f[g(-2)] = 2 as the function f(x) = x - 5 must then be used to evaluate the function f[g(-2)] .
what is function ?A function is a mathematical construct that transforms a set of inputs (referred to as the domain) into a single output from another set (called the range). A function is, in other words, a rule that allots precisely one output to each input in the domain. The notation f(x) is frequently used to denote functions, where f stands for the function name and x for the input value. As an illustration, the function f(x) = 2x + 1 doubles any input x, adds 1, and returns the result.
given
To begin, we must calculate g(-2) using the formula g(x) = x2 + 3:
[tex]g(-2) = (-2)^2 + 3 = 4 + 3 = 7[/tex]
The function f(x) = x - 5 must then be used to evaluate the function f[g(-2)]:
f[g(-2)] = f(7) = 7 - 5 = 2
Hence, f[g(-2)] = 2.
f[g(-2)] = 2 as the function f(x) = x - 5 must then be used to evaluate the function f[g(-2)] .
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For the function y = -1/2 x + 7, find the matching y-value when x = -8
Answer:
11
Step-by-step explanation:
y = -1/2x + 7
x = -8
A double negative equals a positive therefore it would be the same as 8 x 1/2 which is 4.
y = 4 + 7
y = 11
Step-by-step explanation:
y = -1/2 X -8 + 7
y = -0,5 X -8 + 7
y = 4 + 7
y = 11
prove the following identity:
hope you understood the answer
Last year the city of Goose Pimple, Vermont, paid an average of $3,261 per employee in health care costs (including insurance and additional claims). This year the city management decided that they will contract with Grimms Health Maintenance Organization. At the end of the year they would like to know if they have saved any money. They take a sample of 50 and find a sample mean of $3,015 with a standard deviation of $1,745. Present a hypothesis, a null hypothesis, and evaluate the hypothesis.
The answer of the given question based on the hypothesis the answer is the calculated t-value of -2.58 is less than the critical t-value of -2.009, we cannot reject the null hypothesis.
What is Hypothesis?A hypothesis is an educated guess or prediction that is used to explain an observation or set of observations. It is a proposed explanation or possible answer to a research question or problem that is based on prior knowledge, experience, and research. In science, a hypothesis is often tested through experiments or observations to determine if it can be supported or rejected by the evidence.
Hypothesis:
The city of Goose Pimple, Vermont, hypothesizes that contracting with Grimms Health Maintenance Organization will result in a significant reduction in health care costs per employee.
Null Hypothesis:
The null hypothesis is that there is no significant difference in health care costs per employee between last year and this year with the contract with Grimms Health Maintenance Organization having no impact.
Evaluation:
To evaluate the hypothesis, we will perform a one-sample t-test. The test statistic is calculated as:
t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
Assuming a significance level of 0.05, we will reject the null hypothesis if the calculated t-value is greater than the critical t-value.
Population mean = $3,261 (given)
Sample mean = $3,015
Sample standard deviation = $1,745
Sample size = 50
t = (3015 - 3261) / (1745 / sqrt(50)) = -2.58
Using a t-table with 49 degrees of freedom (sample size - 1) and a significance level of 0.05, the critical t-value is ±2.009.
Since the calculated t-value of -2.58 is less than the critical t-value of -2.009, we cannot reject the null hypothesis. This means that there is not enough evidence to suggest that there is a significant difference in health care costs per employee between last year and this year with the contract with Grimms Health Maintenance Organization having no impact.
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g(x) is a function as defined below
g(x) = 3 (x/2)
If you input 4 into g(x), what do you get for an output?
Enter your answer in the simplest form in the space provided below.
(If your answer is a decimal number, round it to two decimal places.)
Answer:
Step-by-step explanation:
If we input 4 into g(x) = 3(x/2), we get:
g(4) = 3(4/2) = 3(2) = 6
Therefore, the output of g(4) is 6.
PLEASE HELPPPPP ASAPP
In conclusion the length of the rectangle is 319 feet.
How to find?
Let's denote the width of the rectangle as w.
According to the problem, the length of the rectangle is 154 feet more than the width, so we can express the length as w + 154.
The perimeter of a rectangle is given by the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.
