We need to find the y-intercept of the equation.
For this, we need to use the slope-intercept form:
[tex]y=mx+b[/tex]Where m represents the slope and b the y-intercept.
Now, to get the form, we need to solve the equation for y:
Then:
[tex]-5x+3y=30[/tex]Solving for y:
Add both sides 5x:
[tex]-5x+5x+3y=30+5x[/tex][tex]3y=30+5x[/tex]Divide both sides by 3
[tex]\frac{3y}{3}=\frac{30+5x}{3}[/tex][tex]\frac{3y}{3}=\frac{30}{3}+\frac{5x}{3}[/tex][tex]y=10+\frac{5}{3}x[/tex]We can rewrite the expression as:
[tex]y=\frac{5}{3}x+10[/tex]Where 5/3x represents the slope and 10 represents the y-intercept.
The y-intercept represents when the graph of the equations intersects with the y-axis, therefore, it can be written as the ordered pair (0,10).
Melissa wants to rent a boat and spend at most $38. The boat costs $6 per hour, and Melissa has a discount coupon for $4 off. What are the possible numbers of hours Melissa could rent the boat?Use t for the number of hours.Write your answer as an inequality solved for t.
ANSWER:
[tex]t\leq7[/tex]EXPLANATION:
Given:
Melissa wants to rent a boat and spend at most $38
Cost of boat per hour = $6
Discount coupon off = $4
Let t represent the number of hours
We can go ahead and set up the below inequality;
[tex]6t-4\leq38[/tex]Let's add 4 to both sides of the inequality;
[tex]\begin{gathered} 6t-4+4\leq38+4 \\ 6t\leq42 \end{gathered}[/tex]Let's divide both sides by 6;
[tex]\begin{gathered} \frac{6t}{6}\leq\frac{42}{6} \\ t\leq6 \end{gathered}[/tex]So Melissa can rent the boat for up to 7 hours
Find an equation for the line that passes through the points (1, -3) and (-5,5).=X$?
To answer this question we will use the following two-point formula for the equation of a line:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1).[/tex]Therefore the equation of the line that passes through the points (1, -3) and (-5,5) is:
[tex]y-(-3)=\frac{5-(-3)}{-5-1}(x-1).[/tex]Simplifying the above result we get:
[tex]\begin{gathered} y+3=\frac{8}{-6}(x-1), \\ y+3=-\frac{4}{3}x+\frac{4}{3}. \end{gathered}[/tex]Subtracting 3 from the above result we get:
[tex]\begin{gathered} y+3-3=-\frac{4}{3}x+\frac{4}{3}-3. \\ y=-\frac{4}{3}x-\frac{5}{3}. \end{gathered}[/tex]Answer:
[tex]y=-\frac{4}{3}x-\frac{5}{3}.[/tex]Assume the normal distribution of data has a mean of 14 and a standard Deviation of 3. use the 65-95-99.7 rule to find the percentage of values that lie below 8
By the 65-95-99.7 rule,
[tex]\begin{gathered} 65\text{ \% of the distribution lies below }\bar{x}+\sigma\text{ and above }\bar{x}-\sigma \\ 95\text{ \% of the distribution lies below }\bar{x}+2\sigma\text{ and above }\bar{x}-2\sigma \\ 99.7\text{ \% of the distribution lies below }\bar{x}+3\sigma\text{ and above }\bar{x}-3\sigma \end{gathered}[/tex]By symmetry,
[tex]\begin{gathered} 47.5\text{ \% of the distribution lies above }\bar{x}-\sigma\text{ and below }\bar{x} \\ \text{ Hence,} \\ 2.5\text{ \% of the values lies below }\bar{x}-\sigma \end{gathered}[/tex]In our case,
[tex]\bar{x}=14,\sigma=3[/tex]Therefore,
[tex]\begin{gathered} 8=14-6=14-2(3) \\ \text{Hence,'} \\ 8=\bar{x}-2\sigma \end{gathered}[/tex]Hence, 2.5 % of the values lie below 8
Janet has a scale drawing in her room
Using the scale drawing, we can see that dimensions of the room are 17 feet by 14 feet.
