Answer:
[tex]y-6=-\dfrac{1}{8}(x-10)[/tex]
Step-by-step explanation:
To find the equation of a line that passes through two points, first find its slope by substituting the given points into the slope formula.
Define the points:
(x₁, y₁) = (10, 6)(x₂, y₂) = (2, 7)Substitute the points into the slope formula:
[tex]\implies m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{7-6}{2-10}=\dfrac{1}{-8}=-\dfrac{1}{8}[/tex]
Therefore, the slope of the line is -¹/₈.
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
To find the equation in point-slope form, simply substitute the found slope and one of the given points into the point-slope formula:
[tex]\implies y-6=-\dfrac{1}{8}(x-10)[/tex]
The percentage of students in the school that attended the talent show for the years 2008 to 2013 are shown.This Year, the school had a total of 360 students. How many students do you expect to attend the talent show this year? Explain.
Considering this year as the last year in the table which is 2013
[tex]\text{the total number of students in 2013=360}[/tex][tex]\text{The percentage of students attendance in 2013=95\%}[/tex]Therefore,
The number of students to attend this year's talent show will be calculated by
[tex]A\text{ttendance}=\text{percentage of students}\times total\text{ number of students}[/tex][tex]\begin{gathered} \text{Attendance}=95\text{ \%}\times360 \\ \text{Attendance}=\frac{95}{100}\times360 \\ \text{Attendance}=\frac{34200}{100} \\ \text{Attendance}=342\text{ students} \end{gathered}[/tex]Hence.
The attendance for this year is 342 students
Question 2 (7 points)Match the fractions and decimals to the corrects percentage.
we can change a fraction to a percentage multiplying the fraction by 100
also, we can change a decimal number to a percentage multiplying by 100
for example
1. 1/5
[tex]\frac{1}{5}\cdot100=20[/tex]In this case, 1/5 represent 20%
4. .625
[tex]0.625\cdot100=62.5[/tex]In this case, 0.625 represent 62.5%
If we do the same process to all the next numbers we will obtain the next solutions.
1. 1/5 ------ a. 20%
2. 8/10 ------ f. 80%
3. 0.08 ------ d. 8%
4. .625 ---- g. 62.5%
5. 32/100 ---- b. 32%
6. 1/2 ------ c. 50%
7. 1.25 ---- e. 125%
make a table of values then graph the following quadratic functions, label atleast 5 points
Given the function below:
[tex]f(x)=\frac{-4(x-3)^2}{9}+4[/tex]Substituting each value of x in the table in the function above, we get
[tex]\begin{gathered} f(0)=\frac{-4(0-3)^2}{9}+4\text{ = }\frac{-4(-3)^2}{9}+4 \\ \\ f(0)=\frac{-4\times9}{9}+4\text{ =-4+4 = 0} \end{gathered}[/tex][tex]f(1)=\frac{-4(1-3)^2}{9}+4\text{ =}\frac{-4\times4}{9}+4=\frac{-16}{9}+4=\frac{20}{9}[/tex][tex]f(6)=\frac{-4(6-3)^2}{9}+4\text{ = }\frac{-4(3^2)}{9}+4\text{ =-4+4 = 0}[/tex]A data set includes weights of garbage discarded in one week from 62 different households. The paired weights of paper and glass were used to obtain the results shown to the right. Is there sufficient evidence to support the claim that there is a linear correlation between weights of discarded paper and glass? Use a significance level of α=0.05. correlation matrix: Variables Paper Glass Paper 1 0.1983 Glass 0.1983
There is not enough evidence to support the claim that there is a linear correlation between the weights of discarded paper and glass for a significance level of α = 0.05.
Given,
A data set includes weights of garbage discarded in one week from 62 different households.
significance level of α=0.05.
Now, According to the question:
The correlation matrix provided is:
Variables Paper Glass
Paper 1 0.1853
Glass 0.1853 1
The hypothesis for the test is:
H₀: ρ = 0 vs. H₀: ρ ≠ 0
The test statistic is:
r = 0.1983 ≈ 0.198
As the alternate hypothesis does not specifies the direction of the test, the test is two tailed.
