag : 100 + 10 + 60 = 170
Fraction of blue marbles = 60 / 170 = 6/17
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What is the area of this parallelogram?
h = 2 in.
A
b= 10 in.
in.
in²
Answers
The area of a parallelogram is 20 inches square
What is the area of a parallelogram?
The area of a parallelogram is the base of the shape multiplied by the height
Area of parallelogram = b × h
Where h = height = 2 In
base = 10 in
Area = 2 × 10
Area = 20 Inches square
Thus, the area of a parallelogram is 20 inches square
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If sin(theta)=0.7 what is tan(theta)?
Answers
The value of tan theta from the given. expression is 7/√51
Trigonometry identityTrigonometry identity are expressions written in terms of sine, cosine and tangents.
Given the following trigonometry values as shown:
sin(theta)=0.7
Convert the decimal to fractions
sin(theta)= 7/10
According to SOH CAH TOA;
sin theta = opp/hyp
Determine the adjacent
adj = √hyp²-opp²
Substitute the values;
adj = √10²-7²
adj = √100-49
adj = √51
Determine the value of tan theta
tan(theta) = opp/adj
Substitute
tan(theta) = 7/√51
Hence the value of tan theta from the given. expression is 7/√51
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In math class, James, Hadley, and Gwen were challenged to go stand on the field in a random location and find the distance between themselves using only one length. They were also each given a protractor to find the angle between each other. Using this diagram, solve for the missing side lengths of the triangle. Round to the nearest hundredth. A triangle where James, Hadley, and Gwen are labelled on the vertices. The angle of James is 61 degrees, Hadley is 73 degrees, and Gwen is 46 degrees. The one length that is labelled is between James and Hadley and measures at 15 meters. Gwen to Hadley is what? Gwen to James is what?
Answers
The interior angles of the triangle of 61°, 73°, and 46°, and the distance from James to Hadley of 15 meters gives;
Gwen to Hadley ≈ 18.24 metersGwen to James ≈ 19.94 metersHow can the distances between the students be found?The given angles are;
At James's location; 61°
At Hadley's location; 73°
At Gwen's location; 46°
The distance between James and Hadley = 15 meters
The angle facing the distance between James and Hadley is the angle at Gwen, 46°
The angle facing the distance between Gwen and James is the angle at Hadley, 73°
The angle facing the distance between Gwen and Hadley is the angle at James, 61°
The angle that faces the 15 meter length is the angle at Gwen, which is 46°
By the rule of sines, the distance from Gwen to Hadley is therefore;
[tex] \frac{15}{sin( 46 ^ \circ)} = \frac{Gwen \: to \: Hadley}{sin( 61 ^ \circ)} [/tex]
Which gives;
[tex] Gwen \: to \: Hadley= \frac{15 \times sin( 61 ^ \circ) }{sin( 46 ^ \circ)} \approx 18.24[/tex]
Gwen to Hadley ≈ 18.24 metersSimilarly, we have;
[tex] \frac{15}{sin( 46 ^ \circ} = \frac{Gwen \: to \: James}{sin( 73 ^ \circ)} [/tex]
Therefore;
[tex] Gwen \: to \: James = \frac{15 \times sin( 73 ^ \circ) }{sin(46 ^ \circ)} \approx 19.94 [/tex]
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You are loading a rental truck with 78-pound boxes and have
60 boxes to load. If the empty truck weighs 8840 pounds,
then the equation W=78b+8840 gives the total weight of
the truck if it is carrying b boxes.
Suppose the truck is not legally allowed to weigh more than
13,200 pounds.
Will your rental truck be able to legally carry the load of 60
boxes?
Explain why you answered yes or no and show all work.
Answers
Answer:
13200 needs to be less than 78*60+8840,
which is false because 13200 < 13520
Step-by-step explanation:
The truck cannot load 60 boxes as it exceeds the weight limit.
What is 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. LHS = RHS is a common mathematical formula.
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:
W=78b+8840
So, b= 60
W= 78 x 66 + 8840
W = 5148 +8840
W = 13988 > 13200 ( limit for the weight)
Hence, the truck cannot load 60 boxes as it exceeds the weight limit.
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32) Find the cost of linoleum flooring for a floor that is 15 feet by 10 feet if it costs $9.00 to cover 12 square feet.
O a.) $110.50
Ob.) $132.50
Oc.) $122.50
Od.) $112.50
Answers
Answer:
d.) $112.50
Step-by-step explanation:
Area of floor:
15 ft × 10 ft = 150 ft²
150 ft² is how many times 12 ft²?
It is 150 ft² / 12 ft² = 12.5.