So the correct option is A.
What are the actual dimensions of the room?
We know that each inch in the scale drawing is equal to 5 feet in the real room, in this case we know that the length of the drawing is 3.4 inches, then the real length is:
L = 3.4*5 ft = 17ft
And the width in the drawing is 2.8 inches, then the real width is:
W = 2.8*5 ft = 14ft
Then the dimensions of the room are 17 feet by 14 feet.
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A loaded S-sided de is loaded so that the number 4 occurs 3/10 of the time while the other numbers occur with equal frequency. What is the expected value of this die? CASS 08.44 OC.48 Next O My
The probablity of obtain a 4 is= 3/10
The probablity of obtain a 1,2,3,5,6,7,8= 1-3/10=7/10
The expect value is:
[tex]E(p)=X1*p1+X2*p2+X3*p3+...+X8*p8[/tex]And p(1)=p(2)=p(3)=p(5)=p(6)=7/10
All have the same frequency, therefore
p(1,2,3,5,6,7,8)=7/10*1/5=7/50=1/10
Where x=1, 2 ,3,4,5,6 and p=3/10 if is 4 and 7/10 for any other number.
Replacing:
[tex]\begin{gathered} E=(1+2+3+5+6)*\frac{7}{50}+4*\frac{3}{10} \\ \\ E=2.38+1.2=3.58\approx4 \end{gathered}[/tex]Samantha received a loan from the bank for $4,500. She plans on payinyoff the loan in 4 years. At the end of 4 years, Samantha will have paid$900 in interest. What is the simple interest rate on the bank loan?
The simple interest rate formular is;
I = A - P
A= I + P
A = P ( 1 + rt )
A is the amount after t years
P is the initial amount = $4,500
r is the rate in percent = ?
t is the time in years = 4
A = $4,500 + $900 = $5,400
Therefore to obtain the rate (r)
5400 = 4500 (1 + r x 4 )
1 + 4r = 5400/4500
1 + 4r = 1.2
4r = 1.2 - 1
4r = 0.2
r = 0.2/4 = 0.05
In percentage;
r = 0.05 x 100 = 5%
Thus, the simple interest rate is 5%
2.) Part A: complete the following table for the functions
Complete the following table for the functions:
[tex]\begin{gathered} f(x)=x^2+1 \\ g(x)=f(x-5) \\ h(x)=f(x+3) \end{gathered}[/tex]The below function represents the transformation of the independent variables:
[tex]\begin{gathered} f(x)=x^2+1 \\ g(x)=f(x-5)\ldots\ldots\text{.f(x) will decrease by 5 units} \\ h(x)=f(x+3)\ldots\ldots.f(x)\text{ will increase by 3 units} \end{gathered}[/tex]a triangular lot is 130 ft on one side and has a property line of length 700 ft. Find the area of the lot in acres.
Area of the lot = 1.03 acres
Explanations:The line length of the triangular lot = 700 ft
The height of the triangular lot = 130 ft
Note:
Area of a triangle = 0.5 x base x height
Calculate the base of the triangular lot using the Pythagora's theorem
[tex]\begin{gathered} \text{Length}^2=Height^2+Base^2 \\ 700^2=130^2+Base^2 \\ \text{Base}^2=700^2-130^2 \\ \text{Base}^2\text{ = }490000\text{ - }16900 \\ \text{Base}^2\text{ = }473100 \\ \text{Base = }\sqrt[]{473100} \\ \text{Base = }687.82 \end{gathered}[/tex]The base of the triangular lot = 687.82 ft
Area of the triangular lot = 0.5 x 687.82 x 130
Area of the triangular lot = 44708.3 ft²
NB
1 ft² = 2.3 x 10^(-5) Acres
44708.3 ft² = 44708.3 x 2.3 x 10^(-5)
44708.3 ft² = 1.03 acres
Therefore:
Area of the lot = 1.03 acres
find the surface area of the cone in terms of pi. SA=__ cm squared. simply
Given the figure of a cone.