Using the given perimeter of 968 feet, we can write:
968 = 2(w + w + 154)
Simplifying and solving for w, we get:
968 = 4w + 308
660 = 4w
w = 165
Therefore, the width of the rectangle is 165 feet.
We can find the length by using the expression we found earlier:
l = w + 154 = 165 + 154 = 319
Therefore, the length of the rectangle is 319 feet.
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What is the loca extrema/ absolute of the polynomial 10x^5 + 22x^4 + 20x^3 -0x^2 + 6
(a) The local extrema of the polynomial are: Local maximum at x = -0.68 and Local minimum at x = -0.32
(b) There is no global minimum or maximum.
What are the local extrema of the polynomial?To find the local extrema and absolute extrema of the given polynomial 10x⁵ + 22x⁴ + 20x³ - 0x² + 6, we need to take the first and second derivatives of the polynomial and find the critical points.
The first derivative is:
50x⁴ + 88x³ + 60x²
The second derivative is:
200x³ + 264x² + 120x
Setting the first derivative to zero, we get:
50x⁴ + 88x³ + 60x² = 0
Factoring out x², we get:
x²(50x² + 88x + 60) = 0
Using the quadratic formula to solve for the roots of the quadratic equation 50x² + 88x + 60 = 0, we get:
x = -0.68 or x = -0.32
These are the critical points of the polynomial. To determine whether they correspond to local extrema or inflection points, we need to look at the sign of the second derivative at each point.
Substituting x = -0.68 into the second derivative, we get:
200(-0.68)³ + 264(-0.68)² + 120(-0.68) = -148.68
Since the second derivative is negative at x = -0.68, this critical point corresponds to a local maximum.
Substituting x = -0.32 into the second derivative, we get:
200(-0.32)³ + 264(-0.32)² + 120(-0.32) = 9.48
Since the second derivative is positive at x = -0.32, this critical point corresponds to a local minimum.
To find the absolute extrema, we also need to evaluate the polynomial at the endpoints of the interval we are interested in. Since the polynomial does not have any real roots, we can assume that the interval of interest is the entire real line.
Taking the limit of the polynomial as x approaches positive or negative infinity, we see that the leading term dominates and the polynomial goes to positive infinity as x approaches infinity and negative infinity.
Therefore, there is no global minimum or maximum.
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Calculate the vertex of the parabola using the equation
Using the formula for x which is x = - b/2a, we know that the vertex of the given parabola is 5 respectively.
What is a parabola?A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics.
It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.
A parabola can be described using a point and a line.
Three different parabolas exist.
Vertex form, standard form, and intercept form are the three forms.
You can access a unique key feature for the graph on each form.
So, we have the equation:
y = -2x² - 8x - 3
Now, we know that x = - b/2a
Solve for x:
x = - b/2a
x = - (-8)/2(-2)
x = 8/-4
x = -2
Now, insert x = -2 in the given equation:
y = -2x² - 8x - 3
y = -2(-2)² - 8(-2) - 3
y = -2(4) + 16 - 3
y = -8 + 16 - 3
y = 8 - 3
y = 5
Therefore, using the formula for x which is x = - b/2a, we know that the vertex of the given parabola is 5 respectively.
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Hannah invested $4,000 in a savings account that earned 2% interest compound quarterly.She determined that if she dose not withdraw or deposit any more money,the value of the account at the end of 3 years will be $4,244.83.What error did Hannah make in her calculations? What will the account balance be after 3 years?Explain.
Hannah made an error in her calculations by using simple interest instead of compound interest. To find the balance of a savings account with compound interest, you need to take into account the effect of compounding, where the interest earned is added to the principal and then earns interest as well.
To calculate the actual balance of the account after 3 years, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the ending balance of the account
P = the principal amount (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years the money is invested
In this case, we have:
P = $4,000
r = 2% = 0.02
n = 4 (since interest is compounded quarterly)
t = 3
Plugging in these values, we get:
A = $4,000(1 + 0.02/4)^(4*3) = $4,493.72
Therefore, the actual balance of the account after 3 years with compound interest is $4,493.72.
Hannah's calculation of $4,244.83 was based on using the formula for simple interest, which only takes into account the initial investment and the annual interest rate, but not the effect of compounding.
