help with math problems graphs
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To fill the table we need to notice that Ali drives 5000 miles per year, then for the distance after a number of years we multiply the mileage for the number of year, then we have that the table will be:
2-10,000
5-25,000
8-40,000
The graph of the points is shown below:
Related Questions
Each of 5 students reported the number of movies they saw in the past year. This is what they reported.13,5,7,11,19Find the mean and median number of movies that the students saw.If necessary, round your answers to the nearest tenth.
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Answer
Mean = 9
median = 11
Explanation
The reported numbers are: 13, 5, 7, 11, 19
Mean:
[tex]\begin{gathered} Mean=\frac{\sum^x}{N} \\ \sum^x=13+5+7+11+19=45 \\ N=5 \\ \\ Mean=\frac{45}{5}=9 \end{gathered}[/tex]Median:
The median is the middle number either in ascending or descending order:
5, 7, 11, 13, 19
The median is the:
[tex]\frac{N+1}{2}=\frac{5+1}{2}=\frac{6}{2}=3rd\text{ }number[/tex]The 3rd number is 11. Therefore, the median = 11
Carla LaFong worked a 52 hr work week last week. She is paid 1 1 2 times her regular hourly rate for all hours over a 40 hr week. Her pay last week was $840. What is her hourly rate?
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If she worked a 52 hours last week and paid [tex]1\frac{1}{2}[/tex] times her regular hourly rate for all hours over a 40 hours week, her last week pay was $840, then the hourly rate is $14.48
Total hours that she worked = 52 hours
Total payment of last week = $840
She paid [tex]1\frac{1}{2}[/tex] times her regular hourly rate for all hours over a 40 hours week.
Number of overtime hours = 52 - 40
= 12 hours
If the hourly rate is x then the over time pay is 1.5x
Then the equation will be
40x + 12×1.5x = 840
Solve the equation
40x + 18x = 840
58x = 840
x = 840/58
x = $14.48
Hence, if she worked a 52 hours work week last week and paid [tex]1\frac{1}{2}[/tex] times her regular hourly rate for all hours over a 40 hours week, her pay last week was $840, then the hourly rate is $14.48
Learn more about hourly rate here
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Midnight Margaret’s school notebooks are onsale this month for 20% off regular prices. If apack of 5 notebooks normally costs $10, howmuch do you save per notebook?
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Explanation:
Discount = 20%
The cost of 5 notebooks = $10
The cost of 1 notebook before applying discount = $10/5 = $2
Applying the discount on the original price:
Discount = $10 × 20% = 10 × 0.20
Discount = $2
The sales price of the 5 notebooks = original price - discount
The sales price of the 5 notebooks = $10 - $2
The sales price of the 5 notebooks = $8
The sales price of 1 notebook = $8/5
The sales price of 1 notebook = $1.6
The amount saved per notebook = The cost of 1 notebook before applying discount -
$2 -
describe the transformation relating the graph of its has 1/2 x -3 2 to the graph of its mass of negative equals x squared
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The parent function
[tex]f(x)=x^2[/tex]The current student population of Memphis is 1600. If the population decreases at a rate of 13.9% each year. What will the student population be in 7 years?Write an exponential growth model for the future population P(x) where x is in years:P(x)=What will the population be in 7 years? (Round to nearest student)
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Answer:
Explanation:
The formula for calculating exponential growth is expressed as
P(x) = Po(1 + r)^x
where
A is the final amount after time t
Po is the initial amount
r is the growth rate
x is the time
In this case, the population is decreasing. The formula would be
P(x) = Po(1 - r)^x
From the information given,
Po = 1600
r = 13.9% = 13.9/100 = 0.139
Thus, the exponential decay model is
P(x) = 1600(1 - 0.139)^x
A = 1600(0.861)^x
In 7 years, the population would be
P(7) = 1600(0.861)^7
P(7) = 561
In 7 years, there would be 561 students
If θ is an angle in standard position and its terminal side passes through the point (-3,2). Find the exact values for sin, cosine, and tangent.
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Answer::
[tex]\sin \theta=\frac{2}{\sqrt[]{13}},\cos \theta=-\frac{3}{\sqrt[]{13}},\tan \theta=-\frac{2}{3}[/tex]Explanation:
If the terminal side passes through the point (-3,2), then the angle is in Quadrant II.