As shown, the slant height = s = 23 cm
And the diameter of the base = d = 18 cm
So, the radius = r = 0.5d = 9 cm
The surface area of the cone will be calculated using the following formula:
[tex]SA=\pi rs+\pi r^2[/tex]Substitute s = 23, and r = 9, writing the surface area in terms of π
[tex]SA=π(18)(23)+π(9)^2=414π+81π=495π[/tex]So, the answer will be:
The surface area of the cone = 495π cm²
nowledge Check 01
On November 1, the company rented space to another tenant. A check in the amount of $9,000, representing three months' rent in advance, was received from the tenant on that date. The payment was recorded with a credit to the Unearned Rent Revenue account.
Complete the necessary December 31 adjusting journal entry by selecting the account names from the pull-down menus and entering dollar amounts in the debit and credit columns.
Debit for unearned rent revenue of $6,000.
Rent Revenue Credit $6,000
What is known as the revenue?The total amount of revenue produced by the purchase of goods or services linked to the company's main operations is referred to as revenue. Because it appears at the top of the revenue statement, revenue, also termed as total sales, is often made reference to as the "top line."For the given question,
It is assumed that the company rented area to another tenant on November 1. On that date, the tenant handed over a check for $9,000, which represented three months' rent in advance. The payment has been recorded as a credit to the account for unearned rent revenue.Now, on December 31, we must prepare this same adjusting entry to record this same Rent Revenue for the two-month period (Nov. 1 to Dec. 31).
For two months, the rent revenue will be 9000×2/3 = $6,000
As a result, the journal entry to track the Rent revenue is as follows:
Debit for unearned rent revenue of $6,000.
Rent Revenue Credit $6,000
(becoming the improvement made for earned Rent Revenue).
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Amy’s grandmother is exactly 6 times older than Amy.
Which three statements below must be true?
The three statements that are true include:
Amy's age is a factor of the age of her grandmother.
The age of Amy's grandmother is a composite number.
The number 6 is a factor if the age of Amy's grandmother.
What is a factor?A factor simply means a number that can be multiplied by another number to get the original number.
Let's say Amy is 10 years. The grandmother will be 69 years. In this case, 10 is a factor of 60. Therefore, Amy's age is a factor of the age of her grandmother.
The complete options are given below.
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Which three statements below must be true?
1.The age of Amy’s grandmother is a prime number.
2.Amy’s age is a factor of the age of her grandmother.
3.The age of Amy’s grandmother has exactly two factors.
4.The age of Amy’s grandmother is a composite number.
5.The number 6 is a factor of the age of Amy’s grandmother.
6.The age of Amy’s grandmother has exactly four factors.
Mark went to the bank to borrow $10,000. He was given 2 options for a $10,000 loan:OPTION 1: 24-month payback at 6%interest will result in a monthly payment of $443.21 per month, or OPTION 2: 36-month payback at 6% interest will result in a monthly payment .of $304.22 per month.Which statement is NOT true?F. Mark will pay a total of $10,637.04 if he chooses Option 1.G. Mark will pay a total of $10,951.92 if hechooses Option 2.H. Mark will save $314.88 if he selects Option 2.J. Mark will pay a lower total amount if he selects Option 1.
Loan= $10.000
Bank options:
24-month payback 6% interest, with a monthly payment of $443.21/month
Then, Mark in option 1 will pay a total of:
[tex]443.21\text{ x 24 months=}10,637.04\text{ in option 1. }[/tex]36-month payback 6% interest, with a monthly payment of $304.22/month.
