Answer:
The slope is 2
Step-by-step explanation:
Take any two points on the line. I am going to use the points (0,-8) and (4,0) Points are in the form (x,y) The y values form the two points is 0 and -8. The x values are 4 and 0.
The slope is the change in y over the change in x.
[tex]\frac{0- -8}{4-0}[/tex] = [tex]\frac{8}{4}[/tex] = 2
Solve the following equation: 5(n + 2) = 3(1 + 2n)
Answer: n=7
Step-by-step explanation:
First distribute the numbers to get 5n+10=3+6n
Next Subtract 6n from both sides to get -n=10=3
Finally divide both sides my -1 to get rid of the -n to get n=7
Hope this helps :)
a survey conducted by a research team was to investigate how the education level, tenure in current employment, and age, are related to annual income. a sample 20 employees is selected and the data is given below. education (no. of years) length of tenure in current employment (no. of years) age (no. of years) annual income ($) 17 8 40 124,000 12 12 41 30,000 20 9 44 193,000 14 4 42 88,000 12 1 19 27,000 14 9 28 43,000 12 8 43 96,000 18 10 37 110,000 16 12 36 88,000 11 7 39 36,000 16 14 36 81,000 12 4 22 38,000 16 17 45 140,000 13 7 42 11,000 11 6 18 21,000 20 4 40 151,000 19 7 35 124,000 16 12 38 48,000 12 2 19 26,000 10 6 44 124,000 for two people a and b with the same years of education and age, suppose a's length of tenure is 2 more years than b, what would the salary difference between a and b? group of answer choices -4387.76 2193.88 2689.24 10011.92 none of the choices
The relationship between a dependent variable, y, and one or more independent variables, X, is described by a linear regression model.
What is linear regression model?The relationship between a dependent variable, y, and one or more independent variables, X, is described by a linear regression model. The response variable is another name for the dependent variable. Explanatory or predictive variables are other names for independent variables. Models with a single predictor are known as simple linear regression. Multiple predictor models are known as multiple linear regression. Models for numerous response variables using multivariate linear regression. Finding the weights (namely, W0 and W1) that result in the best-fitting line for the input data (i.e., the X characteristics) that we have is how linear regression functions. The line with the lowest price is chosen to be the greatest fit.Using an online multiple regression calculator, the estimated multiple linear regression equation that can be used to forecast the annual income using the number of school years completed (Education), length of tenure in the current employment, and age is as follows:
y = - 143481.1924 + 10011.9212x1 - 2193.8838x2 + 2689.2405x3
According to the general form of a multiple linear regression model:
-143481.1924 = intercept(c) ; where regression line crosses the origin
10011.9212x1 - 2193.8838x2 + 2689.2405x3 are weight coefficients of the three predictor variables ; x1, x2, and x3
y = predicted variable
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write equations for the horizontal and vertical lines passing through the point (-7,7)
The vertical line's equation is x = -7, and the horizontal line's equation Is y = 7.
Where the given coordinate is (--7, 7).
What do the vertical and horizontal lines represent?A vertical line is a straight, up and down line in a coordinate plane that is parallel to the y-axis. The horizontal line, on the other hand, is parallel to the x-axis and goes straight, left, and right.Here,
The value of x, is -7, will never change for a vertical line. This holds true for any y value. As a result, x = -7 is the equation for a vertical line passing through this point.
Similarly, the value of y, is 7, will never change for a horizontal line. This holds true for any x value. As a result, the equation for a horizontal line passing through this point is as follows: y =7
As a result, the vertical line's equation is x = -7 and the horizontal line's equation is y = 7.
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please help thanks please give explanation
The price of the car after 15% markup will be $8,280
How to calculate price after 15% of markup ?
The cost price of car for Hanks = $7200
Marking up of price is done by 15%
To find Markup price = Cost price + 15% of cost price
= 7,200 + 7,200 * 15/100
= 7,200 + 1,080 = $8,280
The 15% of car price is $1,080
The price of the car after 15% markup will be $8,280
What is percentage ?