The critical value for the two-tailed test is:
[tex]r_{alpha}/2, (n -2) = r_{0.005}/2 ,(62-2) = 0.250[/tex]
The conclusion is:
Because the absolute value of the test statistic is less than the positive critical value, there is not enough evidence to support the claim that there is a linear correlation between the weights of discarded paper and glass for a significance level of α = 0.05.
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A triangle has two sides of length 13 and 17. What is the largest possible whole numberlength for the third side?
Given two sides of a triangle, x, and z, such that
[tex]x\le z[/tex]then the third side y must satisfy the following condition
[tex]z-xIn our case,x =13, and z = 17
Then, the third side y
lies in
17-13 < x < 17 +13
4 < x < 30
Hence the largest possible whole number of the third side is 29
i do not understand what i am getting wrong for the 3rd question
ANSWER:
-4.1201
SOLUTION
[tex]\log _b\frac{1}{4}=\log _b1-\log _b4[/tex]this is also equivalent to
[tex]\log _b\frac{1\times7}{4\times7}=\log _b\frac{7}{28}=\log _b7-\log _b28=5.7833-9.9034=-4.1201[/tex]5x^2+2x-3 and x+4 how do I find the area
You have a rectangle with the followinf expressions for its sides:
w: width = 5x² + 2x - 3
h: height = x + 4
In order to calculate the area of the rectangle, you use the following formula for the area:
A = w*h
By replacing w and h by the given algebraic expressions you have:
A = (5x² + 2x - 3)(x + 4) use distribution property
A = 5x²(x) + 5x²(4) + 2x(x) + 2x(4) - 3(x) - 3(4) simplify
A = 5x³ + 20x² + 2x² + 8x - 3x - 12 simplify similar terms
A = 5x³ + 22x² + 5x - 12
Hence, the total area of the figure is 5x³ + 22x² + 5x - 12
I need help with this problem. Quick answer is fine
[tex]a^{\frac{-m}{n}}=\frac{1}{a\frac{m}{n}}=\frac{1}{\sqrt[n]{a^m}}[/tex]
i need help with this too
a The value of (2.3 × 10⁴) × (1.5 × 10^-2) is 3.45 × 10^2
b. The value of (3.6 × 10^-5) ÷ (1.8 × 10^2) is 2 × 10^-3. This illustrates the concept of standard form.
What is standard form?The standard form is simply used in Mathematics to illustrate the numbers that are either too large or too small.
It's important to note that the multiplication of exponents is an addition and the division of the power is subtraction.
Therefore, (2.3 × 10⁴) × (1.5 × 10^-2) will be:
= (2.3 × 1.5) × (10^(4-2)
= 3.45 × 10^2
Also, (3.6 × 10^-5) ÷ (1.8 × 10^2) will be:
= (3.6 ÷ 1.8) × 10^(-5 + 2)
= 2 × 10^-3.
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How do I know which score is the highest frequency? how do I figure the scores had a frequency of 2?
To determine the score which presents the highest frequency, we need to check the last column, the frequency one, and find the highest value among them. The score which is in the same row that this value will be the score with the highest frequency.
In the present problem, there are values of frequency equal to 1, 2, 3, and 4. The one with frequency 4 is the one with the highest frequency. (8th row). And the Score related to it is Score 8.Once we check the frequency column once again, we see that the 2nd, the 4th, and the 7th rows have a frequency equal to 2.