150 ft² is 12.5 times 12 ft².
12 ft² cost $9.00, so 12.5 times 12 ft² costs 12.5 times $9.00.
12.5 × $9.00 = $112.5
Answer: d.) $112.50
The Square foot flooring is calculated by doing 15ft x 10ft = 150ft^2. Since it cost $9.00 to cover 12ft^2, you would do 150ft^2/12ft^2 to find out how many times you have to pay 9 dollars. This gives you 12.5 times you have to pay 9 dollars. Therefore, you do $9.00x12.5 which gives you $112.50
Find the z a/2 critical value needed to construct a confidence interval with level .The critical value for the confidence level 90% is.......
( round to two decimal places )
Answers
Using the z-distribution, the critical value for a confidence level of 90% is of Z = 1.65.
What is the critical value for a 90% confidence interval using the z-distribution?In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.65.
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If f (7) = 22, then
f(f-1(22)) = [?]
Answers
Answer: 22
Step-by-step explanation:
[tex]f(f^{-1}(x))=f^{-1}(f(x))=x[/tex]
i need the answer to this.
Answers
The simplifications of all the given ratios are as detailed below.
How to simplify ratios?The simplification of each of the given ratios are;
1) 56 : 49
The highest common multiple is 7 and so we divide by 7 to get;
56 : 49 = 8:7
2) 36:48
The highest common multiple is 12 and so we divide by 12 to get;
36 : 48 = 3:4
3) 48:42
The highest common multiple is 6 and so we divide by 6 to get;
48 : 42 = 8:7
4) 24:36
The highest common multiple is 12 and so we divide by 12 to get;
24 : 36 = 2:3
5) 20:30
The highest common multiple is 10 and so we divide by 12 to get;
20 : 30 = 2:3
6) 24:32
The highest common multiple is 8 and so we divide by 8 to get;
24 : 32 = 3:4
7) 18:27
The highest common multiple is 9 and so we divide by 9 to get;
18 : 27 = 2:3
8) 16:14
The highest common multiple is 2 and so we divide by 2 to get;
16 : 14 = 8:7
9) 9:12
The highest common multiple is 3 and so we divide by 3 to get;
9 : 12 = 3:4
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3. Mr. Black's pay increased by 15% when he got a raise, bringing his new salary to $184. What was Mr. Black's original pay?
Answers
Answer:
$160
Step-by-step explanation:
115% = $184
100% = X
let X be the original salary
(X is unknown)
115% = $184
100% = X
cross mutiply
115 x X = 100 x 184
115X = 18400
X = 18400 divided by 115
X = $160
therefore,Mr Black's original salary before increased by 15% was $160
hope am helpful.
184*100=18400
18400=115x
18400/115=160
x=160
Handre runs a paragliding and adventure touring company. For each paragliding trip (p) he takes he makes $55 and for each adventure tour (a) he makes $75. Last week, he made $2725. Write the equation to represent the relationship between the number of paragliding trips, adventure tours, and his total pay
Answers
The equation that shows the relationship between the number of paragliding trips, adventure tours, and his total pay is 55a + 75p = 2725
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let a represent the number of adventure tours and p represent the number of paragliding trip, hence:
55a + 75p = 2725
The equation that shows the relationship between the number of paragliding trips, adventure tours, and his total pay is 55a + 75p = 2725
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Prove the following identities.
cos(3pi/s+x)=sinx
Answers
[tex]\cos \left(\frac{3\pi}{2}-x \right)=\sin x \\ \\ =\cos \left(\frac{3\pi}{2} \right)\cos x -\sin \left(\frac{3\pi}{2} \right) \sin x \\ \\ =0\cos x -(-1)(\sin x) \\ \\ =\sin x[/tex]
Grace and Jack are playing a game with a gigantic bucket of markers. Jack took a random sample of markers from the bucket and counted 12 yellow markers, 37 blue markers, and 1 red marker. Use the observed frequencies to create a probability model for the color of the next randomly selected marker from the gigantic bucket of markers. Input your answers as fractions or as decimals rounded to the nearest hundredth.