• Adjacent Side, x=-3
,• Opposite Side, y=2
Next, we find the hypotenuse, r:
[tex]\begin{gathered} r^2=(-3)^2+2^2 \\ r^2=9+4 \\ r^2=13 \\ r=\sqrt[]{13} \end{gathered}[/tex]Thus, the exact values of the trig ratios are:
[tex]\begin{gathered} \sin \theta=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{2}{\sqrt[]{13}} \\ \cos \theta=\frac{\text{Adjacent}}{\text{Hypotenuse}}=-\frac{3}{\sqrt[]{13}} \\ \tan \theta=\frac{\text{Opposite}}{\text{Adjacent}}=-\frac{2}{3} \end{gathered}[/tex]A spherical paintball measures 1.5 centimeters in diameter.Approximately how much paint is in it? (Use 3.14 for pi and round your answer to thenearest hundredth.)O 1.77 cubic cmO 14.13 cubic cmO9.42 cubic cmO 7.07 cubic cm
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ANSWER
1.77 cubic cm
EXPLANATION
To find how much paint is in the paintball, we have to find its volume.
The volume of a sphere of radius r is,
[tex]V=\frac{4}{3}\pi r^3[/tex]In this case, we know that the diameter of the paintball is 1.5 cm, so the radius is,
[tex]r=\frac{d}{2}=\frac{1.5cm}{2}=0.75cm[/tex]Using 3.14 for π, the volume is,
[tex]V=\frac{4}{3}\cdot3.14\cdot0.75^3cm^3=1.76625cm^3\approx1.77cm^3[/tex]Hence, there are approximately 1.77 cm³ in the paintball, rounded to the nearest hundredth.
Ve fine a variable, set up an equation, and solve. “Three-eighths of the seventh grade students were taking advanced math at the beginning of the year, but seven students dropped out by the end of the year. If there were 140 students taking advanced math at the end of the year, how many total seventh grade students are there?”
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Let the total number of seventh grade students be x
Let the number of seventh grade students taking advanced math be k
3/8 of x were taking advanced math at the beginning of the year, i.e
[tex]\frac{3}{8}\text{ of x}=\frac{3}{8}\times x=\frac{3x}{8}[/tex]7 students dropped out by the end of the year, i.e
[tex]\frac{3x}{8}-7=k[/tex]If there were 140 students taking advanced math at the end of the year
[tex]k=140[/tex]Substitute 140 for k into the derived expression to find x
[tex]\begin{gathered} \frac{3x}{8}-7=k \\ \frac{3x}{8}-7=140 \\ \text{Collect like terms} \\ \frac{3x}{8}=140+7 \\ \frac{3x}{8}=147 \\ \text{Crossmultiply} \\ 3x=147\times8 \\ 3x=1176 \\ \text{Divide both sides by 3} \\ \frac{3x}{3}=\frac{1176}{3} \\ x=392 \end{gathered}[/tex]Hence, the total number of seventh grade students there is 392
In parallelogram WWXY, diagonal XV is drawn. If m>XWV = 80° and m
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The diagonals of a parallelogram bisect each other at the center of the parallelogram. Therefore:
[tex]\begin{gathered} SW=US \\ so\colon \\ 12=3y \\ solve_{\text{ }}for_{\text{ }}y\colon \\ y=\frac{12}{3} \\ y=4 \end{gathered}[/tex][tex]\begin{gathered} ST=SV \\ 2x+8=20 \\ solve_{\text{ }}for_{\text{ }}x \\ 2x=20-8 \\ 2x=12 \\ x=\frac{12}{2} \\ x=6 \end{gathered}[/tex]Find x. Round your answer to the nearest integer. 15 X 53° O A. 6 O B. 9 O c. 12 O D. 8
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Given:
The right triangle with one angle 53 degree and hypotenuse is 15 units.
Using the sin ratio,
[tex]\begin{gathered} \sin \theta=\frac{Opposite\text{ side}}{\text{hypotenuse}} \\ \sin 53^{\circ}=\frac{x}{15} \\ 0.7986=\frac{x}{15} \\ x=11.97\approx12 \end{gathered}[/tex]Answer: option C) 12.
the high school marching band rehearses with either 6 or 10 members in every line what is the least number of people that can be in the marching band '?a.60b.12c.16d.30
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Answer:
The least number of people that can be in the marching band is 30
Explanation:
Given that the high school marching band rehearses with either 6 or 10 members in every line.
the least number of people that can be in the marching band is the Lowest common multiple LCM of 6 and 10.
