The total number of hours that Laurie worked for the week is; 35 hours
How to solve Algebra Word Problems?The parameters given are;
Total number of hours worked for the week = 4s + 3 hours
Rate of earning = 2s + 4 dollars per hour
Gross Amount earned = $700
Thus;
(4s + 3)(2s + 4) = 700
8s² + 6s + 16s + 12 = 700
8s² + 22s + 12 = 700
8s² + 22s - 688 = 0
Solving this with an online quadratic calculator gives;
s = 8
Thus;
Total hours worked = 4(8) + 3 = 35 hours
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A humpback whale can swim at a maximum speed of 495 meters per minute. If it is swimming south at one-third of its top speed, how much time will it take the whale to swim 2,310. meters?
Write your answer as a whole number.
(blank) minutes.
Find the equation of a line perpendicular to y= 4/3 x−1 that passes through the point (-4,-8)(−4,−8).
4y = -3x-12 the equation of a line perpendicular to y= 4/3 x−1 that passes through the point (-4,-8).
How do you find the equation of a line parallel or perpendicular?A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value at which the line intersects the y-axis.
The slope of parallel lines is the same. The slopes of perpendicular lines are opposing reciprocals. To put it another way, if m=a/b, then m⊥= -b/a.
y= 4/3 x - 1
Slope = 4/3
Equation of line perpendicular to this line
y= -( 3/4) x+b
As slope is -1/m
Now as line passes through (-4,-8)
Plug it in
-8 = (-3/4)(-4) +b
-8= 3+ b
Gives b = -12
So the equation of line will be
y = (-3/4) x -12
or 4y = -3x-12
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Which expression represents the product of 3 and 7? 7 ÷ 3 7 + 7 + 7 37 3 × 7
Answer:
3x7
Step-by-step explanation:
product is multiplication so 3x7 is only correct answer
Hopes this helps please mark brainliest
Using the graph below:
Find the values of x and y that maximize the objective function C=3x+4y for the graph.
What is the minimum value? Show why.
What is the maximum value? Show why.
Regarding the objective function C = 3x + 4y, the minimum and the maximum value are given as follows:
Minimum value: C = 0 at (0,0).Maximum value: C = 16 at (0,4).How to find the extrema values of the objective function?The objective function is defined as follows:
C = 3x + 4y.
The extremas of the function, that is, the minimum and the maximum values, can be obtained at either of these following points:
Intercepts = vertices of the curve.Intersection point between two curves.These extreme values are the numeric values at these points.
In this problem, there is only a single curve, hence the vertices are given as follows:
(0,0), (0,4) and (4,0).
Then the numeric values of the objective function are these points are given as follows:
(0,0): C = 3(0) + 4(0) = 0 -> minimum value.(0,4): C = 3(0) + 4(4) = 16 -> maximum value.(4,0): C = 3(4) + 4(0) = 12.More can be learned about maximizing functions at https://brainly.com/question/28788613
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Solve the equation
25^x+3= 1/5
Answer:
X = -4
Step-by-step explanation:
25^(x+3) = 1/5
5^2^(x+3) = 5^(-2)
5^(2x+6) = 5^(-2)
2x+6 = -2
2x = -8
x = -4
Answer:
x = -7/2
or can be written,
x = -3.5
Step-by-step explanation:
25 is a power if 5 and so is 1/5. If you can write both sides as 5 to "some" power. Then the equation is just getting those two exponents equal. See image.
Using logarithms is a nice shortcut. But then you need need a calculator. See image.
Kegler bowling buys scorekeeping equipment with an invoice cost of $190,000. The electrical work required for the installation costs $20,000. Additional costs are $4,000 for delivery and $13,700 for sales tax. During the installation, the equipment was damaged and the cost of repair was $1,850. Required: indicate whether each cost should be included in the cost of the equipment or excluded and expensed as incurred.
The total Cost of the equipment is $2,27,700. In which the following included, excluded and expensed as incurred are
Invoicing costs - included in the price
Electrical work required for installation - Included in the price
Delivery costs - included in the price
Sales tax - included in the price
Repair costs - not included or excluded
A machine used by a company to produce products and services is known as a machine tool. It is a vital long-term asset as it speeds up the production process such as transportation, computers and other equipment. These costs will include the costs that were necessary to start opening the plant property. There are equipment costs.
We have given the following details ,
Total Cost DR Machinary DR Expense
Invoice cost $190,000 $190,000
electric work
and $20,000 $20,000
installation cost
delivery cost। $4,000 $4,000
sales tax $13,700 $13,700
repair cost $1,850 $1,850
total $22,9550 $22,7700 $ 1,850
Accordingly, all the mentioned costs except for the repair of the part will be included in the cost of the machinery.