Answer:
Her account balance after 3 years is $4,246.71
Step-by-step explanation:
In this question, we are tasked with calculating what Hannah's account balance will be after 3 years and the error she made in her calculations
Mathematically, to calculate the account balance after 3 years, we use the formula for the compound interest as follows.
Mathematically, the amount A earned on a compound interest is calculated as
A = P
where A is the account balance after the number of years which is what we want to know
P is the initial amount invested which is $4000
r is the interest rate which is 2%(2/100 = 0.02) according to the question
n is the number of times interest is compounded per year which is 4(quarterly means every 3 months)
t is the number of years which is 3
We plug the values into the question;
A = 4000(1 + 0.02/4)^(3)(4)
A = 4000(1+0.005)^12
A = 4000(1.005)^12
A = $4,246.71
P.S ; I do not see Hannah's calculation and as such I cannot spot where she made the error in her calculations
Help with math problems
An inequality which has solutions represented by the graph include the following: C. x > 4
What is an inequality?In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).Next, we would determine the solution as follows;
5 - x > 4
-x > 4 - 5
x > 1 (False).
2x + 1 ≥ 9
2x ≥ 9 - 1
2x ≥ 8
x ≥ 4 (False).
2x - 5 > 3
2x > 3 + 5
2x > 8
x > 4 (True).
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PLEASE GET THIS DONE AS SOON AS POSSIBLE!!!
[tex]\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ V=167\pi \end{cases}\implies 167\pi =\cfrac{4\pi r^3}{3}\implies \cfrac{3}{4\pi }\cdot 167\pi =r^3 \\\\\\ \cfrac{501}{4}=r^3\implies \sqrt[3]{\cfrac{501}{4}}=r\implies 5.0\approx r \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ V=683\pi \end{cases}\implies 683\pi =\cfrac{4\pi r^3}{3}\implies \cfrac{3}{4\pi }\cdot 683\pi =r^3 \\\\\\ \cfrac{2049}{4}=r^3\implies \sqrt[3]{\cfrac{2049}{4}}=r\implies 8.0\approx r[/tex]
Below is the entire graph of function f.
Graph f^-1, the inverse of f.
The inverse of the graph of f is added as an attachment
Graphing an Inverse FunctionTo graph an inverse function from the a graph, follow these steps:
Make a plot the orginal graph (the given graph)Reflect the points of the graph over the line y = x to obtain the inverse graph i.e. we swap the x and the y coordinates of the points on the graphLabel the new graph as the inverse function of the original graph.Using the above steps, we have the inverse graph added as an attachment
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Mr Davis buys a 4 pizza for a family dinner. He cuts each pizza into sixths. How many pieces of pizza does Mr.Davis have for the family dinner?
Answer: 24 pieces of pizza
Step-by-step explanation:
If you have one pizza and cut that into 6 pieces (which is what it means by sixths) that means you have 6 pieces per pizza. Since you have 4 pizzas and 6 slices each that means you multiply 4 by 6 to get the answer. Which ends up being 24 pieces.
Mr. Davis has 24 pieces of pizza for the family dinner.
What is an expression?In mathematics, an expression is a combination of symbols and numbers that represent a mathematical quantity or relationship.
It can consist of variables, constants, operators, and functions, and may include arithmetic operations, exponents, and other mathematical operations.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To find the total number of pizza slices, we need to first determine the total number of slices in one pizza, and then multiply that by the number of pizzas.
Since each pizza is cut into sixths, there are 6 slices in one pizza.
So,
For 4 pizzas, the total number of slices is:
Total number of slices
= 4 x 6 = 24
Thus,
Mr. Davis has 24 pieces of pizza for the family dinner.
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The track team needs to sell x coupon books. The team members have already sold 18 books. How many more books does the team need to sell?
Answer:
s=x-18
Step-by-step explanation:
The total of number of books they need to sell is
the total minus 18. And that will equal the amount of books they still need to sell.
Can someone please help me
The graphs of the exponential functions are introduced in the image attached below.
The solution to the system of two exponential functions is 35 representatives and 7.735 minutes of average wait time.