Mark in option 2 will pay a total of:
[tex]304.22\text{ x 36months=}10,951.92\text{ in option 2. }[/tex]Then, Mark will pay a lower total amount of money if he selects option 1 (10.637.04 is less than 10,951.92), saving a total of:
[tex]10,951.92\text{ - 10.637.04= 314.88 if he chooses option 1. }[/tex]Therefore, the statement that is NOT true is:
H. Mark will save $314.88 if he selects option 2.
A flagpole casts a shadow 3.5 meters long, Anita is standing near the pole. Her shadow is 0.75 meters long, Anita's height is 1.5 meters.How tall is the flagpole? Draw a diagram, label, and solve. Type your answer as a whole number or a decimal with no labels. EX5.2
Solution:
The heights and the shadows are in the same ratio because the sun is shining from the same angle, so the triangles formed are similar.
Notice that Anita's height is twice as long as her shadow, so the height of the flagpole will be
[tex]2\text{ x }3.5\text{ = 7m}[/tex]We can also write a direct proportion:
[tex]\frac{x}{3.5}\text{ = }\frac{1.5}{0.75}\text{ }\frac{\leftarrow\text{heights}}{\leftarrow shadows}[/tex]solving for x, we get:
[tex]x\text{ =}\frac{3.5\text{ x }1.5}{0.75}\text{ = 7m}[/tex]then, we can conclude that the correct answer is:
[tex]x\text{ = 7m}[/tex]Given that p = 6 and q = 2, which yields a quotient greater than -9? ОА -3 a -р B 3 O a O С Зр. (-9) (0) D (-p) (-39)
For the polynomial below, 3 is a zero.f(x) = x^3+ 3x^2-11x-21Express f(x) as a product of linear factors.f (x) = ?
EXPLANATION
Given the polynomial f(x) = x^3 +3x^2 -11x -21
Separating the expression into groups as shown as follows:
WhaGraph the piecewise-defined function. Use the graph to determine the domain and range of the function. x + 2 if x < -1F(x)={ - 2x + 3 if x ≥ - 1
The domain of the function is all possible x-values a function can have; therefore, we see here that the domain of the function is all real numbers (including -1).
The range of a function is all possible y values a function can take. We see from the graph above that can take only the values that are greater than or equal to 1; therefore, the range of the function is all real numbers greater than or equal to 1.
A kite is flying 95 ft off the ground, and its string is pulled taut. The angle of elevation of the kite is 48º. Find the length ofthe string. Round your answer to the nearest tenth.
Given data:
Kite is flying off the ground = 95ft. ( Perpendicular)
Angle = 48 degree
[tex]\sin 48^{\circ}=\frac{Perpendicular}{Hypotenues}[/tex][tex]\text{Hypotenues}=\frac{Perpendicular}{\sin 48^{\circ}}[/tex][tex]\begin{gathered} H=\frac{95}{0.7431} \\ H=127.84ft \end{gathered}[/tex]Thus, the length of the string is 127.8 ft.
The padlock for your gym locker uses a 3 number sequence to open the lock. If the numbers go from 1 to 27, how many different sequences are there on the dial without repeating a number?A. 17,550B. 33,696C. 16,848D. 8,775
SOLUTION:
We want to the different sequences possible without repeating a number.
For the first number, there are 27 ways to select it.
Since we aren't allowed to repeat numbers;
There are 26 ways to select the second number.
There are also 25 ways to select the third number.
Therefore, the different sequences possible are;
[tex]No\text{. of ways =}27\times26\times25=17550\text{ ways}[/tex]WILL GIVE BRAINLYEST 200 PO9NTS SENCE IM GIVING EXTRA
The range of the data set increased by 12 and the median of the data set is at 50.
Range of a Data SetThe Range of a data set is the difference between the lowest and highest values.
The range is the difference between the smallest and highest numbers in a list or set. To find the range, first put all the numbers in order. Then subtract (take away) the lowest number from the highest. The answer gives you the range of the list.
The given data set is;
15, 17, 19, 19, 22, 23, 25, 27, 32, 34
The range of this data set will be
range = 34 - 15 = 19.