Included in price Excluded
invoice repair cost
electric and installation
delivery
sales tax
Hence , the total equipment cost is $22,7700.
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-x+3(1 + x) = 3(x +2)
The given equation, -x + 3(1 + x) = 3(x +2), solved for x, is x = -3
Solving linear equationsFrom the question, we are to solve the given equation.
The given equation is
-x + 3(1 + x) = 3(x +2)
To solve this equation, we will determine the value of the variable in the equation.
The variable in the equation is x.
Thus, we will solve for x in the equation.
-x + 3(1 + x) = 3(x +2)
Clear the parentheses by applying the distributive property
-x + 3 + 3x = 3x + 6
Collect like terms
-x + 3x - 3x = 6 - 3
-x = 3
Multiply both sides of the equation by -1
-1 × -x = -1 × 3
x = -3
Hence, the value of x is -3
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There were 20 illustrations in Julio's sketch pad. While at a museum, he drew x more illustrations in the sketch pad. Which expression represents the total number of illustrations in Julio's sketch pad after his museum visit?
The expression that represents the total number of illustrations in Julio's sketch pad after his museum visit is given as follows:
Total number = 20 + x.
How to obtain the expression for the total number of illustrations?The expression that represents the total number of illustrations in Julio's sketch pad after his museum visit is obtained adding the previous amount of illustrations to the number of illustrations that were added during the visit to the museum, hence:
Total number of illustrations = Previous number of illustrations + number of illustrations added during the visit.
In the context of this problem, the values of these parameters are given as follows:
Previous number of illustrations = 20 -> as stated in the problem.Number of illustrations added during the visit = x.Hence the expression is defined as follows:
Total = 20 + x.
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find the following percentiles for the standard normal distribution. interpolate where appropriate. (round your answers to two decimal places.)
The interpolations;
(a) 81st
= NORM.INV(0.81;0;1)
0.878
(b) 19th
=NORM.INV(0.19;0;1)
-0.878
(c) 76th
=NORM.INV(0.76;0;1)
0.706
(d) 24th
=NORM.INV(0.24;0;1)
-0.706
(e) 11th
=NORM.INV(0.11;0;1)
-1.227
Given,
Data near the mean are more likely to occur than data distant from the mean, according to the normal distribution, which is a probability distribution that is symmetric around the mean.
"A numerical measurement used in statistics of a value's relationship to the mean (average) of a set of values, assessed in terms of standard deviations from the mean," according to Wikipedia, is the Z-score.
For this case we can find the percentiles with the Norm.inv function in Excel and we got:
(a) 81st
= NORM.INV(0.81;0;1)
0.878
(b) 19th
=NORM.INV(0.19;0;1)
-0.878
(c) 76th
=NORM.INV(0.76;0;1)
0.706
(d) 24th
=NORM.INV(0.24;0;1)
-0.706
(e) 11th
=NORM.INV(0.11;0;1)
-1.227
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PLS HELPPPP THIS IS URGENT
find the missing number so that the equation has no solution x+19=2x-4-7x
The missing number so that the equation has no solution is -3 5/6.
What is the missing number?A linear equation is an equation that has a single variable that is raised to the power of one. When shown on a graph, a linear equation is a straight line that slopes either upwards or downwards.
If the equation has no solution, it means that the value of the left hand equation and the value of the right hand equation are equal.
In order to determine the solution, take the following steps:
x + 19 = 2x - 4 - 7x
Combine similar terms together: 19 + 4 = 2x - 7x - x
Add similar terms together: 23 = -6x
Divide both sides of the equation by -6: x = 23 / - 6
x = -3 5/6
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Explain why there are no solutions to the equation (2x - 7)² = -9.
Answer:
A square number is always nonnegative. So a quantity squared must be nonnegative.
. If he is paid $15 per hour and $200 for each car that he sells, how many hours did he work if he sold 2 cars and made $520?
Answer:
8 hours
Step-by-step explanation:
2 cars will be $400 since 2x200=400
500-400=120
He made $120 from hours alone so now we divide by 15
120/15=8
He worked 8 hours
Hopes this helps please mark brainliest
What is the method to solve this?
Side-Side-Side can be used to prove this pair of triangles is congruent.
If the three sides and the three angles of both angles are equal in any orientation, two triangles are said to be congruent. When two or more triangles are taken that are similar to one another, their corresponding sides and angles are also similar to one another.
According to this question,
Two respective sides of triangles are equal.
One side is common between these two triangles.