Answers
Using the given frequencies, the probabilities for the next color chosen is:
P(yellow) = 0.24.P(blue) = 0.74.P(red) = 0.02What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
There were 50 markers, of which 12 were yellow, 37 blue and 1 red, hence the probabilities for each are given as follows:
P(yellow) = 12/50 = 0.24.P(blue) = 37/50 = 0.74.P(red) = 1/50 = 0.02More can be learned about probabilities at https://brainly.com/question/14398287
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Consider the equation 4x^4 - 38x^3 = 17x^2 + 30x. One of the real solutions to the equation is 10. What are the other solutions, both real and nonreal
Answers
Answer: Option (1)
Step-by-step explanation:
[tex]4x^4 -38x^3 -17x^2 -30x=0[/tex]
Dividing both sides by [tex]x-10[/tex] (10 is a root, so x-10 is a factor), yields
[tex]4x^3 +2x^2 +3x=0\\\\x(4x^2 +2x+3)=0\\\\x=0, 4x^2 +2x+3=0[/tex]
Solving the second case by the quadratic formula yields [tex]x=\frac{-1 \pm i\sqrt{11}}{4}[/tex].
So, the answer is Option (1).
If y = square root 81, what is the value of y?
Answers
If f(x)f(x) is an exponential function where f(3.5)=12f(3.5)=12 and f(9)=75f(9)=75, then find the value of f(7.5)f(7.5), to the nearest hundredth.
Answers
Using an exponential function, it is found that f(7.5) = 45.5.
What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex].
In which:
a is the initial value.b is the rate of change.For this problem, we have that f(3.5) = 12, then:
[tex]y = ab^x[/tex]
[tex]12 = ab^{3.5}[/tex]
[tex]a = \frac{12}{b^{3.5}}[/tex]
We also have that f(9) = 75, then:
[tex]y = ab^x[/tex]
[tex]75 = ab^9[/tex]
Since [tex]a = \frac{12}{b^{3.5}}[/tex]:
[tex]75 = \frac{12}{b^{3.5}} \times b^9[/tex]
[tex]b^{5.5} = \frac{75}{12}[/tex]
[tex]\sqrt[5.5]{b^{5.5}} = \sqrt[5.5]{\frac{75}{12}}[/tex]
[tex]b = \left(\frac{75}{12}\right)^{\frac{1}{5.5}[/tex]
b = 1.39542165
Then:
[tex]75 = ab^9[/tex]
[tex]a = \frac{75}{1.39542165^9}[/tex]
a = 3.7386
Hence:
[tex]y = 3.7386(1.39542165)^x[/tex]
When x = 7.5, we have that:
[tex]y = 3.7386(1.39542165)^{7.5} = 45.5[/tex]
Hence f(7.5) = 45.5.
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Point S is on line segment \overline{RT}
RT
. Given ST=2x,ST=2x, RT=4x,RT=4x, and RS=4x-4,RS=4x−4, determine the numerical length of \overline{RS}.
RS
.
Answers
[tex]\underset{\leftarrow \qquad \textit{\LARGE 4x}\qquad \to }{R\stackrel{4x-4}{\rule[0.35em]{7em}{0.25pt}} S\stackrel{2x}{\rule[0.35em]{20em}{0.25pt}}T} \\\\\\ RT~~ - ~~ST~~ = ~~RS\implies \stackrel{RT}{4x} - \stackrel{ST}{2x}~~ = ~~\stackrel{RS}{4x-4} \\\\\\ -2x=-4\implies x=\cfrac{-4}{-2}\implies \boxed{x=2}~\hfill \stackrel{4(2)~~ - ~~4}{RS=8}[/tex]
AHAISNSHKWSN HELP PLEASEEE
Answers
Answer:
best answer is c. (2,3),(4,4),(6,5),(8,6)
Step-by-step explanation:
multiply x and y components 2*3,4*4,6*5,8*6
Which of the following has the least steep graph?
Answers
Explanation
you are looking for “least steep” on the graph, so you are looking for the least amount of slope. Slope is the number next to x in the slope intercept y=mx+b.
1/2 on a graph would be 1 up and 2 to the right
The other three options would be 1 up 1 over, 2 up 1 over, 3 up 1 over, all having a steeper slope.
The RLX Company just paid a dividend of $2.85 per share on its stock. The dividends are expected to grow at a constant rate of 4.5 percent per year, indefinitely. Assume investors require a return of 10 percent on this stock. What is the current price?
Answers
The current stock price is $54.15.
Given that RLX Company just paid a dividend of $2.85 per share on its stock and dividends are expected to grow at a constant rate of 4.5 percent per year, indefinitely.
Stock valuation alludes to the valuation of the natural worth per portion of an organization's stock which can help the organization in deciding its reasonable worth in case of twisting up or consolidation. One of the models used to esteem the stock cost is the profit development model. It expects the cost of the stock to be the current worth representing things to come profits of the stock accepted to develop at a consistent rate.
Dividend (D0) = $2.85
Growth rate (g) = 4.5%
Required return (r) = 10%
Firstly, we have to calculate the value of the current stock price.
The current stock price can be calculated by using the dividend growing model.