Assuming we add another age of 46, the range will become
range = 46 - 15 = 31
This will impact the range of the data by 31 - 19 = 12.
The range will be impacted by an increase with 12.
Median of a Data SetThe median is the value that's exactly in the middle of a dataset when it is ordered. It's a measure of central tendency that separates the lowest 50% from the highest 50% of values. The steps for finding the median differ depending on whether you have an odd or an even number of data points.
The data set given is
48, 63, 75, 40, 32, 52, 35, 68, 83, 40
We have to rearrange the data points first before finding the median;
32, 35, 40, 40, 48, 52, 63, 68, 75, 83.
The median of the data set will be the average between 48 and 52 which is 50.
the median of the data is 50.
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Calculate the variance and the standard deviation for the following set of data: 7, 2, 5, 3, 3, 10
We need to know about variance and standard deviation to solve the problem. The variance of the set is 7.67 and the standard deviation is 2.77
Variance is a measure of dispersion which means it measures how far a set of numbers is spread out from the mean value. Standard deviation is the square root of variance. Inorder to calculate the variance we need to calculate the mean of the data set first.
mean=7+2+5+3+3+10/6=30/6=5
variance=[(7-5)^2+(2-5)^2+(5-5)^2+2(3-5)^2+(10-5)^2]/6=4+9+8+25/6=46/6=7.67
standard deviation =[tex]\sqrt{var}[/tex]=2.77
Therefore the variance of the data set is 7.67 and the standard deviation is 2.77
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247474647447x4747474747
Answer:
1174879639277360520909 in exact form
or
in decimal form 1.17487963 x 10^21
Step-by-step explanation:
Determine if the 2 lines are parallel, perpendicular, or neither based on their slope- intercept equations.
Equations of lines H & I;
Line H: y=z
Line I: y=-7z - 33
O Not Enough Information
O Perpendicular
O Neither
POSSIBLE PO
O Parallel
Equations of lines H & I; Line H: y=z Line I: y=-7z - 33 is Perpendicular. The lines are not parallel if the slopes differ. Perpendicular lines do meet, but parallel lines do not.
How can you demonstrate that two lines in an equation are parallel?Only if the slopes of two lines are equal can they be said to be parallel. The conventional version of the equation is 2x - 3y = 4. Since a line with the equation Ax + By = C typically has a slope of -A/B, line q must have a slope of -2/-3 = 2/3.
Their equations allow us to compare the slopes of two lines to determine if they are parallel. The lines are parallel if the slopes are the same and the y-intercepts are different.
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The following probability table shows probabilities concerning Favorite Subject and Gender. What is the probability of selecting an individual who is a female or prefers science?
Gender Favorite Subject Total
Math English Science
Male 0.200 0.050 0.175 0.425
Female 0.100 0.325 0.150 0.575
Total 0.300 0.375 0.325 1.000
Answer: 2
Step-by-step explanation: 0.300 0.375 0.325 1.000 = 2
a^2 - b^4 Evaluate is a= -5 and b= 2
21
Explanations:Given the expression
[tex]a^2-b^4[/tex]We are to find the resulting value given that a = -5 and b = 2
[tex]\begin{gathered} =(-5)^2-(2)^2 \\ =25-4 \\ =21 \end{gathered}[/tex]Hence the value of the expression if a = -5 and b = 2 is 21
At the farmer’s market, Joan bought apples at $1.20 per pound, cherries for $2.00 per pound and pears for $0.80 per pound. She bought a total of 9 pounds of fruit for $11.00. Joan bought twice as many pounds of apples than cherries. Let A be the weight of the apples, C be the weight of the cherries, and P be the weight of the pears. Formulate a system of equations to determine how many pounds of each type of fruit were bought. Do Not Solve.
We have here a case in which we need to translate a problem into algebraic expressions to solve a problem, and we have the following information from the question:
• We have that Joan bought:
0. Apples at $1.20 per pound
,1. Cherries at $2.00 per pound
,2. Pears at $0.80 per pound
• We know that she bought a total of 9 pounds of fruit.