Therefore, the third side of the triangles is equal as well.
As all respective sides of the triangles are equal, we can say that the triangles are congruent by Side-Side-Side.
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need answers for questions 23-26
The following are the answers:
23. The cost for 7 lessons is $82, and the cost of 11 lessons is $122, we have;
The total cost of lessons is; f(x) = y = 10·x + 12 and one lesson costs $22
24. The equation of population of Laredo, Texas is :
p = 92500t/17 + 123000
25. The linear equation to represent the temperature T at an elevation of x, where x is in thousands of feet is T = -(2000/3)x + (4228/3).
26. The equation to represent the amount 'R' Natalia and her friends raised after selling 'c' cakes will be;
⇒ R = 4c
Given:
23. Lydia wants to purchase guitar lessons.
7 lessons = $82
11 lessons = $122
we are asked to determine the linear equation which finds the total cost C for d lessons.
The general equation for the total cost of lessons is;
Let a represent the cost of 7 guitar lessons, and let b represent the cost of 9 guitar lessons, given that the cost increases linearly with the number of lessons, we have;
The cost increase per lesson = The slope of the linear function representing the total cost of a guitar lesson
Therefore,
slope = b-a/11-7 = b-a/4
Expressing the equation in slope and intercept form, we get:
(y-a) = b-a/4 . (x-7)
y = b-a/4 . x-7 × b-a/4 + a = b-a/4 . x + 11.a-7.b/4
y = b-a/4 . x + 11.a-7.b/4 = 1/4.((b-a).x+11.a-7.b
where a=$82 and b=$122 we ahve:
y = 1/4 . (122-82) . x+1/4 . (11×82-7×122) = 10x+12
The total cost of a lesson is:
y = 10×1+12
= 22
24. Given:
t = the number of years after 1990.
So, for 1990, t = 0. So the coordinate is (0, 123000).
For 2007, t = 17. So the coordinate is (17, 215500).
using point slope formula:
m = 215500-123000/17-0
m = 92500/17
⇒ p = 92500t/17 + 213000
25. The equation of a line in slope-intercept form is y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at
x = 0.
We know the slope is (y₂ - y₁)/(x₂ - x₁).
∴ Here the temperature is y and the height is x.
And the points are (6000, 76) and (12000, 49)
So, slope =(12000 - 6000)/(49 - 76).
Slope = (6000/-27).
Slope = -(2000/9).
Now we have to determine the y-intercept by putting any of the points in y = mx + b.
So, 76 = -(2000/9)×6000 + b.
76 = -(12000/9) + b.
76 = -(4000/3) + b.
b = 4000/3 + 76.
b = 4228/3.
∴ y = -(2000/3)x + (4228/3) or T = -(2000/3)x + (4228/3).
26. The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
he friends sold 15 cakes on the first day and 22 cakes on the second day of the bake sale.
On first day, they collect = $60
On second day, they collect = $88
Now,
We have to find the equation as;
⇒ R = mc + b
We need to find the value of m and b.
Since, The first point = (15, 60)
The second point = (22, 88)
Hence, Slope (m) = (88 - 60) / (22 - 15)
m = 28 / 7
m = 4
And, To find b substitute R = 60 , c = 15 and m = 4 in above equation,
⇒ R = mc + b
⇒ 60 = 4 x 15 + b
⇒ b = 0
Thus, Substitute m = 4 and b = 0 in equation (i) we get;
⇒ R = mc + b
⇒ R = 4c + 0
⇒ R = 4c
Therefore, The equation to represent the amount 'R' Natalia and her friends raised after selling 'c' cakes will be;
⇒ R = 4c
Hence we get the required answers.
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Does anyone know how to solve this?
(2x^2)-6x+9 can be written in the form (a(x-b)^2)+c where a b c can be written as integers or fractions in their simplest form.
a) work out the values of a b c
b) using your answer to part a), solve (2x^2)-6x+9=12.5. give any fractions or surds in your answers in their simplest forms.
Answer:
it needs to be written step by step
is smoking during pregnancy associated with premature births? to investigate this question, researchers selected a random sample of 115 pregnant women who were smokers. the average pregnancy length for this sample of smokers was 259 days. from a large body of research, it is known that length of human pregnancy has a standard deviation of 16 days. the researchers assume that smoking does not affect the variability in pregnancy length.
The 99% confidence interval is ( 255.157, 262.843 ).
The subset chosen from the larger set to make assumptions is known as a random sample. A range of values is a confidence interval.