Checking the Scores of the related rows, we are able to say that the scores with frequency 2 are: 2, 4, and 7.Determine a third pair of congruent parts to establish congruence between the triangles. Give the congruence postulate involved
In this problem, we have that
mYO ≅ XO
The third pair of congruent parts is
m by vertical angles
therefore
triangle YOT ≅ triangle XOB ----> by ASA congruence postulate
In 1980 approximately 4,825 million metric tons of carbon dioxide emissions were recorded for the United States. That number rose to approximately 6,000 million metric tons in the year 2005. Here you have measurements of carbon dioxide emissions for two moments in time. If you treat this information as two ordered pairs (x, y), you can use those two points to create a linear equation that helps you make predictions about the future of carbon dioxide emissions!A) Organize the measurements into ordered pairs. B) Find the slope,C) Set up an equation in point-slope form,D) Show the equation in slope-intercept form,E) Predict emissions for the year 2020,
ANSWER and EXPLANATION
A) To organize the measurements in ordered pairs implies that we want to put them in the form:
[tex](x_1,y_1);(x_2,y_2)[/tex]Therefore, the measurements in ordered pairs are:
[tex]\begin{gathered} (1980,4825) \\ (2005,6000) \end{gathered}[/tex]Note: 4825 and 6000 are in millions (10⁶) of metric tons
B) To find the slope, apply the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Therefore, the slope is:
[tex]\begin{gathered} m=\frac{6000-4825}{2005-1980} \\ m=\frac{1175}{25} \\ m=47\text{ million metric tons per year} \end{gathered}[/tex]C) To find the in point-slope form, we apply the formula:
[tex]y-y_1=m(x-x_1)_{}[/tex]Therefore, we have:
[tex]y-4825=47(x-1980)[/tex]Note: the unit is in million metric tons
D) To show the equation in point-slope form, we have to put it in the form:
[tex]y=mx+b[/tex]To do that, simplify the point-slope form of the equation:
[tex]\begin{gathered} y-4825=47(x-1980) \\ y=47x-93060+4825 \\ y=47x-88235 \end{gathered}[/tex]E) To predict the emissions for the year 2020, substitute 2020 for x in the equation above:
[tex]\begin{gathered} y=47(2020)-88235 \\ y=94940-88235 \\ y=6705\text{ million metric tons} \end{gathered}[/tex]That is the prediction for the year 2020.
Answer the statistical measures and create a box and whiskers plot for the following set of data.
Solution
The picture below is the solution to the problem
Brief explanantion
From the data given, It is obvious that:
Minimum = 2
Maximum =
The total number of the data is 3, so the number 7th term is the median
Thus,
Median = 8
To find Q1
[tex]\begin{gathered} Q_1=\frac{1}{4}(n+1)th\text{ term} \\ Q_1=\frac{1}{4}(13+1)=\frac{14}{4}=3.5 \end{gathered}[/tex]Q1 is between the third and fourth term
Therefore, Q1 is
[tex]Q_1=0.5(4)+0.5(6)=5[/tex]Similarly, to find Q3
[tex]\begin{gathered} Q_3=\frac{3}{4}(n+1)th\text{ term} \\ Q_3=\frac{3}{4}(13+1)=3\times\frac{14}{4}=3\times3.5=10.5 \end{gathered}[/tex]Q3 is between the tenth and the eleventh term
Therefore, Q3 is
[tex]Q_3=0.5(11)+0.5(11)=11[/tex]solve the inequality for h. h-8> 4h+5. write the answer in simplest form
Subtract '4h' from both RHS (Right-Hand side) and LHS of the inequality (Left-Hand side).
[tex]\begin{gathered} h-8-4h>4h+5-4h \\ (h-4h)-8>5+(4h-4h) \\ -3h>5 \end{gathered}[/tex]Add '8' on both LHS and RHS of the above expression.
[tex]undefined[/tex]Divide both RHS and LHS of the above expression with '-3'. Whenever an inequality is divide or multiple with a negative value, the sign of the inequality shifts. Here, the above expression is dividing with '-3'. Thus, the > symbol shifts to < symbol.
[tex]\begin{gathered} \frac{-3h}{-3}<\frac{5}{-3} \\ h<\frac{-5}{3} \end{gathered}[/tex]Thus, the iniequality for h is h<-(5/3).
A portion of $ 100,000 (x) is invested with a 3% after one year. The rest of the investment (and) obtained a return of 1%. The total return on investment was $ 1,800. 1) What equation shows the return on investment? 2) What equation shows how the $ 100,000 was divided?3) how much money was invested at a 3% rate of return?4) how much money was invested at a rate of return of 1%
We can write a system of equations that describe our problem.
Since we don't know how the original $100,000 was divided, we call the two parts X and Y
So we know that X + Y = 100000
Then we know the Combined Interest coming from the accounts.