How to represent two exponential functions and find graphically the solution of the resulting system
In this problem we must represent two exponential functions describing average wait time, in minutes, as a function of number of customer service representatives. The functions are described by:
A(x) = 15.7 · 0.98ˣ
B(x) = 11 · 0.99ˣ
Now we draw each of the two functions by the help of a graphing tool. The solution to the system of exponential functions is:
Number of Customer Service Representatives: 35
Average Wait Time: 7.735 minutes
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find the surface area of each figure. Round your answers to the nearest hundredth if necessary
5) The total surface area of the pentagonal prims is 500 cm².
6) The total surface area of the pentagonal prims is 243 mi².
What is the formula surface area of prism?The formula for determining the surface area of the prism is expressed as:
Total Surface Area of Pentagonal Prism,
T = 5ab + 5bh sq. units.
where is altitude, b is base and h is height
5) here, a = 5.5 cm
b = 8 cm
h = 7 cm
Total Surface Area = 5ab + 5bh
T = 5(5.5)(8) + 5(7)(8)
T = 220 + 280
T = 500 cm²
The total surface area of the pentagonal prims is 500 cm².
6) here, a = 4.1 mi
b = 6 mi
h = 4 mi
Total Surface Area = 5ab + 5bh
T = 5(4.1)(6) + 5(4)(6)
T = 123 + 120
T = 243 mi²
The total surface area of the pentagonal prims is 243 mi².
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The complete question is in the attached figure:
Find the surface area of each figure. Round your answers to the nearest hundredth if necessary
A plaque is made with a rhombus in the middle. If the diagonals of the rhombus measure 7 inches and 9 inches, and the plaque has dimensions 7.5 inches by 10 inches, how much space is available for engraving text onto the award?
Hence, there are 43.5 square inches accessible on the award for text engraving.
what is square ?A square is a geometric figure with four equal sides and four right angles. It is a particular kind of rectangle with equal-length sides. It is also possible to describe it as a regular quadrilateral with equal-length sides and right-angled corners. By multiplying one side of a square by itself, the area of the square can be calculated. A = s2 is the formula for calculating the area of a square, where A stands for the area and s for the length of one side. The perimeter of a square is calculated similarly by adding the lengths of its four sides. P = 4s is the formula for calculating a square's perimeter, where P stands for the perimeter.
given
The plaque's available engraving space is equal to the plaque's surface area less the rhombus's area in the centre.
The plaque's location is:
Area plaque is equal to 7.5 x 10 inches, or 75 square inches.
The rhombus's surface area is:
(diagonal1 x diagonal2) / 2 = (7 x 9) / 2 = 31.5 square inches is the area of a rhombus.
Thus, the following is the engraving area:
Area available equals Area plaque minus Area rhombus, or 75 minus 31.5, or 43.5 square inches.
Hence, there are 43.5 square inches accessible on the award for text engraving.
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Problem solving
What percentage of the triangle is shaded?
Mandy is making a pair of cube-shaped bookends. Each bookend has an edge that is 9 centimeters (cm) long. Find the volume, in cubic centimeters, for both bookends.
The volume of both book end is 1458 [tex]cm^3[/tex].
What is volume?The space taken up by any three-dimensiοnal sοlid cοnstitutes a vοlume, tο put it simply. A cube, cubοid, cοne, cylinder, οr sphere can be οne οf these sοlids. Cubic units are used tο measure the vοlume οf sοlids. The vοlume will be given in cubic metres, fοr instance, if the dimensiοns are given in metres.
Here the side length of cube = 9cm
Now using volume of cube formula then,
=> Volume of cube V = [tex]v^3[/tex] cubic unit.
=> V = [tex]9^3[/tex]
=> V = 9*9*9 = 729 [tex]cm^3[/tex].
Here we had pair of book end then volume = 2V = 2*729 = 1458 [tex]cm^3[/tex].
Hence the volume of both book end is 1458 [tex]cm^3[/tex].
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Sheila manages a team of editors at a publishing company. To help determine deadlines, she developed a model based on past
projects. In the model below, x represents the number of pages which require editing, and y represents the total number of days required to complete the editing.
y = 1/85x
The linear equation that models the number of days it will take Sheila's team to edit x pages, y = (1/85)·x indicates that the correct statement is option C.
C. Her team can edit 85 pages in one day
What is the slope-intercept form of linear equations?The slope-intercept form of linear equations is; y = m·x + c, where the coefficient m is the slope and c is the y-intercept.