According to the given question,
n = number of pregnant women who are smokers
n = 115
μ = average pregnancy length for the sample
μ = 259
σ = standard deviation
σ = 16
At a 99% confidence level,
α = 0.01
z(α/2) = 2.576
The confidence interval is
CI = μ ± z(α/2).(σ/√n)
= 259 ± (2.576)(16/√115)
= 259 ± (2.576)(16/10.724)
= 259 ± (2.576)(1.492)
= 259 ± 3.843
= ( 259 - 3.843, 259 + 3.843)
CI = ( 255.157, 262.843 )
Therefore, the 99% confidence interval to estimate the length of pregnancy for women who smoke is ( 255.157, 262.843 ).
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The complete question is
Is smoking during pregnancy associated with premature births? To investigate this question, researchers selected a random sample of 115 pregnant women who were smokers. The average pregnancy length for this sample of smokers was 259 days. From a large body of research, it is known that the length of human pregnancy has a standard deviation of 16 days. The researchers assume that smoking does not affect the variability in pregnancy length.
Find the 99% confidence interval to estimate the length of pregnancy for women who smoke.
Note: The critical z-value to use is 2.576
Select the expression that is equivalent to x + x + y × y × y.
Answer: x+x+y.y.y = 2x+y^3 ( y cube)
Step-by-step explanation:
Answer:
2x+y^3
Step-by-step explanation:
x's are added while y's are multiplied
the international air transport association surveys business travelers to develop quality ratings for transatlantic gateway airports. the maximum possible rating is . suppose a simple random sample of business travelers is selected and each traveler is asked to provide a rating for the miami international airport. the file miami contains the ratings obtained from the sample of business travelers. develop a confidence interval estimate of the population mean rating for miami. round your answers to two decimal places.
The confidence interval estimate is (6.41, 7.11) of the population mean rating for Miami
The question includes a sample of the data.
The sample size, n = 50
The sample mean:
x= ∑X /n
= 6.76
The sample standard deviation;
s= √∑(X-x)²/(n-1)
=2.55
The confidence level =0.95
The significance level , α = 0.05
The sample mean, X
= 6.76
The sample standard deviation, s = 2.55
The sample size , n= 50
Degree of freedoms :
Df = n-1
=49
Using the t-distribution table, the critical value of t is:
t critical = t α/2, df
= t 0.025,49
= 0.098
95% confidence interval :
μ = X ± t.s/√n
t.s /
= 6.76 2.01 2.55 / √50
= 6.76 0.7249
Therefore, The confidence interval is ( 6.41, 7.11)
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149° + 13x + 5° = 180°
Answer:
Your answer should be x = 2
Step-by-step explanation:
149 + 13(2) + 5 = 180.
Hope this helps.
Answer:
x=2
Step-by-step explanation:
You add 149 and 5, which is 154. Then you take the total which is 180, and subtract it by 154. So 180-154=26 Then you take and do 26/13 which is 2.
149+13(2)+5=180
149+26+5=180
Definitely 2.
Hope this helps!!!
What is the value sinθ?
question options:
A. 5/13
B. 13/5
C. 12/13
D.5/12
The value of sin θ of the given right angle triangle using trigonometric ratios is; A: 5/13
How to solve Trigonometric ratios?The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). They are based on the angles formed from the ratio of sides of a right angle triangle. Thus;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
From the given image, we see that;
Hypotenuse = 13
Adjacent = 12
Opposite = 5
Thus;
tan θ = 5/12
θ = tan⁻¹(5/12)
sin θ = 5/13
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Determine the largest integer value of a in the solution of the following inequality.
4x+6 -13
The largest integer value of x in the solution of the following inequality is 7/4.
We have given equation is 4x+6 ≥13
In the question we have to determine the largest integer value of a in the solution of the following inequality.
So first we have to solve this inequality equation:
4x+6 ≥13
4x≥13-6
4x≥7
x≥7/4
So the largest value of x is 7/4
Hence, the largest integer value of a in the solution of the following inequality is 7/4.
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The right answer is
Determine the largest integer value of x in the solution of the following inequality.
4x+6≥13
George was able to solve 36 math problems in 15 minutes. Urban was able to solve 42 math problems in 20 minutes. Who was able to solve math problems at a greater rate? What was the rate?
Question 2 options:
A: George;
B: Urban;
C: George;
Answer:
Urban
Step-by-step explanation:
help please i will give you a snack
Answer:
26
Step-by-step explanation:
you are given 45° and 90° so you know the third angle will also be 45° because the sum of all angles always is 180°
with all 3 angles you apply the sine law
a / sin( α ) = b / sin( β ) = c / sin( γ )
then you'll see that a = 26
How to find a percent change. (Decrease and Increase). Please use simple terms and include a formula. (Also please use a visual demonstration) Thank you!