,• We also know that she spent $11.00 for the 9 pounds of fruit.
,• Joan bought twice as many pounds of apples than cherries.
We need to label weights as follows:
• Weight of apples ---> A
,• Weight of cherries ---> C
,• Weight of pears ---> P
Now to find a system of equations to determine the number of pounds of each type of fruit was bought, we can proceed as follows:
1. We know that if we multiply the price of the fruit per pound by the weight in pounds, we will obtain the amount of money Joan spent in total. Then we have:
[tex]1.20a+2.00c+0.80p=11.00\rightarrow\text{ \lparen First equation\rparen}[/tex]2. We also know that the total weight of the fruits was equal to 9 pounds. Then we can translate it into an algebraic expression as follows:
[tex]a+c+p=9\rightarrow(\text{ Second equation\rparen}[/tex]3. And we know that Joan bought twice as many pounds of apples than cherries, and we can translate it as follows too:
[tex]\begin{gathered} 2a=c \\ \\ \text{ If we subtract c from both sides of the equation, we have:} \\ \\ 2a-c=c-c \\ \\ 2a-c=0\text{ \lparen Third equation\rparen} \end{gathered}[/tex]Now we have the following equations:
[tex]\begin{gathered} 1.20a+2.00c+0.80p=11.00 \\ \\ \begin{equation*} a+c+p=9 \end{equation*} \\ \\ \begin{equation*} 2a-c=0 \end{equation*} \end{gathered}[/tex]Therefore, we have that the correct option is the first option:
• 1.20a + 2.00c + 0.80p = 11.00
• a + c + p = 9
,• 2a - c = 0
[First option].
find two vectors each of norm 1 that I perpendicular to vector A={3,2}
(2√13/13 , 3√13/13) and (-2√13/13 , -3√13/13) are two vectors of norm 1 that are perpendicular to A = (3 , 2) .
What is perpendicular vectors ?In Cartesian coordinates, the given vector can be represented by the line y = -2x/3. The vector is the line segment that connects (0,0) and (3,-2).y = 3x/2 can be used to represent the normal.
If the vector is represented by a line connecting (0,0) to a point (p,q), then,p2 + q2 = 1 because the normal is one length, and q = 3p/2.
As a result,p² + 9p²/4 = 1, 13p²/4 = 1, p = ±√(4/13) = ±2/√13, q = ±3/√13.
After rationalization, one normal vector is (2√13/13 , 3√13/13) and the other is (-2√13/13 , -3√13/13).The two vectors of norm 1 perpendicular to A = (3 , 2) is :
(2√13/13 , 3√13/13) and (-2√13/13 , -3√13/13).
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Simplify. 3 6 4 2m n 4 6m Write your answer using only positive exponents. . X Х ?
we have the expression
[tex](\frac{2m^6n^4}{6m^4})^3[/tex][tex](\frac{2m^6n^4}{6m^4})^3=\frac{(2^3)(m^{(18)})(n^{(12)})}{(6^3)(m^{(12)})}[/tex]simplify
[tex]\frac{(8)(m^{(18-12)})(n^{(12)})}{216}=\frac{(m^6)(n^{(12)})}{27}[/tex]Jodie is an event planner who believeseach person requires 3.75 feet ofpersonal space at her events. Her nextevent will be at a venue that measures40 feet by 75 feet. How many peopleshould she include on the guest list?
The venue measures 40 ft by 75 ft . This means the venue has the shape of a rectangle. A rectangle
A translation 6 units right maps P onto P'. Complete the translation function.
If we have a point P=(x,y) and we apply a translation 6 units to the right we will get a point P' that is:
[tex](x,y)\longrightarrow(x+6,y)[/tex]We can test it by trying with P=(0,0).
Then P' would be (6,0), that is 6 units to the right from P.
Answer: (x,y) --> (x+6,y)
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