[tex]\begin{gathered} 6=2\times3 \\ 10=2\times5 \\ \text{LCM}=2\times3\times5=30 \end{gathered}[/tex]The least number of people that can be in the marching band is 30
Which of the following is equivalent to the expression below(-3m + 5) + (m - 11)A: 4m - 16B: -4m - 6C: 2m - 16D: -2m - 6
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D: - 2m - 6
Explanations:The given expression is:
(-3m + 5) + (m - 11)
Remove the brackets
-3m + m + 5 - 11
Note:
-3m + m = -2m
5 - 11 = -6
The expression therefore becomes:
- 2m - 6
Which of the following equations represents a direct proportional relationship?Y=4x Y=1/2x-1 Y=8/x Y=x+2/5
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Answer
y = 4x
Step-by-step explanation
Direct proportional relationships follow the next general formula:
[tex]y=kx[/tex]where k is the constant of proportionality.
From the given choices, only the next equation satisfies this formula:
[tex]y=4x[/tex]where k = 4.
Joey buys a home for $266,490. His home is predicted to increase in value 5% eachyear. What is the predicted value of his home in 14 years? Round answer to thenearest whole number.
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SOLUTION
The cost of the house was $266,490
Increase rate = 5%
The cost of the house in n years time is given as
[tex]A=266,490(1.05)^n[/tex]In 14 years, the cost will be
[tex]A=266,490(1.05)^{14}[/tex]Calculate the value
[tex]\begin{gathered} A=266,490\times1.9799 \\ A=527650 \end{gathered}[/tex]Therefore, the value of the house in 14 years will be $527,650
A 6-digit code using digits 0 - 9 is given to all cashiers at a store to let them log onto thecash register. How many different codes can there be?
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There can be 21 different codes
Explanation:Parameters:
Number of codes = 6
Number to choose from = 9
It is not stated that a number cannot be used more than once, so, the different codes that can be there is:
[tex]\begin{gathered} 9C6=\frac{9!}{(9-6)!6!} \\ \\ =\frac{362880}{17280} \\ \\ =21 \end{gathered}[/tex]What is an equation in point-slope form of the line shown?
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we know that
The equation in point slope form is equal to
y-y1=m(x-x1)
step 1
Find the slope
we have the points (-4,1) and (4,-3)
m=(-3-1)/(4+4)
m=-4/8
m=-1/2
step 2
Find the equation
we have
m=-1/2
(x1,y1)=(-4,1)
substitute
y-1=-(1/2)(x+4) ------> equation in ponit slope form
with the point (4,-3)
the equation is
y+3=-(1/2)(x-4)In a soccer game, flipping a coin is the common practice to choose a favorable goal post by a team. Is this process fair for both teams?NoYesCan’t be determined
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In a soccer game, flipping a coin is the common practice to choose a favorable goal post by a team. This process is fair for both the team as long as the coin is unbiased.
Note: If the coin is biased then it cannot be determined.
Hey, there I just need help with question 10) please!
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9)
Using the ordered pairs:
[tex]\begin{gathered} (x1,y1)=(0,1) \\ (x2,y2)=(1,-2) \end{gathered}[/tex]Since the values are increasing at a constant rate, we can model the function as a linear equation of the form:
[tex]\begin{gathered} y=mx+b \\ where\colon \\ m=\frac{y2-y1}{x2-x1}=\frac{-2-1}{1-0}=-\frac{3}{1} \\ m=-3 \end{gathered}[/tex]Using the point-slope equation:
[tex]\begin{gathered} y-y1=m(x-x1) \\ y-1=-3(x-0) \\ y-1=-3x-0 \\ y=-3x+1 \end{gathered}[/tex]We do not understand how to figure this out when part of the cone is missing.
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we have that
the surface area of a truncated solid is equal to
[tex]SA=\pi\cdot\lbrack LR+Lr+R^2+r^2\rbrack[/tex]where
L is the slant heigh --------> L=6 cm
R=8 cm
r=4 cm
substitute
[tex]SA=\pi\cdot\lbrack6\cdot8+6\cdot4+8^2+4^2\rbrack[/tex][tex]\begin{gathered} SA=\pi\cdot\lbrack48+24+64+16\rbrack \\ SA=\pi(152) \\ SA=477.52cm2 \end{gathered}[/tex][tex]4 \sqrt{28x} + \sqrt{63x = } [/tex]what are the steps to solving this?
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We are given the following radical expression
[tex]4\sqrt[]{28z}+\sqrt[]{63z}[/tex]Let us simplify the expression.