Percentage change expresses the ratio of the change in the amount of an initial quantity to the initial quantity as a percentage.
What is the mathematical formula for percentage change?Mathematically, the formula for percentage change, C, can be presented as follows;
[tex]C = \dfrac{x_{2} - x_{1} }{ x_{1} } \times 100[/tex]
Where:C = The percentage change
[tex]x_{1} [/tex] = The original value
[tex]x_{2} [/tex] =The new value
Graphically, percentage change can be presented as follows;
When the number of fruits that drops from a three each month, changes from 10 to 8, the percentage change is therefore;
[tex] C = \dfrac{10-8}{10} = 20\% [/tex]The percentage change is 20%
Initial number of fruits that drops monthly from the tree;
##########
The new number of fruits that drops from the tree on the specified month;
########
The difference in the number of fruits that drops from the tree is 2, which corresponds to the 20 % calculated for the percentage change.
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Jackie travels 60 km to work. Since she began taking a new
route (still 60 km to work) she gets there 30 minutes sooner
because she can drive 10 km/hour faster. Which of the
following equations could you use to solve the problem?
According to the distance-speed-time formula, the equation that could be used to solve this formula is 60/x+10 - 60/x = 1/2
Distance-speed-time
Basically, the formula for speed is speed = distance ÷ time.
In order to work out what the units are for speed, you need to know the units for distance and time.
Given,
Jackie travels 60 km to work. Since she began taking a new route (still 60 km to work) she gets there 30 minutes sooner because she can drive 10 km/hour faster.
Here we need to find the equations could you use to solve the problem.
Let us consider x be the speed of Jackie.
Therefore, the time has been calculated as,
Time1 = 60/ x
Now, the speed is increased as 10, then it can be written as,
=> x + 10
Therefore, the new time Time2 is calculated as,
=> Time2 = 60 / x + 10
So, the equation is obtained by calculating the difference of the times,
So, the equation is,
=> Time 2 - Time1
=> 60/x+10 - 60/x
Now, we know in this one she gets there 30 minutes sooner,
So, it can be written as,
=> 60/x+10 - 60/x = 30/60
=> 60/x+10 - 60/x = 1/2
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As a fraction in simplest terms, what would you multiply the first number by to get
the second?
First number: 79
Second number: 65
First number 79 about friction is correct statement with initial velocity .
What is friction?
Friction is a force that opposes motion between any surfaces that are touching. Friction can work for us yet against of us .
It is the action of one surface or object rubbing against another .
According to the given question in this case force of friction has a tendency to rotate the cube in anticlock wise direction. So normal reaction will shift in forword direction to balance the force due to torque of friction.
Thus, During motion the normal reaction shift towards posetive x- axis from the centre of mass is correct.
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Find an equation of the line passing through the given points. Use function notation to write the equation,
(-1,6) and (-2,11)
f(x) =
Equation of the line passing through the given points is y = -1/5(x) + 29/5.
Given points:
(-1,6) and (-2,11)
slope m = 11 - 6 / -2 - (-1)
= 5/-2+1
= 5/-1
m = -1/5.
substitute m and (-1,6) in y=mx+c.
y = mx + c
6 = -1/5(-1) + c
6 = 1/5 + c
c = 6 - 1/5
= 30 - 1 / 5
c = 29/5.
y = mx + c
y = -1/5(x) + 29/5.
Therefore equation of the line passing through the given points is y = -1/5(x) + 29/5.
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3/4x+2=9/10 Rewrite the equation below so that it does not have fractions.
Do not use decimals in your answer
Answer:
im not sure if this helps but you can write it with letter like this y = mx + b
Step-by-step explanation:
the point p p is on the unit circle. if the x-coordinate of p p is 3 4 34 , and p p is in quadrant iv , then what is the value of y? evaluate by using the one of the pythagorean identities.
The value of y coordinate of the unit circle is given by [tex]\sqrt{7}/4[/tex]
Given that,
x - coordinate of p =-3/4 . Let the co-ordinate of point P = (-3/4 , y).
To find : The y coordinate in Quadrant IV
By using the formula for unit circle,
Unit circle means a circle whose radius is one or 1
x²+ y² = 1
y²+ (-3/4)² = 1
y²+ (9/16) = 1
y² = 1 -9/16
y² = 7/16
y= [tex]\sqrt{7/16}[/tex]
y = ± [tex]\sqrt{7}/4[/tex]
It is given that point P is in quadrant IV so in IV quadrant y is positive.
Therefore, y = [tex]\sqrt{7}/4[/tex]
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