If Nelly makes 8 dollars an hour and she starts by owing her mother 7 dollars, how many hours will she need to work to pay her back and still have 49 dollars in her account. Write the equation and solve for the variable, b.
A. b = -1
B. b = 49
C. b = 21/4
D. b = 7
Answers
The answer is B. $49
Related Questions
4. If x=4 and y=10, what is the value of the expression 3x²y + y/2 - 6x?
1. 221
2. 461
3. 872
4. 1916
Answers
Answer:
2
Step-by-step explanation:
3*4^2*10+10/2 - 6*4
4*4=16 5 24
3*16*10 + 5 - 24 = 19
480 - 19
When writing a linear equation from a word problem, the rate of change is the slope, m.
True
False
Answers
Sorry for my bad handwriting
Answers
Answer:
No it is good
Step-by-step explanation:
I like it. good luck
Answer:
Rs 18.30
Step-by-step explanation:
100-(25.75+20.50+35.45)=100-81.70=Rs18.30
Given the function f(x) = 0.5|x - 41-3, for what values of x is f(x) = 7?
x = -24, x = 16
x= -16, x = 24
x=-1, x = 9
x = 1, x = -9
Answers
The values of x for which f(x) = 7 are x = 61 and x = 21.
To find the values of x for which f(x) = 7, we can set up the equation and solve for x.
The given function is f(x) = 0.5|x - 41| - 3.
Setting f(x) equal to 7, we have:
0.5|x - 41| - 3 = 7.
First, let's isolate the absolute value term:
0.5|x - 41| = 7 + 3.
0.5|x - 41| = 10.
To remove the absolute value, we can consider two cases:
Case: (x - 41) is positive or zero:
0.5(x - 41) = 10.
Multiplying both sides by 2 to get rid of the fraction:
x - 41 = 20.
Adding 41 to both sides:
x = 61.
So x = 61 is a solution for this case.
Case: (x - 41) is negative:
0.5(-x + 41) = 10.
Multiplying both sides by 2:
-x + 41 = 20.
Subtracting 41 from both sides:
-x = -21.
Multiplying both sides by -1 to solve for x:
x = 21.
So x = 21 is a solution for this case.
Therefore, the values of x for which f(x) = 7 are x = 61 and x = 21.
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Select all the true statements. The Slope of q is -5/2The Slope of p is the negative reciprocal of the slope of qThe slope of p is -5/2The slope of n is 2/5The slope of m is -2/5
Answers
Answer:
The Slope of p is the negative reciprocal of the slope of q
The slope of p is -5/2
The slope of m is -2/5
Step-by-step explanation:
Slope:
To find the slope of a line, we need two points. The slope is the change in y divided by the change in x.
The Slope of q is -5/2
Two points of line q are: (6,15) and (8,20)
Change in y: 20 - 15 = 5
Change in x: 8 - 6 = 2
Slope: 5/2
The slope of q is 5/2, so this statement is false.
The Slope of p is the negative reciprocal of the slope of q
Two points of line p are: (6,15) and (10,5)
Change in y: 5 - 15 = -10
Change in x: 10 - 6 = 4
Slope: -10/4 = -5/2
The slope of p is -5/2, which is the negative reciprocal of the slope of q(5/2). So this statement is true.
The slope of p is -5/2
From the statement above, this is true.
The slope of n is 2/5
Two points of line n are: (-5,0) and (0,-2)
Change in y: -2 - 0 = -2
Change in x: 0 - (-5) = 0 + 5 = 5
Slope: -2/5
This statement is false.
The slope of m is -2/5
Two points of line m are: (-2,7) and (3,5)
Change in y: 5 - 7 = -2
Change in x: 3 - (-2) = 3 + 2 = 5
Slope: -2/5
This statement is true.
Write an expression for the area of the figure.