Re-write the radicals as
[tex]4\sqrt[]{28z}+\sqrt[]{63z}=4\sqrt[]{4\cdot7z}+\sqrt[]{9\cdot7z}[/tex]Apply the product rule below
[tex]\sqrt[]{a\cdot b}=\sqrt[]{a}\cdot\sqrt[]{b}[/tex]So applying the above rule, the expression becomes
[tex]4\sqrt[]{4\cdot7z}+\sqrt[]{9\cdot7z}=4\sqrt[]{4}\cdot\sqrt[]{7z}+\sqrt[]{9}\cdot\sqrt[]{7z}[/tex]We know that 4 and 9 are perfect squares so the expression becomes
[tex]4\sqrt[]{4}\cdot\sqrt[]{7z}+\sqrt[]{9}\cdot\sqrt[]{7z}=4\cdot2\cdot\sqrt[]{7z}+3\cdot\sqrt[]{7z}=8\cdot\sqrt[]{7z}+3\cdot\sqrt[]{7z}[/tex]Finally, Combine the radicals
[tex]8\cdot\sqrt[]{7z}+3\cdot\sqrt[]{7z}=(8+3)\sqrt[]{7z}_{}=11\sqrt[]{7z}[/tex]Therefore, the simplified expression is
[tex]11\sqrt[]{7z}[/tex]Lonnie has three whole packages of pasta and one-third of a fourth package of pasta as 3 3/4 explain and correct Lonnie’s error
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We have 3 whole packages plus 1/3 of a package
3+1/3
3 1/3 packages
Write an equation of the parabola with vertex at (1,4) and the directrix y =16/5
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Givens.
• The vertex is (1,4).
,• The directrix is y = 16/5.
The parabola opens vertically because the directrix is a horizontal line that passes through the point (0,16/5).
But, we know that the focus point has the same distance from the vertex as the directrix, so the focus point would be F(1, 11.2). Given that the parabola opens up, the equation has the following form.
[tex]x^2=4py[/tex]Where p = 7.2, use this value to find the equation.
[tex]\begin{gathered} x^2=4(7.2)y \\ x^2=28.8y \\ y=\frac{1}{28.8}x^2 \end{gathered}[/tex]But, we still have something to add, use the vertex to find the exact equation, remember that the x-coordinate of the vertex goes with x, and the y-coordinate of the vertex goes with y.
[tex]\begin{gathered} y-4=\frac{1}{28.8}(x-1)^2 \\ y=\frac{1}{28.8}(x-1)^2+4 \end{gathered}[/tex]Therefore, the equation of the parabola is[tex]y=\frac{1}{28.8}(x-1)^2+4[/tex]Given the uniform distribution below, find the probability of the shaded region. Give your answer infraction form.
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we know that
To find out the probability of the shaded region, divide the area of the shaded region by the total area
so
Area of the shaded region is
[tex]\begin{gathered} A=\frac{1}{9}\cdot(8-6) \\ A=\frac{2}{9}\text{ units\textasciicircum{}2} \end{gathered}[/tex]Find the area of the total region
[tex]A=\frac{1}{9}\cdot(9)=1\text{ units\textasciicircum{}2}[/tex]Find the probability
[tex]P=\frac{(\frac{2}{9})}{1}=\frac{2}{9}[/tex]therefore
the answer is2/9As part of a class project, Sarah and Geoffrey conducted a survey asking their peers whether they planned on taking a music class the next year.Of the 90 students they surveyed, 43 responded favorably. Sarah and Geoffrey calculated the margin of error for different confidence intervals.Their work is shown.Which student incorrectly found the margin of error and why?
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We have to find the mistake in the calculations of the margin of error.
The survey and the margin of error have the following characteristics:
• The number of students surveyed is 90, so the sample size is n = 90.
,• The sample proportion is p = 43/90 or approximately 0.48.
,• For a 95% confidence interval, the critical value is z = 1.96 and for a 90% confidence interval, the value is z = 1.65.
The margin of error can be calculated with the following formula:
[tex]ME=z_c\cdot\sqrt{\frac{p(1-p)}{n}}[/tex]Then, if we check each formula for Sarah and Geoffrey we can see that Geoffrey uses 133 in the denominator, a value that does not correspond to the sample size n, which is 90.
Answer: Geoffrey incorrectly found the margin of error because he used the wrong sample size [Option D]
3In the figure shown, AD and BE are perpendicular bisectors of each other.Prove AACB ADCE.Explain your reasoning.ABXED
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Since AD and BE are perpendicular bisectors of each other, we can conclude:
[tex]\begin{gathered} CA=CD \\ CE=CB \end{gathered}[/tex]Besides, ∠ACB and ∠ECD are vertical angles, so, we can conclude:
[tex]\angle ACB=\angle ECD[/tex]If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent, therefore:
[tex]\Delta ACB\cong\Delta DCE[/tex]By Side-Angle-Side (SAS) Congruence.