The parameters of the model, y = (1/85)·x are;
x = The number of pages that require editing
y = The number of days required to complete the editing
Therefore, the model is in the slope and intercept form of a linear equation, where;
1/85 = The slope
The y-intercept is zero
The slope indicates that 85 pages can be edited in one day, therefore the number of days to edit 170 (2 × 85) pages is 2 days
Similarly, when the number of days, y = 1, and the number of pages to be edited, x = 1, we get;
y = (1/85)·x
1 = (1/85)·x
x = 1/(1/85) = 85
The number of pages that can be edited in one day is 85 pages
The correct statement is therefore;
C. Her team can edit 85 pages in one day
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Each month, a shopkeeper spends 8x+15 dollars on rent and electricity. If he spends 3x−7 dollars on rent, how much does he spend on electricity? Use pencil and paper. For which value(s) of x is the amount the shopkeeper spends on electricity less than $100? Explain how you found the value(s).
According to given equations, any value of x less than 15.6 will result in the shopkeeper spending less than $100 on electricity.
What is an equation?
An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, a left-hand side and a right-hand side, separated by an equals sign (=). The left-hand side and the right-hand side of an equation may contain one or more variables, and the equation is true only for certain values of these variables.
Let E be the amount the shopkeeper spends on electricity. Then, we have:
Total monthly expenses = Rent + Electricity = 8x + 15
Rent = 3x - 7
Substituting the value of Rent in the equation of total monthly expenses, we get:
8x + 15 = (3x - 7) + E
Simplifying this equation, we get:
5x + 22 = E
Therefore, the shopkeeper spends 5x + 22 dollars on electricity.
To find the value(s) of x for which the shopkeeper spends less than $100 on electricity, we can set up an inequality:
5x + 22 < 100
Solving for x, we get:
5x < 78
x < 15.6
Therefore, for any value of x less than 15.6, the shopkeeper will spend less than $100 on electricity. To verify this, we can plug in a value of x less than 15.6 and see if the resulting amount spent on electricity is less than $100. For example, if we let x = 10, then:
5x + 22 = (5 * 10) + 22 = 72
Since 72 is less than $100, we have verified that any value of x less than 15.6 will result in the shopkeeper spending less than $100 on electricity.
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You are given a t-statistic of -0.38. Write a short paragraph on whether the t-statistic means
that there are differences between two groups. It is up to you decide how to name the two groups
in your paragraph.
we can conclude that there is no strong evidence of a statistically significant difference between the means of the two groups.
What is the t-statistic?
A t-statistic is a test statistic that is used to determine if there is a significant difference between two groups based on their means.
A t-statistic with an absolute value greater than 1.96 indicates statistical significance at the 0.05 level of significance.
In this case, the t-statistic is -0.38, which is less than the absolute value of 1.96.
This means that the difference between the means of the two groups is not statistically significant at the 0.05 level of significance.
Without information on the specific groups being compared, it is not possible to make definitive conclusions about the differences between them based solely on the t-statistic.
Hence, we can conclude that there is no strong evidence of a statistically significant difference between the means of the two groups.
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21. In the voting for City Council Precinct 5, only of all eligible voters cast votes. What fraction of all eligible voters voted for Shelley? Morgan? Who received more votes?
All eligible voters voted for Shelley= 3/20 ,
All eligible voters voted for Morgan= 31/100, Morgan received most votes.
What is mean by multiplication?Multiplication is a mathematical operation that embodies the basic idea of numerous additions of the same number. The outcomes of multiplying two or more numbers are referred to as the product of those numbers, and the factors are the quantities that are multiplied. Multiplication facilitates the process of adding the same number again.
Let's suppose Precinct 5 has 100 registered voters. There were 50 voters who participated in the election because only 50% of those who were eligible to vote actually did so.
3/10 of the votes were cast for Shelley, which translated as 3/10 x 50 or 15 votes.
With 5/8 of the vote, Morgan received 5/8 x 50 votes, or 31.25 votes. Therefore, we must round this figure down to 31 votes as we are dealing with whole voters.
We must divide the number of votes received by the total number of eligible voters in order to determine the percentage of all eligible voters who cast a ballot for Shelley: 100 eligible voters x 15 votes = 3/20.