Answers
Area of A = \(8 \cdot 2x = 16x\)
Area of B = \(8 \cdot x = 8x\)
Area of shape = Area of A + Area of B = \(16x + 8x\)
The area of the figure can be given from the expression 24x
What is the Area of a Rectangle?
The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
The entire figure can be split into 2 figures of different length and width
Let the top figure be A and the bottom figure be B
So , Area of the figure = Area of A + Area of B
Now , the Length of B = 16
Width of B = x
Area of B = Length of B x Width of B
So , Area of B = 16x
And from figure , we can conclude that
Length of A = 16 - 8
= 8
And Width of B = x
Area of B = Length of B x Width of B
So , Area of B = 8x
Therefore , total area of figure = Area of A + Area of B
= 16x + 8x
= 24x
Hence , the area of the figure is 24x
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Katie bought 2 blocks of cheese and 3 loaves of bread for $12.00. Jenny bought 4 blocks of cheese and 2 loaves of bread for $ 16.00. How much does each block of cheese cost? How much does each loaf of bread cost?
Answers
Answer:
cheese = $3 load of bread = $2
Step-by-step explanation:
to check:
2c + 3b = 12
2(3) + 3(3) = 12
6+6=12
iew
Give the slope and y-intercept of
the line.
slope = H, y-intercept = |
Enter the number that belongs in the green box.
Enter
Answers
Answer:x
Step-by-step explanation:
carey correctly graphs a liner function. the slope of the function is -1. the y-intercept is 3. which is careys graph
Answers
Carey's graph will be a straight line with a slope of -1 and a y-intercept of 3.
Carey correctly graphs a linear function with a slope of -1 and a y-intercept of 3. A linear function is represented by the equation y = mx + b, where m is the slope and b is the y-intercept.
In this case, the slope is -1, which means that for every unit increase in the x-coordinate, the y-coordinate decreases by 1 unit. The y-intercept is 3, indicating that the graph intersects the y-axis at the point (0, 3).
To plot the graph, Carey starts by marking the point (0, 3) on the graph. Then, for every unit increase in the x-coordinate, Carey moves one unit downward. Similarly, for every unit decrease in the x-coordinate, Carey moves one unit upward. These steps ensure the correct slope of -1.
After connecting the points, Carey will obtain a line that starts at the y-intercept (0, 3) and slants downward, with a slope of -1. The resulting graph will be a straight line extending to both sides of the coordinate plane.
In conclusion, it is represented by the equation y = -x + 3.
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What's the unit prices??
Answers
Brand A:
unit price = 2.36/18 = .131
So, Brand A sells each pencil for $.131.
Rounded to the nearest cent would be .1
or 10 cents
Brand B:
unit price = 4.09/24 = .170
Rounded to the nearest cent would be .2 or 20 cents
So, Brand B sells each pencil for $.170
Since we know the unit rates, we know that Brand A sells each pencil for less, so Brand A is a better deal.
The diagonals of parallelogram ABCD intersect at P. Which statements must be true? Select all that apply.
Answers
The statements that will be true about parallelogram ABCD are: A, B, D, and E.
Properties of a Parallelogram -
Diagonals of a parallelogram bisect each other into congruent segments.
Opposite angles and sides of a parallelogram are always congruent.
Alternate interior angles are always congruent in measure.
Thus, the following would be true of parallelogram ABCD:
AP ≅ CP (congruent segment's of a bisected diagonal)
BC ≅ AD (congruent opposite sides)
∠CAD ≅ ∠ACB (congruent angles)
∠BPC ≅ ∠APD (congruent angles)
Therefore, the statements that will be true about parallelogram ABCD are: A, B, D, and E.
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2) Kari is flying her kite at the park. She has let
out 65 yards of kite string. The kite is 30 yards
directly above her friend, Sharla. How far apart
are Kari and Sharla? Round to the nearest
tenth.