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100.Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.The formula used to calculate percentage is: (value/total value)×100%.To find 50 apples as a percentage of 1250 apples, one first computes the ratio 50/1250 = 0.04, and then multiplies by 100 to obtain 4%.To learn more about percentage refer :
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suppose the length of a rectangular room is (x + 4) meters and the width is (x - 4) meters, what expression that can be used to represent the area of the room?
Answer:
Step-by-step explanation:
area=l*w
(x+4)(x-4)
x^2-16 (use foiling)
10 POINTS! PLS HELP! If 4 < a < 5 and 5 < b < 8, which of the following best describes a-b?
a) between -4 and -8
b) between -4 and 0
c) between 2 and 3
d) between -1 and 0
I don't know how to do this, so pls explain how to do it in your answer :)
Answer:
Between -4 and 0
Step-by-step explanation:
Hey! I saw your most recent and I'm assuming it is this question we're talking about it so let's help you with that!
Let's start by looking at what each of them mean, the first one means that 4 is lower than a but a is lower than 5 (Inequality 1) The second one means 5 is lower than b but b is lower than 8 (Inequality 2). Now, in order to find out [tex]a-b[/tex], we need to find the largest and smallest value of [tex]a-b[/tex]. The reason why we do this is because we want to look for the range of what [tex]a-b[/tex] can give us and in finding the largest and smallest value, if we were to evaluate both inequality 1 and 2 using [tex]a-b[/tex], we know that it can't be beyond the largest value or smaller than the lowest value.
In order to figure out the largest possible value of [tex]a-b[/tex], we need to take the maximum x value of inequality 1 and subtract it by the minimum y value of inequality 2, so we get:
[tex]5-5=0[/tex]
In order to figure out the smallest possible value of [tex]a-b[/tex], we need to take the minimum x value of inequality 1 and subtract it by the maximum y value of inequality 2, so we get:
[tex]4-8=-4[/tex]
So, in this case! The answer is b) between -4 and 0
Answer:
B
Step-by-step explanation:
suppose that 30% of the 10,000 signatures on a certain recall petition are invalid. would the number of invalid signatures in a sample of 3000 of these signatures have (approximately) a binomial distribution? explain. g
Approximately, all of the signatures in the sample of 3000 signatures are invalid . We get this outcome by using binomial distribution .
This problem it is said that 30% of 10000 signatures on certain recall petition are invalid . So, here is the two outcomes possible one is the signatures are invalid and other signature are valid .
Probability of Success (signature are valid ) = p = favourable outcomes / total outcomes
Favourable outcomes for Success = 70% of 10,000= 7000
Total number of possible outcomes = 10,000
P = 7000/10,000 = 7/10
Probability of failure (signature are invalid ) = q= 1- p = 1- 7/10 = 3/10
We have to find out probability of getting invalid signature from a sample of 3000 signatures..
Using the binomial distribution,
P(X = x ) = ⁿ C ₓ pˣ (1- p)⁽ⁿ⁻ˣ⁾
n = 3000 , x= 0 for none of signatures from 3000 are invalid.
P(X=0) = ³⁰⁰⁰C ₀ (3/10)⁰ ( 7/10) ³⁰⁰⁰
= 1 . 1 . (7/10)³⁰⁰⁰ = (7/10)³⁰⁰⁰ = 0
Probability of getting invalid signature out of sample 3000 is
1 – ( 7/1000)³⁰⁰⁰ = 1
This implies that all the signatures in sample of 3000 are invalid.
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a jar contains 22 red marbles number 1 to 22 and 52 blue marbles number 1 to 50 to a marble is drawn at random from the drawer find the probability of the given event around solution to three decimal places
We are given a jar that contains 22 red marble( 1 to 20) and 52 blue marbles (1 to 52). We can proceed to find the solution for each part of the question.
PART 1
Let the probability that the marble is red be P(r).