[tex]\begin{aligned}\text{Current stock price}&=\frac{D_{0}\times(1+g)}{r-g}\\ &=\frac{2.85\times (1+0.045)}{0.10-0.045}\\ &=\frac{2.85\times 1.045}{0.055}\\ &=\frac{2.97825}{0.055}\\ &=54.15\end[/tex]
Hence, the current stock price when dividend of $2.85 are expected to grow at a constant rate of 4.5 percent per year, indefinitely is $54.15.
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A solid right square prism is cut into 5 equal pieces parallel to its bases. The volume of each piece is V = 1/5s2h.Solve the formula for s. help asap
Answers
The solution of the formula for s is:
[tex]s = \sqrt{\frac{5V}{h}}[/tex]
What is the symbolic equation?The equation is:
[tex]V = \frac{1}{5}s^2h[/tex]
To solve for s, we isolate it, hence:
[tex]s^2 = \frac{5V}{h}[/tex]
[tex]s = \sqrt{\frac{5V}{h}}[/tex]
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Add.
−5/6+(−2 5/8)
Enter your answer as a simplified fraction by filling in the boxes.
pllzzzzz helppppp
Answers
We know we have
-5/6 added to -2 5/8
First we have to make the denominator the same for both fractions. 24 is a number that is divisible by both 6 and 8. See attachment for the math.
Now we have -20/24 and -2 15/24
Combine negative numbers to add them together.
Now we have -2 35/24, you need to reduce to simplest terms. Your fraction -35/24 is an improper fraction so divide -35/24 and you get -1 11/24 so combine that with your -2 for a total of
-3 11/24
Select the correct answer from each drop-down menu.
What structural element of the paragraph is the underlined sentence, and how does it connect ideas in the text?
The underlined sentence
1.the thesis statement for the text
2.the conclusion of the text
3.a piece of evidence for the texts argument
4.a piece of reasoning in the text
It connects ideas in the text by
1.making the main claim of the text
describing why the information provided matters to readers
3. relating a fact or story that demonstrates the texts argument
4. suggesting how a specific example relates to the broader argument
Answers
The underlined sentence in the text simply functions as; the conclusion of the text and connects ideas in the text, by making the main claim of the text describing why the information provided matters to readers.
What is the function of the underlined text in the passage?The underlined text in the passage functions as the conclusion to the passage in which case, the information intended to be conveyed is that on the occasion that, regular feeding, good housing, occasional gentle corrections and kindness are in place, there'd be no need for such a cat to steal.
Therefore, the structural element of the paragraph in the underlined sentence, and how it connect ideas in the text is; by making the main claim of the text
describing why the information provided matters to readers.
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How many liters each of a 35% acid solution and a 80% acid solution must be used to produce 60 liters of a 65% acid solution? (Round to two decimal places if necessary.)
Answers
Solving a system of equations we will see that we need to use 40 liters of the 80% acid solution, and the other 20 liters are of the 35% acid solution.
How many liters of each solution do we need to use?
First, we need to define the variables:
x = liters of the 35% acid used.y = liters of the 80% acid used.We know that we want to produce 60 liters of 65% acid, then we have the system of equations:
x + y = 60
x*0.35 + y*0.80 = 60*0.65
(in the second equation we wrote the percentages in decimal form).
To solve this we need to isolate one of the variables in one equation and then replace it in other one, isolating x we get:
x = 60 - y
Replacing that in the other equation:
(60 - y)*0.35 + y*0.80 = 60*0.65
y*(0.80 - 0.35) = 60*(0.65 - 0.35)
y*0.45 = 60*0.30
y = 60*0.30/0.45 = 40
So we need to use 40 liters of the 80% acid solution, and the other 20 liters are of the 35% acid solution.
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27. Which is wrongly spelt? A. reliable B. sociable C. viable D. avialable
Answers
Answer:
D. Avialable
Step-by-step explanation:
the correct spelling is available :)
The answer is D.
The correct spelling of the word in the given option is : Available
Instead, here the places of a and i have been interchanged, causing it to be misspelt.
Given f(x) =
4x + 2, find f(x + 3).
Answers
Answer:
f(x + 3) = 2(x + 7)
Step-by-step explanation:
Now lets find out what does f(x + 3) means.
f(x + 3) means shifting the entire function 3 units to the left. Which also means, all x values will be shifted to the left by that number of units. (Excluding the constant that is multiplied or divided by x, eg. 5x + 6 shifted by 7 units to the left is 5(x + 7) + 6 and not 5x + 7 + 6.)
From the above,
f(x + 3) = 4(x + 3) + 2 = 4x + 12 + 2 = 4x + 14 = 2(x + 7)