Answers
Answer:
approx 58 yard we can determine it by pithagoras theorem
Equivalent to 28 to the second power-3
Answers
Answer:
13 since the second power (-3) is doubled.
please answer asap no trolls
Answers
Answer:
It would probably be 15 actually
Answer:
3
Step-by-step explanation:
Triangle inequalities.
a-b < c < a+b
13-11<x<13+11
2<x<24
X has to be greater than 2.
The next whole number greater than 2 is 3.
So the smallest whole number for the third side is 3.
A rectangular room is 1.3 times as long as it is wide, and its perimeter is 27 meters. Find the dimension of the room.
Answers
The dimensions of the room are approximately 5.87 meters by 7.63 meters.
Let's assume the width of the room is "x" meters.
According to the problem, the length of the room is 1.3 times the width, so the length would be 1.3x meters.
The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 27 meters.
Perimeter = 2(length + width)
Substituting the values we know:
27 = 2(1.3x + x)
Simplifying:
27 = 2(2.3x)
27 = 4.6x
Dividing both sides by 4.6:
x = 27 / 4.6
x ≈ 5.87
The width of the room is approximately 5.87 meters.
To find the length, we can multiply the width by 1.3:
Length = 1.3 * 5.87 ≈ 7.63
The length of the room is approximately 7.63 meters.
Therefore, the dimensions of the room are approximately 5.87 meters by 7.63 meters.
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Mid-West Publishing Company publishes college textbooks. The company operates an 800 telephone number whereby potential adopters can ask questions about forthcoming texts, request examination copies of texts, and place orders. Currently, two extension lines are used, with two representatives handling the telephone inquiries. Calls occurring when both extension lines are being used receive a busy signal; no waiting is allowed. Each representative can accommodate an average of 15 calls per hour. The arrival rate is 30 calls per hour.
How many extension lines should be used if the company wants to handle 90% of the calls immediately?
fill in the blank 1
lines should be used
What is the average number of extension lines that will be busy if your recommendation in part (a) is used? Round your answer to four decimal places.
L = fill in the blank 2
What percentage of calls receive a busy signal for the current telephone system with two extension lines? Round your answer to two decimal places.
fill in the blank 3
%
Answers
The various answers to the question are:
To answer 90% of calls instantly, the organization needs four extension lines.The average number of extension lines that will be busy is FourFor the existing phone system with two extension lines, 34.25 % of calls get a busy signal.How many extension lines should be used if the company wants to handle 90% of the calls immediately?a)
A number of extension lines needed to accommodate $90 in calls immediately:
Use the calculation for busy k servers.
\($$P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{k} \frac{\left(\frac{\lambda}{\mu}\right)^{t}}{i !}}$$\)
The probability that 2 servers are busy:
The likelihood that 2 servers will be busy may be calculated using the formula below.
\(P_{2}=\frac{\frac{\left(\frac{20}{12}\right)^{2}}{2 !}}{\sum_{i=0}^{2} \frac{\left(\frac{20}{12}\right)^{t}}{i !}}$$\approx 0.3425$\)
Hence, two lines are insufficient.
The probability that 3 servers are busy:
Assuming 3 lines, the likelihood that 3 servers are busy may be calculated using the formula below.
\(P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{2} \frac{\left(\frac{\lambda}{\mu}\right)^{i}}{i !}}$ \\\\$P_{3}=\frac{\frac{\left(\frac{20}{12}\right)^{3}}{3 !}}{\sum_{i=0}^{3} \frac{\left(\frac{20}{12}\right)^{1}}{i !}}$$\approx 0.1598$\)
Thus, three lines are insufficient.
The probability that 4 servers are busy:
Assuming 4 lines, the likelihood that 4 of 4 servers are busy may be calculated using the formula below.