Therefore,
[tex]P(r)=\frac{Number\text{ of red balls}}{\text{Total number of balls}}[/tex]This gives,
[tex]\begin{gathered} P(r)=\frac{22}{22+52}=\frac{22}{74} \\ \therefore P(r)=\frac{11}{37}=0.297 \end{gathered}[/tex]Therefore, the probability that the marble is red is:
ANSWER= 0.297
PART 2:
Let the probability of picking odd-numbered balls be P(o)
Therefore,
[tex]P\mleft(o\mright)=\frac{Number\text{ of odd balls}}{\text{Total number of balls}}[/tex]We already know that the total number of balls is 72 for the previous question. Therefore, the total number of oddballs will be the sum of odd red balls and odd blue balls. This consists of 11 odd red balls and 26 odd blue balls.
Therefore,
[tex]\begin{gathered} P(o)=\frac{26+11}{74}=\frac{37}{74} \\ \therefore P(o)=0.5 \end{gathered}[/tex]The probability of picking odd-numbered balls is
ANSWER = 0.5
PART 3:
Let the probability of picking a red or odd-numbered ball be P(r U o)
[tex]P(r\cup o)=P(r)+p(o)-p(r\cap o)[/tex]Since we already have the values of P(r) and P(o), therefore we only need to find p(r n o).
p(r n o) is the probability of the ball being red and odd. The number of the red and oddball is 11.
Therefore,
[tex]\begin{gathered} P(r\cap o)=\frac{nu\text{mber of red and odd balls}}{\text{Total number of balls}} \\ =\frac{11}{74} \\ =0.149 \end{gathered}[/tex]This implies that,
[tex]\begin{gathered} P(r\cup o)=P(r)+p(o)-p(r\cap o) \\ P(r\cup o)=0.297+0.5-0.149 \\ \therefore P(r\cup o)=0.648 \end{gathered}[/tex]Hence, the probability of picking a red or odd-numbered ball is
ANSWER = 0.648
PART 4:
Let the probability of picking a blue or even-numbered ball be P(b U e)
Therefore,
[tex]P(b\cup e)=p(b)+p(e)-p(b\cap e)[/tex]From the above formula, we would need to figure out all the parts. p(b) represents the probability of blue marble. This gives,
[tex]\begin{gathered} p(b)=\frac{Number\text{ of blue balls}}{\text{Total number of balls}} \\ \therefore p(b)=\frac{52}{74}=0.703 \end{gathered}[/tex]p(e) represents the probability of even balls. The total number of even balls will be the sum of the even red balls and even blue balls.
[tex]\begin{gathered} p(e)=\frac{26+11}{74}=\frac{37}{74} \\ \therefore p(e)=0.5 \end{gathered}[/tex]p(b n e) represents the probability of blue and even balls. We have 26 blue and even balls
[tex]\begin{gathered} p(b\cap e)=\frac{Number\text{ of blue and even balls}}{\text{Total number of balls}} \\ P(b\cap e)=\frac{26}{74}=0.351 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} P(b\cup e)=p(b)+p(e)-p(b\cap e) \\ P(b\cup e)=0.703+0.5-0.351 \\ \therefore P(b\cup e)=0.852 \end{gathered}[/tex]Therefore, the probability of picking a blue or an even ball is:
ANSWER = 0.852
Which of the following is a disadvantage of using a check casher, compared to a bank?
Responses
You wait longer to get your money at a check casher than at a bank
You wait longer to get your money at a check casher than at a bank
You pay a higher fee to cash checks at a check casher than at a bank
You pay a higher fee to cash checks at a check casher than at a bank
You can only cash checks worth more than $500 at a check casher
You can only cash checks worth more than $500 at a check casher
You can cash fewer checks at a check casher than at a bank
The main disadvantage of using a check cashier is that, 'You pay a higher fee to cash checks at a check casher than at a bank'
Check casher;
A check casher is someone who works in the check-cashing industry, with the exception of someone who doesn't cash checks for others on any one day that total more than $1,000 in cash, money, or other assets.