We use the Interest formula for return on investment:
I = P * r * t
were P is the principal, r is the percent rate (in decimal form), and t is the number of years (in our case 1)
Then the interest from the 3% account (let's call it I1) (if X amount of money was deposited there) is:
I1 = X * 0.03 * 1 = 0.03 X
Similarly, the interest I2 coming from the 1% account (if Y amount of money was deposited there) is given by:
I2 = Y * 0.01 * 1 = 0.01 Y
Then, the addition of these two interest is our total return of $1800:
0.03 X + 0.01 Y = 1800
Then our system of equations is:
X + Y = 100000
0.03 X + 0.01 Y = 1800
which we solve by substituting for example for Y in the first equation:
Y = 100000 - X
and replacing the Y by this expression in our second equation:
0.03 X + 0.01 (100000 - X) = 1800
use distributive property to eliminate parenthesis:
0.03 X + 1000 - 0.01 X = 1800
combine like terms
0.02 X + 1000 = 1800
subtract 1000 from both sides
0.02 X = 800
divide both sides by 0.02 to completely isolate X:
X = 800 / 0.02
X = $40000
This is the amount deposited on the 3% account
Then we easily calculate the amount deposited in the other account by replacing x with $40000 in the equation we use for substitution:
Y = $100000 - $40000 = $60000
Then, the amount deposited in the 1% account was $60000
and the amount deposited in the 3% account was $40000.
Graph the linear equation.
x=-2/12/12
X=
Use the graphing tool to graph the linear equation.
Click to
enlarge
graph
3
10
8
6
2
d
4
6
8
40
The graph of (3, 2) is located 3 units to the right of the y-axis and 2 units above the x-axis, while the graphs of (-3, 2), (-3, -2) and (3, -2) are located 3 units to the left of the y-axis and 2 units below the x-axis, 3 units to the right of the y-axis, and 3 units to the bottom of the x-axis, respectively.
What is linear equations?The ordinate of the point is the distance from the x-axis that it is placed at, and the abscissa of the point is the distance from the y-axis that it is located at. An algebraic equation of the type known as a linear equation.
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how can you obtain the points for the log below from its inverse?
Answer
Check Explanation
Explanation
The laws of logarithms will come in handy in helping to obtain the points for the log from its inverse.
Before we commence, the two laws of logarithms that we will be using is that
log₄ 4ᶜ = c (log₄ 4)
And
log₄ 4 = 1
So, no matter the value of inverse given, a simple mathematical evaluation will give the log points.
when x = 1
f(x) = log₄ x
f(1) = log₄ 1 = log₄ 4⁰ = 0 log₄ 4 = 0 × 1 = 0
when x = 4
f(x) = log₄ x
f(4) = log₄ 4 = log₄ 4¹ = 1 (log₄ 4) = 1 × 1 = 1
when x = 16
f(x) = log₄ x
f(16) = log₄ 16 = log₄ 4² = 2 (log₄ 4) = 2 × 1 = 2
when x = 64
f(x) = log₄ x
f(64) = log₄ 64 = log₄ 4³ = 3 (log₄ 4) = 3 × 1 = 3
Hope this Helps!!!
Please help:What are the zeros of the quadratic function?f (z )= 3z^2 − 11z − 4Enter your answers, as simplified fractions if necessary, in the boxes.The zeros of f (z) are __ and __.
We need to find the zeros for the next function:
[tex]f(z)=3z^2−11z−4[/tex]We can find those zeros using the quadratic formula given by:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Use the form ax²+bx+x.
Where a=3
b= -11
c=-4
Replacing :
[tex]\begin{gathered} x=\frac{-(-11)\pm\sqrt{(-11)^2-4(3)(-4)}}{2(3)} \\ Simplify \\ x=\frac{11\pm\sqrt{169}}{2\ast3} \\ x=\frac{11\pm13}{2\ast3} \\ Therefore: \\ x_1=\frac{11-13}{6}=\frac{-2}{6}=-\frac{1}{3} \\ x_2=\frac{11+13}{6}=\frac{24}{6}=4 \end{gathered}[/tex]Therefore, the zeros of f (z) are -1/3 and 4.