\(P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{k} \frac{\left(\frac{\lambda}{\mu}\right)^{t}}{i !}}$ \\\\$P_{4}=\frac{\frac{\left(\frac{20}{12}\right)^{4}}{4 !}}{\sum_{i=0}^{4} \frac{\left(\frac{20}{12}\right)^{7}}{i !}}$\)
Generally, the equation for is mathematically given as
To answer 90% of calls instantly, the organization needs four extension lines.
b)
The probability that a call will receive a busy signal if four extensions lines are used is,
\(P_{4}=\frac{\left(\frac{20}{12}\right)^{4}}{\sum_{i=0}^{4} \frac{\left(\frac{20}{12}\right)^{1}}{i !}} $\approx 0.0624$\)
Therefore, the average number of extension lines that will be busy is Four
c)
In conclusion, the Percentage of busy calls for a phone system with two extensions:
The likelihood that 2 servers will be busy may be calculated using the formula below.
\(P_{j}=\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}$$\\\\$P_{2}=\frac{\left(\frac{20}{12}\right)^{2}}{\sum_{i=0}^{2 !} \frac{\left(\frac{20}{12}\right)^{t}}{i !}}$$\approx 0.3425$\)
For the existing phone system with two extension lines, 34.25 % of calls get a busy signal.
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Bethany has a photo website where she places photos that she has taken so others can see them. Below is how many likes each of her current photos were given: 10, 13, 15, 15, 17, 29 What is the average amount of likes each of her photos got? Hint: The average is your mean. 22 15 15.5 16.5
Answers
The average number of likes will be 16.5. the correct option is D.
What is a mean?Mean is defined as the ratio of the sum of the number of data sets to the total number of data. The mean is calculated by adding all the data points and dividing it by the total number of the data.
Given that Bethany has a photo website where she places photos that she has taken so others can see them. Below is how many likes each of her current photos was given: 10, 13, 15, 15, 17, 29.
The average will be calculated as:-
Mean = ( 10 + 13 + 15 + 15 + 17 + 29 ) / 6
Mean = 99 / 6
Mean = 16.5
Therefore, the average number of likes will be 16.5. the correct option is D.
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let $s$ be the set of complex numbers $z$ such that the real part of $1/z$ is equal to $1/6$. this set forms a curve. find the area of the region inside the curve.
Answers
The area of the region inside the curve formed by the given complex number is 28.26 sq. units.
What are complex numbers?
A complex number in mathematics is part of a number system that includes an element with the symbol i, often known as the imaginary unit, to expand the real numbers. The formula a + bi, where a and b are real numbers, can be used to express any complex number.
Given a complex number z.
Let z = a +bi
Then,
\(\frac{1}{z} = \frac{1}{a+bi} =\frac{a -bi}{(a+bi)(a-bi)} = \frac{a -bi}{(a^2+b^2)}\)
The real part of the above equation is a / (a²+b²)
This value is given as 1/6.
a / (a²+b²) = 1/6
(a²+b²) = 6a
a² - 6a + 9 - 9 + b² = 0
(a - 3)² + b² = 9
This is an equation of a circle with a centre of (3,0) and a radius of 3.
This is the curve formed.
Therefore for the given complex number the area of the region inside the circle = πr² = 3.14 * 3² = 28.26 sq. units
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You deposit $5000 in an account earning 5% interest compounded continuously. How much will you have in the account in 5 years? Round to the nearest cent.
Answers
Plz help me this is 7th grade math
Answers
Answer:
the picture is too small i can not see clearly
Step-by-step explanation:
Keiko is going for a walk.she takes 3 hours to walk 7.5 miles.what is her speed
Answers
Answer:
2.5 mph
Step-by-step explanation:
The highway fuel economy of a 2016 Lexus RX 350 FWD 6-cylinder 3.5-L automatic 5-speed using premium fuel is a normally distributed random variable with a mean of μ = 26.50 mpg and a standard deviation of σ = 3.25 mpg.
(a) What is the standard error of X¯¯¯
, the mean from a random sample of 25 fill-ups by one driver? (Round your answer to 4 decimal places.)