Disadvantage of Check cashers;
Fees for cash checking services can be as low as $1 or as much as 2% of the check amount depending on where you are. These costs reduce one's capacity to make ends meet or have extra money available. Always be aware of the prices and fees before using a check cashing service.
That is,
The main disadvantage of using a check cashier is that, 'You pay a higher fee to cash checks at a check casher than at a bank'
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bricklayer brenda would take nine hours to build a chimney alone, and bricklayer brandon would take 1010 hours to build it alone. when they work together, they talk a lot, and their combined output decreases by 1010 bricks per hour. working together, they build the chimney in 55 hours. how many bricks are in the chimney?
When seen as a function, a relationship exists between a set of inputs and outputs.
The number of bricks in the chimney exists 900.
What is meant by functions?A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Simply described, a function is an input-output connection where each input is coupled to exactly one output range, codomain, and domain are included in each function. A function exists generally denoted by f(x) where x exists the input.
Let x be the number of bricks in the chimney. The work done exists the rate multiplied by the time.
Using w = rt, we get
[tex]$x=\left(\frac{x}{9}+\frac{x}{10}-10\right) \cdot 5[/tex]
Expanding the above equation, we get
[tex]$\left(\frac{x}{9}+\frac{x}{10}-10\right) \cdot 5: \quad \frac{19 x}{18}-50$[/tex]
x = (19x / 18) - 50
Multiply both sides by 18
[tex]$x \cdot 18=\frac{19 x}{18} \cdot 18-50 \cdot 18[/tex]
Simplifying the above equation,
x × 18 = 19x - 900
Subtract 19x from both sides
x × 18 - 19x = 19x - 900 - 19x
Simplifying the above equation, we get
-x = -900
Divide both sides by -1
[tex]$\frac{-x}{-1}=\frac{-900}{-1}[/tex]
x = 900
Therefore, the value of x exists 900.
The complete question is:
Bricklayer Brenda would take nine hours to build a chimney alone, and bricklayer Brandon would take hours to build it alone. When they work together, they talk a lot, and their combined output decreases by bricks per hour. Working together, they build the chimney in hours. How many bricks are in the chimney?
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What is the slope of the line that passes through the points (-6, 1) and (-6,-4)?
Write your answer in simplest form.
Answer:
The slope is undefined
Step-by-step explanation:
Ivy is competing in a Read-A-Thon. Each day , she reads for 25 minutes before school and 45 minutes after school. Find the total number of minutes Ivy spends reading after 5 days. How can you find the total number of minutes Ivy spends reading?
A) Multiply 5 and 25. Then, add 45
B) Multiply 5 and 45. Then, add 25
C) Add 25 and 45. Then, Multiply by 5
D) Add 25 and 45. Then, add 5
Answer: C
Step-by-step explanation:
It the only one that includes both.
The admission fee at an amusement park is 1.5 dollars for children and 4 dollars for adults. On a certain day, 281 people entered the park, and the admission fees collected totaled 684 dollars. How many children how many adults were admitted?
Answer:
176 children and 105 adults.
Explanation:
Let's call x the number of children and y the number of adults.
If 281 people entered the park, we can write the following equation
x + y = 281
If they collected 684 dollars, we can write the following equation
1.5x + 4y = 684
because it cost $1.5 for children and $4 for adults.
Now, we have the following system of equations
x + y = 281
1.5x + 4y = 684
First, we need to solve the first equation for y, so
x + y = 281
x + y - x = 281 - x
y = 281 - x
Then, replace this expression on the second equation
1.5x + 4y = 684
1.5x + 4(281 - x) = 684
1.5x + 4(281) - 4(x) = 684
1.5x + 1124 - 4x = 684
-2.5x + 1124 = 684
Finally, we can solve the equation for x
-2.5x + 1124 - 1124 = 684 - 1124
-2.5x = -440
-2.5x/(-2.5) = -440/(-2.5)
x = 176
So, the value of y is equal to
y = 281 - x
y = 281 - 176
y = 105
Therefore, they admitted 176 children and 105 adults.