4.Identify each sequence as arithmetic or geometric AND find the common ratio or difference: -6,-3,0,3,6,…A. Arithmetic or GeometricB. Common ratio/rate: 5,20,80,320,1280,…A. Arithmetic or GeometricB. Common rate/ratio:
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In order to check if the sequence is arithmetic, we can subtract each term by the term before. If result is always the same, the sequence is arithmetic and the difference between terms is the common rate.
The geometric sequence is similar, but we need to divide by the term before instead of subtracting.
So we have:
[tex]\begin{gathered} A\text{.} \\ -3-(-6)=-3+6=3 \\ 0-(-3)=0+3=3 \\ 3-0=3 \\ 6-3=3 \end{gathered}[/tex]So the first sequence is arithmetic, with the common rate equal to 3.
[tex]\begin{gathered} B\text{.} \\ 20-5=15 \\ 80-20=60 \\ 320-80=240 \\ \ldots \end{gathered}[/tex]The differences are not the same, so let's try dividing them now:
[tex]\begin{gathered} \frac{20}{5}=4 \\ \frac{80}{20}=4 \\ \frac{320}{80}=4 \\ \frac{1280}{320}=4 \end{gathered}[/tex]So the second sequence is geometric, and the common ratio is equal to 4.
Suppose that the funcation p and q are defined as follows
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Given the functions p(x) and q(x) defined as:
[tex]\begin{gathered} p(x)=x^2+3 \\ q(x)=\sqrt[]{x+2} \end{gathered}[/tex]We can use the definition of composite functions:
[tex](f\circ g)(x)=f(g(x))[/tex]Then, to calculate (p o q)(2) = p(q(2)), we need to calculate q(2) first:
[tex]q(2)=\sqrt[]{2+2}=\sqrt[]{4}=2[/tex]Using this result on the composition:
[tex]\begin{gathered} (p\circ q)(2)=p(q(2))=p(2)=2^2+3=4+3 \\ \Rightarrow(p\circ q)(2)=7 \end{gathered}[/tex]Now, for (q o p)(2) = q(p(2)), we already calculate p(2) = 7. Then:
[tex]\begin{gathered} (q\circ p)(2)=q(p(2))=q(7)=\sqrt[]{7+2}=\sqrt[]{9} \\ \Rightarrow(q\circ p)(2)=3 \end{gathered}[/tex]-413.765: Is it a terminating decimal
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Answer
-413.765 is a terminating decimal since the numbers after the decimal point (0.765) are finite, that is, they have a known ending.
Explanation
A terminating decimal is a decimal that contains a definite (finite) number of digits after the decimal point.
Refer to the scenario below to answer the following questions: (a) Why are triangles RST and VUT similar? (b) What is the height of the tree?
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The triangles are similar because they have the same internal angles. That is,
∠S ≅ ∠U
∠T ≅ ∠T
∠R ≅ ∠V
Given that they are similar, then their sides are in proportion, as follows:
[tex]\frac{SR}{UV}=\frac{RT}{TV}[/tex]Replacing with data and solving for x,
[tex]\begin{gathered} \frac{1.7\text{ m}}{x\text{ m}}=\frac{1.2\text{ m}}{31.5\text{ m}} \\ 1.7\cdot31.5=1.2\cdot x \\ 53.55=1.2\cdot x \\ \frac{53.55}{1.2}=x \\ 44.625\text{ m =x} \end{gathered}[/tex]In triangle ABC, with right angle at C, if c=6 and a=4, the CosA=
Answers
ANSWER
cos A = √20/6 ≈ 0.75
EXPLANATION
Triangle ABC is:
Since this is a right triangle we can use the trigonometric ratios to find cosA:
[tex]\cos A=\frac{\text{adjacent side}}{hypotenuse}[/tex]the hypotenuse of this triangle is side c, and the adjacent side is side b. We don't have side b, but we have two sides and again, as this is a right triangle, we can use the Pythagorean theorem to find the missing side:
[tex]\begin{gathered} c^2=a^2+b^2 \\ b=\sqrt[]{c^2-a^2} \\ b=\sqrt[]{6^2-4^2} \\ b=\sqrt[]{36-16} \\ b=\sqrt[]{20} \end{gathered}[/tex]The cosine of A is then:
[tex]\cos A=\frac{b}{c}=\frac{\sqrt[]{20}}{6}[/tex]Rounded to the nearest hundredth:
[tex]\cos A\approx0.75[/tex]