Answers
The standard error represents the average deviation of the sample means from the true population mean. Rounding this value to four decimal places, the standard error of X¯¯¯ is approximtely 0.6500 mpg.
A smaller standard error indicates that the sample means are more likely to be close to the population mean.To calculate the standard error of X¯¯¯, the mean from a random sample of 25 fill-ups by one driver, we can use the formula:
Standard Error (SE) = σ / sqrt(n),
where σ is the standard deviation and n is the sample size.
In this case, the standard deviation (σ) is given as 3.25 mpg, and the sample size (n) is 25.
Plugging in these values into the formula, we have:
SE = 3.25 / sqrt(25).
Calculating the square root of 25, we get:
SE = 3.25 / 5.
Performing the division, we find:
SE ≈ 0.65.
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completing the square.
Which of the following is equivalent to 0 equals 2 x squared plus 8 x minus 24 when completing the square?
Answers
The equivalent expression to 0 equals 2 x squared plus 8 x minus 24 when completing the square is x = 2 or x = -6
How to solve using completing the square method?0 = 2x² + 8x - 24
divide through by 2
x² + 4x - 12
x² + 4x = 12
x² + 4x + (4/2)² = 12 + (4/2)²
x² + 4x + 16/4 = 12 + 16/4
x² + 4x + 4 = 12 + 4
x² + 4x + 4 = 16
(x + 2)² = 16
Find the square root of both sides
(x + 2) = ±√16
x + 2 = ± 4
x + 2 = + 4 or x + 2 = -4
x = 4 - 2 or x = -4 - 2
x = 2 or x = -6
Therefore, x = 2 or x = -6 is equivalent to 0 = 2x² + 8x - 24 when solved using completing the square method.
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x = 2, w = -1, y = 6, z = 4 x²+4w - 2y
Answers
Answer:
-12Step-by-step explanation:
\(x = 2\\ w = -1\\ y = 6\\ z = 4\\x^2+4w-2y\\\)
\((2)^2 +4(-1) -2(6)\\4 -4 -12\\0-12\\\\=-12\)
Answer:
4x² + 4w - 2y
4(2)² + 4(-1) - 2(6)
4×4 + (-4) - 12
16 - 4 - 12
12 - 12
0 is the answer
(v-7)(v+5)(v-3)=0 solve the quadraticequation
Answers
A quadratic equation, or second-order polynomial equation with a single variable, has the form ax^2 + bx + c = 0. The solution to the given equation is v = 7, -5 and 3
Solving quadratic equations?The form ax^2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
Given the quadratic expression below:
(v-7)(v+5)(v-3)=0
Required
The solution to the system of equation
Equate each expression to zero calculate the value of 'v' as shown:
v - 7 = 0
v = 0 + 7
v = 7
Also, v + 5 = 0
v = 0 - 5
v = -5
Similarly, v - 3 = 0
v = 0 + 3
v = 3
Hence the solution to the given equation is v = 7, -5 and 3
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A group of foreign students visited the Smithsonian Museum.
Some students took taxis and 3 students took a subway from
their hotel. Each taxi carried 4 students. On the way back,
8 students took the subway while the rest took taxis. Each taxi
carried 3 students. The number of taxis and the number of
students were the same for both trips. How many students
and how many taxis were there for each trip?
Answers
Answer:
23 students
5 taxis
Step-by-step explanation:
4x + 3 = 3x + 8
x + 3 = 8
x = 5
4(5) + 3 = 23
3(5) + 8 = 23
There were 23 students and 5 taxis.
what is 25.2 divided by -0.2
Answers
We have the following:
\(\begin{gathered} \frac{25.2}{-0.2} \\ 0.2=\frac{1}{5} \\ \text{ replacing} \\ \frac{25.2}{-\frac{1}{5}}=-\frac{5\cdot25.5}{1}=-126 \end{gathered}\)The answer is -126
A student wrote four statements during math class. Which statement contains an error?