Just answer what the ss says
The scatterplot of the data is attached accordingly. The Linear Regression equation for Y is ŷ = 0.82X + 2.31. Note that there is a positive correlation. This is because the y variable tends to increase as the x variable increases.
What is linear regression?Linear regression is a statistical method for modeling the connection between a scalar output and one or more explanatory factors. When there is only one independent factor, simple linear regression is employed; when there are more than one, multiple linear regression is utilized.
Note that the regression equation is usually given as:
ŷ = bX + a; where
y = dependent variable
b = Slope/coefficient
X = Independent Variable
a = Constant/ Intercept.
Notice that the regression line splits evenly between the data points exhibiting a linear relationship that is positively correlated.
From the graphing calculation, we have:
The sum of X = 21
The sum of Y = 33.39
Mean X = 3
Mean Y = 4.77
Sum of squares (SSₓ) = 28
Sum of products (SP) = 22.96
Recall that the regression equation is given as:
ŷ = bX + a;
Where;
b = SP/SSₓ and
a = [tex]M_{y}[/tex] -[tex]bM_{x}[/tex]
Hence,
b = 22.96/28
= 0.82
a = [tex]M_{y}[/tex] - bMₓ = 4.77 - (0.82*3) = 2.31
hence,
ŷ = 0.82X + 2.31.
Lets find Y if x = 10
y = 0.82 (10) + 2.31 [plugging in the value]
= 8.2 +2.31
= 10.51
Let's find X where Y = 10
10 = 0.82X + 2.31. [Plugging in the value]
collect like terms over the equation sign
10-2.31 = 0.82X
⇒ 7.69 = 0.82X [Divide both sides by 0.82
7.69/0.82 = X
X = 9.37804878049
X [tex]\approx[/tex] 9.38
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Hello! I think I have this correct but want to make sure.
Solution;
y=5x
Explanation;
[tex]\begin{gathered} y\propto x \\ y=kx \\ k=\frac{y}{x} \\ when\text{ x=1 and y=5;} \\ k=\frac{5}{1}=5 \\ Therefore; \\ y=5x \end{gathered}[/tex](6-6)x 6=0
(6 + 6):6=2
6? 6?6 = 4
Answer:
I don't know if you can use permutations but
(6P2-6)/6=4 ????
if 6x-1=29, what is the value of x2+x
We are given
[tex]6x-1=29[/tex]Therefore the value of x can be gotten by simplifying the above equation
[tex]\begin{gathered} 6x=29+1 \\ 6x=30 \\ x=\frac{30}{6} \\ x=5 \end{gathered}[/tex]Given that x is 5, we can proceed to find the value of the expression.
[tex]\begin{gathered} x^2+x \\ \Rightarrow(5)^2+5 \\ \Rightarrow25+5 \\ \Rightarrow30 \end{gathered}[/tex]This implies that
[tex]x^2+2\Rightarrow30[/tex]Solve for x in terms of the other pronumerals
ax+ b/4 = x+c/3
Answer:
[tex]x=\cfrac{4c-3b}{3a-4}[/tex]==============================
Given expression[tex]\cfrac{ax+b}{4}=\cfrac{x+c}{3}[/tex]Solve it for x in steps below[tex]\cfrac{ax+b}{4}=\cfrac{x+c}{3}[/tex] Given
[tex]3(ax+b)=4(x+c)[/tex] Cross-multiply
[tex]3ax + 3b=4x+4c[/tex] Distribute
[tex]3ax-4x=4c-3b[/tex] Collect terms with x
[tex]x(3a-4)=4c-3b[/tex] Factor out x
[tex]x=\cfrac{4c-3b}{3a-4}[/tex] Divide both sides by 3a - 4
(6) If the store likes to keep 30 tiles in stock at all times how many bundles do they need to order now, after selling the 150 tiles to the customer? Think about how many you had left over from the customer when ordered 150 tiles.
function:
number of tiles: 12b+38
Where;
b=number of bundles
150+30 = 12b+38
Solve for b:
150+30 = 12b+38
180 = 12b+38
180-38 =12b
142 =12b
142/12 =b
11.8 =b
12 bundles
Remington purchased a new cell phone for $350 and added an annual warranty plan that cost him $35 per year. In what year will Remington's average annual cost of owning the phone be $122.50? Type your answer....