Simplify the following: (4x + 3) -2(4x - 7) - 3(x +7)
Simplify: (4x + 3) -2(4x - 7) - 3(x +7)
Explanation:
[tex]\begin{gathered} (4x+3)-2(4x-7)-3(x+7) \\ =4x+3-8x+14-3x-21 \\ =4x-11x+17-21 \\ =-7x-4 \end{gathered}[/tex]Final answer: -7x-4 is required simplify form .
What is the solution to 4x-8=12 please explain
Given the equation 4x-8=12 you need to clear the value of x.
First step is to leave the value of x in one side of the equation and the integers in the other side, to do so you have to add 8 to both sides of the equation
[tex]\begin{gathered} 4x-8=12 \\ 4x-8+8=12+8 \\ 4x=20 \end{gathered}[/tex]Next you have to divide both terms of the equation by 4 to get the value of x
[tex]\begin{gathered} 4x=20 \\ \frac{4x}{4}=\frac{20}{4} \\ x=5 \end{gathered}[/tex]The value of x=5
Nikki and four friends had lunch at their favorite restaurant. The total bill was $29.00, and they wanted to leave a 15% tip. Which amount of money is closest to the 15% tip? A $3.00 B $3.50C $4.00D $4.50
Total bill = $29
Tip left = 15%
The valu of the tip = 15% of $29
[tex]\begin{gathered} \frac{15}{100}\text{ x 29} \\ \\ =\text{ \$4.35} \end{gathered}[/tex]The value of the tip = $4.35
Let us consider the options given
$4.35 - $3 = $1.35
$4.35 - $3.5 = $0.85
$4.35 - $4 = $0.35
$4.5 - $4.35 = $0.15
Looking t the deviation from the real value of the tip ($4.35), the least deviation is $0.15. Hence, we can conclude that $4.5 is the closest to the tip.
The answer is option D ($4.50)
Olivia goes out to lunch. The bill, before tax and tip, was $13.90. A sales tax of 6% was added on. Olivia tipped 23% on the amount after the sales tax was added. How much was the sales tax? Round to the nearest cent.
According to the information given in the exercise, the bill before the tax and tip was $13.90 and the sales tax of 6% was added to that amount.
By definition, you can write 6% as a Decimal number by dividing it by 100. Then, this is:
[tex]\frac{6}{100}=0.06[/tex]Let be "t" the amount (in dollars) of the sales tax.
To find the value of "t", you can set up the following equation:
[tex]t=(13.90)(0.06)[/tex]Finally, evaluating, you get that this is:
[tex]t=0.834[/tex]Rounded to the nearest cent, this is:
[tex]t\approx0.83[/tex]The answer is: $0.83
How else can you write 6p in mathematic terms?
In mathematic terms, the expression 6p is written as 6 times p.
Mathematic terms
Mathematic terms means a single mathematical expression. The terms may be a single number, a single variable, several variables multiplied but never added or subtracted. Some of the terms contain variables with a number in front of them. Those number in front of a term is called a coefficient.
Given,
Here we have the expression 6p.
Now, we have to write it as a mathematic term.
While we looking into the expression 6p.
The only operation word in this expression is p which is multiplied with the constant that is the number 6.
So, in the verbal phrase it can be written as 6 times p.
Here p take any valid number in the real numbers.
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A coin is tossed nine times what is the probability of getting all tails express your answer as a simplified fraction or decimal rounded to four decimal places
The probability of getting a tail on each toss is:
[tex]\frac{1}{2}[/tex]Since there is only one way of getting all tails, it follows that the required probability is given by:
[tex](\frac{1}{2})^9\approx0.0020[/tex]Hence, the required probability is approximately 0.0020
r is the midpoint of op and qr is perpendicular to op in the diagram below find the the length of qr
Given:
OP = 20 in
QP = 26 in
Since R is the midpoint of OP, then, OR = RP
Thus
[tex]OR=RP=\frac{OP}{2}=\frac{20}{2}=10\text{ in}[/tex]To find the length of QR, use pythagoras theorem below:
[tex]\begin{gathered} a^2+b^2=c^2 \\ \\ RP^2+QR^2=PQ^2 \end{gathered}[/tex]Input values into the formula:
[tex]10^2+QR^2=26^2[/tex]Subtract 10² from both sides:
[tex]\begin{gathered} 10^2-10^2+QR^2=26^2-10^2 \\ \\ QR^2=26^2-10^2 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} \sqrt[]{QR^2}=\sqrt[]{26^2-10^2} \\ \\ QR=\sqrt[]{676-100} \\ \\ QR=\sqrt[]{576} \\ \\ QR=24 \end{gathered}[/tex]Therefore, the length of QR is 24 in
name each angle pair as corresponding, alternate interior, alternate exterior, consecutive interior angle, or no relationship. identify the transversal that connects each angle pair.