If Josh traveled 198 miles at an average speed of 33 miles per hour, he was traveling for exactly 6 hours.
If Rhonda traveled 273 miles at an average speed of 39 miles per hour, she was traveling for exactly 7 hours.
If Will traveled 376 miles at an average speed of 47 miles per hour, he was traveling for exactly 8 hours.
If Yolanda traveled 487 miles at an average speed of 53 miles per hour, she was traveling for exactly 9 hours.
Answers
Answer:
Last statement.
Step-by-step explanation:
1. We need to divide 198 by 33 to determine if this statement has an error.
198 / 33 = 6.
This statement doesn't have an error.
2. We need to divide 273 by 39 to determine if this statement has an error.
273 / 39 = 7.
This statement doesn't have an error.
3. We need to divide 376 by 47 to determine if this statement has an error.
376 / 47 = 8.
This statement doesn't have an error.
4. We need to divide 487 by 54 to determine if this statement has an error.
487 / 53 = 9.2
This statement does have an error because the answer isn't exactly 9 hours.
It is known that 5% of flashlight bulbs manufactured by a certain company are defective. a. Use the normal approximation to estimate the probability that, out of a random sample of 600 lightbulbs, at least 25 are defective. (5 points) b. Use the normal approximation to estimate the probability that, out of a random sample of 600 lightbulbs, fewer than 20 are defective. (5 points)
Answers
Using the normal approximation to the binomial, the probabilities are given by:
a) 0.8485 = 84.85%.
b) 0.0244 = 2.44%.
Normal Probability DistributionIn a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with \(\mu = np, \sigma = \sqrt{np(1-p)}\).In this problem, we have that:
There are 600 bulbs, hence n = 600.5% are defective, hence p = 0.05.The mean and the standard deviation of the approximation are given, respectively, by:
\(\mu = np = 600(0.05) = 30\)
\(\sigma = \sqrt{np(1-p)} = \sqrt{600(0.05)(0.95)} = 5.3385\)
Item a:
Using continuity correction, the probability is P(X > 24.5), which is one subtracted by the p-value of Z when X = 24.5, hence:
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{24.5 - 30}{5.3385}\)
\(Z = -1.03\)
\(Z = -1.03\) has a p-value of 0.1515.
1 - 0.1515 = 0.8485.
0.8485 = 84.85% probability.
Item b:
This probability is P(X < 19.5), which is the p-value of Z when X = 19.5, hence:
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{19.5 - 30}{5.3385}\)
\(Z = -1.97\)
\(Z = -1.97\) has a p-value of 0.0244.
The probability is of 0.0244 = 2.44%.
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1)
Find the value of x in
the triangle below:
17
A) 20.2
B) 18.7
C) 19.5
D) 21.1
E) 22.6
K
84⁰
65°
Mrs. Wilson
Mrs. Crane
Mr. Haynes
Ms. Lindstrom
Mr. Swasey
O Gina Wilson (All Things Algebra), 2014
Answers
The correct option is A) 20.2.
What is triangle sum?
The triangle sum is a property of triangles that states that the sum of the interior angles of a triangle is always equal to 180 degrees. In other words, if you add up the measures of the three angles inside a triangle, the result will always be 180 degrees.
Using the given information and the fact that the angles in a triangle sum to 180 degrees, we can find the value of x as follows:
Start by finding the measure of angle K by subtracting the measures of angles A and B from 180 degrees:
K = 180 - A - B
= 180 - 84 - 65
= 31 degrees
Use the law of sines to set up an equation relating the side lengths and corresponding angle measures:
sin(A)/x = sin(K)/17
Substitute the values we know into the equation and solve for x:
sin(84)/x = sin(31)/17
x = sin(84)*17/sin(31)
Using a calculator, we get:
x ≈ 20.2
Therefore, the value of x in the triangle is approximately 20.2.
So, the correct option is A) 20.2.
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