Answer:
3 years and 6 months
Step-by-step explanation:
35 × 3= 105 + 17 = 122
2.916 a month × 6 = 17. 496. And round to the nears while number = 17.50 = 105 + 17.50 = 122.5 or 122.50 zero fir place holder.
Hi can you help explain this question. I have trouble writing statement and reasons for this question please. I get lost.
For the given figure, we will prove the triangles BGH and BDH are congruent.
So, the proof will be as follows:
Statement Reason
1) m∠F = m∠FEG = m∠FGE Given
2) ΔFGE is an equilateral triangle from (1), the definition of an equilateral Δ
3) FG = GE from (2), the definition of equilateral Δ
4) FG = ED Given
5) m∠ GEH = m∠DEH Given
6) EH = EH Reflexive property
7) ΔGEH ≅ Δ DEH SAS postulate
8) GH = DH from (7) CPCTC
9) m∠GHE = m∠DHE from (7) CPCTC
10) m∠GHB = m∠DHB Definition of supplementary angles
11) HB = HB Reflexive property
12) ΔBGH ≅ ΔBDH SAS postualte
13) ΔAGB is an isosceles Δ Given
14)AG = AB Definition of isosceles Δ
15) ΔBCD is an isosceles Δ Given
16) CB = CD Definition of isosceles Δ
17) CB = AG Given
18) m∠CDB = m∠CBD Definition of isosceles Δ
19) m∠ABG = m∠AGB Definition of isosceles Δ
20) m∠CDB = m∠AGB Given
21) m∠ABG = m∠CBD Transitive property
22) Δ AGB ≅ ΔCBD AAS postualte
Find discriminate 7x^2+23x+168=6x^2+3x+7
The most appropriate choice for Quadratic equation and discriminant will be given by -
Discriminant = -244
What is Quadratic equation and discriminant?
At first it is important to know about equation.
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A two degree equation is known as Quadratic equation.
If [tex]ax^2 + bx + c = 0[/tex] ([tex]a\neq0[/tex]) is a quadratic equation, discriminant is given by
[tex]D = b^2-4ac[/tex].
Here,
The given equation is
[tex]7x^2+23x+168=6x^2+3x+7[/tex]
[tex]7x^2 - 6x^2 + 23x - 3x + 168 - 7 = 0 \\x^2 + 20x +161 = 0\\[/tex]
Discriminant = [tex]20^2 - 4 \times 1 \times 161[/tex]
= [tex]400 - 644[/tex]
= -244
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3. 40 ounces of granola costs $6.52
a. How much does granola cost per ounce? (Give your answer to the nearest cent.) pleasee help
Answer: $0.2
Step-by-step explanation:
To find the answer you divide 6.52 by 40 which will get 0.163. To check the answer and make sure its correct you can multiply 0.163 by 40 to get 6.52 making the answer correct so 0.2 is the answer to the nearest cent. Hope this helps :)
Here is the answer again
I need help with number 12. you have to spligy the expression and the answer will reveal a letter
8+9x+4(11-2x)
As a first step we are going to use distributive property of multiplication:
8+9x+44-8x
Solving ths:
52+x
Answer would be M
Which of the following are solutions to the equation below?Check all that apply.x-5x+ 1 = 0A. x =5+29B. x = 5 - 292.C. x= 5+ V212D. x= -1 - 212E. x = =*+,x21F. x =5 - 2152
It is calculated using the quadratic formula
[tex]x\text{ = }\frac{-b\text{ }\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In the equation
[tex]x^2-5x+1=0[/tex]a = 1, b = -5 and c = 1
Substitute the given to the quadratic formula
[tex]\begin{gathered} x\text{ = }\frac{5+\sqrt[]{21}}{2} \\ x\text{ = }\frac{5-\sqrt[]{21}}{2} \end{gathered}[/tex]Select the correct answer. A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the center of the circle and the length of the radius? A. (-7, -1), 36 units B. (7, 1), 36 units C. (7, 1), 6 units D. (-7, -1), 6 units
The coordinates for the center of the circle is (-7,-1) and the length of the radius is 6 units , the correct option is (D) .