Morgan won the most votes since she received more than Shelley.
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Teaching Textbooks Geometry! Can I get some help finding the measure of angle KLN?!? Please answer fast? :D
The measure of angle KLN in the given set of intersecting lines is 100°.
What is intersecting lines?In geometry, intersecting lines are lines that cross or meet each other at a point. The point at which the lines intersect is called the point of intersection. Intersecting lines are a fundamental concept in geometry and are used to define many other geometric shapes and concepts. For example, the intersection of two lines can form an angle, and the measurement of this angle can provide information about the relative positions of the lines.
Here,
Since the sum of angles in a quadrilateral is 360 degrees, we can set up an equation:
M + 100 + (x-y) + m<KLN = 360
We also know that m<MOL = m<KLN, since they are opposite angles of a line. Therefore:
m<KLN = m<MOL
We can use the fact that the sum of angles in a triangle is 180 degrees to set up another equation:
m<MOL + m<MON + m<NOL = 180
Since m<MOL = m<KLN, we can substitute m<KLN for m<MOL:
m<KLN + m<MON + m<NOL = 180
Now we have two equations:
M + 100 + (x-y) + m<KLN = 360
m<KLN + m<MON + m<NOL = 180
We need to solve for m<KLN. Let's isolate m<KLN in the second equation:
m<KLN = 180 - m<MON - m<NOL
Now we can substitute this expression for m<KLN in the first equation:
M + 100 + (x-y) + (180 - m<MON - m<NOL) = 360
Simplifying, we get:
280 - m<MON - m<NOL + x - y = M
Rearranging, we get:
m<MON + m<NOL = 280 + x - y - M
100=x-y
y=2/7x
100=x-2x/7
x=700/5
x=140
y=2*140/7
y=40
x-y=100°
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If Linda can walk 6 miles in 80 minutes. What is her walking rate per hour?
3 miles per hour
4 miles per hour
4.5 miles per hour
5.5 miles per hour
The walking rate per hour of Linda if Linda can walk 6 miles in 80 minutes is 4.5 miles per hour
Calculating the walking rate per hour of Linda?Given that we have the following parameters
Distance = 6 miles
Time = 80 minutes
When the minutes is converted to hours, we have the following readings
Distance = 6 miles
Time = 4/3 hours
The walking rate per hour of Linda is then calculated as
Walking rate = 6/(4/3)
Evaluating the expression, we have
Walking rate = 4.5
Hence, the walking rate is 4.5 miles per hour
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Solve for x. 3(2 + x) - 2x = 11 + 2(2 + 5x)
Answer: x = -1
Step-by-step explanation:
Step 1: Distribute. 6 + 3x - 2x = 11 + 4 + 10x
Step 2: Subtract like-terms. x + 6 = 10x + 15
Step 3: Leave x by itself. x + (6-6) = 10x + (15-6)
Step 4: Subtract 10x to x, and simplify. (x - 10x) = (10x - 10x) + 9
Step 5: Divide. -9x/9 = 9/9
The answer is x = -1. Hope this helps
Bridget has a rectangular brick of cement which is too large by 5 cm in each dimension( length, breadth and height). She is about to trim the excess off , when Jill passes by and observes that she can get two identical bricks each of exactly the same dimensions. H splitting the brick in half. What are the dimensions of the brick?
The dimensions of each half rectangular brick are, length 15 cm, and height 10 cm.
What are the dimensions of the brick?Let the original dimensions of the rectangular brick be length L, breadth B, and height H.
According to the problem statement, each dimension of the original brick is 5 cm larger than the desired dimensions of each half brick.
Therefore, the dimensions of each half brick are;
(L-5)/2, (B-5)/2, and (H-5)/2.
Since the two half bricks have identical dimensions, we have:
(L-5)/2 = (B-5)/2 = (H-5)/2
Simplifying this equation, we get:
L-5 = B-5 = H-5
Therefore, L = B = H + 5.
Now, the volume of the original brick is L x B x H, and the volume of each half brick is [(L-5)/2] x [(B-5)/2] x [(H-5)/2].