There is a 40% chance that it will be cloudy tomorrow.
If it is cloudy, there is a 79% chance that it will rain.
What is the probability that it will rain?
Answer:
3.16%
Step-by-step explanation:
a*(79/100)*40/100
3.16a/100
3.16%
Answer:
O. 316
Step-by-step explanation:
40/100 × 79/100 =0.316
Pep Boys Automotive paid $208.50 for a pickup truck bed liner. The original selling price was $291.90, but this was marked down 35%. If operating expenses are 28% of the cost, find the absolute loss
Step 1: State the given in the question
THe following were given:
[tex]\begin{gathered} \text{Amount Paid (}A_{\text{paid}})=208.50 \\ (Originalsellingprice)SP_{ORIGINAL}=291.90 \\ \text{Marked Percentage=35\%} \\ \text{Operating expenses=28\%} \end{gathered}[/tex]Step 2: State what is to be found
We are to find the absolute loss
Step 3: Calculate the selling price
Please note that the selling price is the marked down price
The marked down price would be
[tex]\begin{gathered} P_{\text{MARKED DOWN}}=(100-35)\text{ \% of original selling price} \\ P_{\text{MARKED DOWN}}=65\text{ \% of }SP_{ORIGINAL} \\ P_{\text{MARKED DOWN}}=\frac{65}{100}\times291.90=189.74 \end{gathered}[/tex]The selling price is the marked down price which is $189.74
Step 4: Calcualte the operating expenses
Please note that the cost price is amount paid. Therefore, the operating expenses would be as calculated below:
[tex]\begin{gathered} E_{\text{OPEARATING}}=28\text{ \% of Amount Paid} \\ E_{\text{OPERATING}}=28\text{ \% of }A_{\text{paid}}=\frac{28}{100}\times208.50 \\ E_{\text{OPERATING}}=0.28\times208.50=58.38 \end{gathered}[/tex]Hence, the operating expenses is $58.38
Step 5: Calculate the total cost price
The total cost price is the addition of the cost price and the operating expenses. This is as calculated below:
[tex]\begin{gathered} C_{\text{TOTAL COST PRICE}}=E_{OPERATING}+A_{PAID} \\ C_{\text{TOTAL COST PRICE}}=58.38+208.50=266.88 \end{gathered}[/tex]Hence, the total cost price is $266.88
Step 6: Calculate the absolute loss
The absolute loss is the difference between the total cost price and the marked down price (or the actual selling price). This is as calculated below:
[tex]\begin{gathered} L_{\text{ABSOLUTE LOSS}}=C_{TOTAL\text{ COST PRICE}}-P_{MARKED\text{ DOWN}} \\ L_{\text{ABSOLUTE LOSS}}=266.88-189.74=77.14 \end{gathered}[/tex]Hence, the absolute loss is $77.14
Find the measures in the parallelogram4. Find AB and AC
Okay, here we have this:
Considering that in a parallelogram the opposite sides are congruent, we obtain the following:
AB=CD
AB=9 units
AC=BD
AC=4 units
Find x when the f(x) = 350 - 125x ; when f(x) = 0.
ANSWER
x = 2.8
EXPLANATION
The function given is:
f(x) = 350 - 125x
We want to find the value of x when f(x) = 0.
This means that:
[tex]\begin{gathered} f(x)\text{ = 350 - 125x} \\ \Rightarrow\text{ 0 = 350 - 125x} \\ \Rightarrow\text{ 125x = 350} \\ \frac{125x}{125}\text{ = }\frac{350}{125} \\ x\text{ = 2.8} \end{gathered}[/tex]That is the value of x