If the equation of the circle is x² + y² + 2fx + 2gy + c = 0
then the center is (-f,-g)
and the radius is √(f²+g²-c)
In the question ,
it is given that the
equation of the circle is x² + y² + 14x + 2y + 14 = 0
So , on comparing it with the general form of equation , we get
2f = 14
f = 7
and 2g = 2
g = 1
hence, the center is (-7,-1) .
the radius is √(7² + 1² - 14)
= √(49 + 1 - 14)
= √(50 - 14)
= √36
= 6
Therefore , The coordinates for the center of the circle is (-7,-1) and the length of the radius is 6 units .
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a total of tickets were sold for the school play. they were either adult tickets or student tickets. there were 53 more student tickets sold than adult tickets. how many adult tickets were sold?
Total 250 adult tickets are sold.
Let a = number of adult tickets sold
Let s = number of student tickets sold
a + s = 553
s = a + 53
From above equations;
a + a + 53 = 553
2a = 553 - 53
2a = 500
a = 250
Total 250 adult tickets are sold.
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A heavy box is pulled across a wooden floor with a rope. The rope forms an angle of 60.0° with the floor. A tension of 80.0 N is maintained on the rope. What are the horizontal and vertical components of the force?
The vertical component of the force is 69.28 N and the horizontal component of the force is 40 N.
What is the resolution of the forces?Resolution of forces is the process of separating a force into two or more pieces so that the combined effect on the body is the same as if it had been a single force. We can analyze motion individually in different directions thanks to the resolution of forces.
Given that a heavy box is pulled across a wooden floor with a rope. The rope forms an angle of 60.0° with the floor. A tension of 80.0 N is maintained on the rope.
The vertical component and the horizontal component will be calculated as:-
Vertical component = 80sin60=69.28 N
Horizontal component = 80cos60 = 40 N
Therefore, the vertical component of the force is 69.28 N and the horizontal component of the force is 40 N.
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help me these two questions please
The values are given as;
1. - 2a - 9 = 6a + 15, a = -3
2. 14 + 3n = 5n - 6, n = 10
What is an algebraic expression?An algebraic expression can simply be described as a mathematical expression that composed of arithmetic operations, such as;
ParenthesesAdditionsubtractionBracketDivisionMultiplicationThey are also known to be made up of terms, variables, constants, factors and coefficients.
Given the algebraic expression;
- 2a - 9 = 6a + 15
Let's take the following steps;
collect like terms
- 2a - 6a = 15 + 9
add or subtract like terms
-8a = 24
Make 'a' the subject
a = 24/-8
Find the quotient
a = -3
14 + 3n = 5n - 6
collect like terms
3n - 5n = -6 - 14
-2n = -20
Make 'n' the subject of formula
n = 10
Hence, the values are -3 and 10
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which of the following graphs could be the graph of g (x)= (x+1) (x-2) (x+5)
D
1) Taking the function g(x)= (x+1) (x-2) (x+5), as we can see this a 3rd degree ploynomial
g (x)= (x+1) (x-2) (x+5)
g(x) =x³+4x²-7x-10
As the coefficient is positive, then we'll have
Examining the options, we have as the roots S={-5,-1,2} So the answer is D