Since the two half bricks have the same dimensions, their volumes are equal. Thus, we have:
(L-5)/2 x (B-5)/2 x (H-5)/2 = (L x B x H)/2
Substituting L = B = H + 5, we get:
(H+5-5)/2 x (H+5-5)/2 x (H-5)/2 = (H x H x (H+5))/2
Simplifying this equation, we get:
(H+5)/2 x (H-5)/2 x H/2 = (H x H x (H+5))/2
Cancelling out the factor of 1/2, we get:
(H+5)(H-5)H = H x H x (H+5)
Simplifying this equation, we get:
H³ - 125H = H³ + 5H²
Subtracting H³ from both sides, we get:
-125H = 5H²
Dividing both sides by 5H, we get:
H = -25 or H = 0
Since H represents the height of the brick, it must be positive. Therefore, we have H = 0, which implies that the original brick has zero height. This is not a valid solution, so we reject it.
Therefore, the only valid solution is:
H = 25 cm
Substituting this value of H in the equation L = B = H + 5, we get:
L = B = 30 cm
Therefore, the dimensions of the original brick are:
Length = L + 5 = 35 cm
Breadth = B + 5 = 35 cm
Height = H + 5 = 30 cm
And the dimensions of each half brick are:
Length = Breadth = 15 cm
Height = 10 cm
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A box of six pencils cost £1.56. A box of eight rubbers cost £2.72. What is the difference in cost between one pencil and one rubber?
By answering the presented question, we may conclude that As a result, inequality the cost difference between one pencil and one rubber is £0.08.
What is inequality?In mathematics, an inequality is a non-equal connection between two expressions or values. As a result, imbalance leads to inequity. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal symbol is typically used (). Various disparities, no matter how little or huge, are utilised to contrast values. Many basic inequalities may be solved by altering the two sides until just the variables remain. Yet, a lot of factors contribute to inequality: Negative values are split or added on both sides. Exchange left and right.
To determine the cost difference between one pencil and one rubber, we must first determine the cost per item for each product.
The price of a pencil is 1.56 / 6 = £0.26.
The price of a rubber is 2.72 / 8 = £0.34.
Therefore the cost difference between one pencil and one rubber is:
£0.34 - £0.26 = £0.08
As a result, the cost difference between one pencil and one rubber is £0.08.
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it cost josiah 9.75 to send 65 text message. how many texts did he sent if he spent 28.20
Answer: 188 messages
Step-by-step explanation:
We will set up and solve a proportion.
[tex]\displaystyle \frac{9.75}{65} =\frac{28.2}{x}[/tex]
Now, we will cross-multiply.
9.75 * x = 65 * 28.2
9.75x = 1,833
Lastly, we will divide both sides of the equation by 9.75.
x = 188 messages
A parabola opening up or down has vertex (0, -3) and passes through (4, -7). Write its
equation in vertex form.
Answer:
Since the vertex is (0,-3), we know that the equation of the parabola will have the form:
y = a(x - 0)^2 - 3
where "a" is the coefficient that determines whether the parabola opens up or down.
To find the value of "a", we can use the fact that the parabola passes through the point (4, -7):
-7 = a(4 - 0)^2 - 3
-7 + 3 = 16a
-4 = 16a
a = -1/4
Substituting this value of "a" into the equation for the vertex form, we get:
y = -(1/4)x^2 - 3
So the equation of the parabola in vertex form is y = -(1/4)x^2 - 3, with vertex (0, -3) and passing through (4, -7).
Step-by-step explanation:
The prices of 10 iPads at a local electronic store are listed. Find the mean, median, and mode (if one exists). Round to the nearest
dollar.
$665, $891, $949, $954, $923, $958, $622, $877, $986, $993
Part: 0/3
E
Answer:
Mean = 880.8
Median = 936
Mode = None
Step-by-step explanation:
1.
To find the mean of a list of numbers, simply add them all up and divide them by the number of numbers listed.
(655+891+949+954+923+958+622+877+986+993)/10 = 880.8
Mean = 880.8
2.
To find median, put the numbers in order and choose the one in the middle
622 665 877 891 (923 949) 954 958 986 993
Because we were given two numbers in the middle, find the mean of those two numbers
(923+949)/2 = 936
Median = 936
3.
To find mode, you find the number that is listed the most.
Since all the numbers listed are different, there is no mode.