the amount of vertical change in your position when you drive 200 feet is 16 feet
you are driving on a road that has a 8% uphill grade.
this means that the slope of the road is 8/100.
approximate the amount of vertical change in your position when you drive 200 feet
Therefore our proportion is: (where x is the "vertical" rise)
Slope is defined as rise so
8/100 = x/200
(8*200)/100 = x
16 feet = x
Hence , the amount of vertical change in your position when you drive 200 feet is 16 feet
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The number of bacteria in a culture triples every 3 hours. If there were 2 bacteria present at noon one day, how many were there at noon the next day assuming that all bacteria survived?
11. Find the area of the shaded region. Each square is 1 cm wide.
Answer:[tex]26cm^{2}[/tex]
Step-by-step explanation: To do this you have to dissect the shapes into singular shapes.
First, you do the parallelogram at the bottom. 4×2
Then the middle rectangle. 3×4
Then the triangle at the top. 4×3÷2
Area= [tex]26m^{2}[/tex]
help pls!! i have sparx and i literally dont understand
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Answer:
3 and 2
Step-by-step explanation:
the scale factor is the ratio of corresponding sides, image to original
shape on left
consider the length of the horizontal sides
P = 2 and Q = 6 , then
scale factor = [tex]\frac{6}{2}[/tex] = 3
shape on right
consider the length of the horizontal sides
R = 2 and T = 4 , then
scale factor = [tex]\frac{4}{2}[/tex] = 2
Noah wants to sign up for a streaming service. Company A charges a one-time fee of $10 and a costs $6 per month. Company B charges a one-time fee of $20 and costs $3 per month. If x represents the number of months using the service and y represents the total cost of the service, which system of equations represent this situation?
PLEASEEEEEEEE HELPpppppppp
As per the distance concept, the speed of the buses are 79 km/h and 69km/h if the two buses leave a station at the same time and travel in opposite directions.
Distance
Distance refers the physical length or an approximation based on other physics or common usage considerations.
Given,
Two buses leave a station at the same time and travel in opposite directions. One bus travels 10 slower than the other. If the two buses are 276 miles apart after 2 hours,
Here we need to find the rate of each bus.
Let us consider the speed of the first bus is x km/h.
Then the speed of the other bus = (x - 10) km/h
We know the formula of distance is,
Distance = time × speed
When we combined speed then we get,
=> x + x - 10 = (2x - 10) km/h
=> 2(2x - 10) =276
When we expand the equation, then we get,
4x - 40 = 276
4x = 316
After calculating,
x = 79 km/h
The speed of first bus x = 79 km/h
Speed of the second bus = x - 10 = 79 - 10 = 69 km/h
Therefore, the speed of the buses are 79 km/h and 69/km/h if the two buses leave a station at the same time and travel in opposite directions.
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A football team scored a total of 50 points in one game. They scored 14 times. The scoring
was made up of touchdowns (6 points each), field goals (3 points each), and PATS (1 point
each). They had 3 more touchdowns than field goals. How many of each type of score did the
team have?
Answer:
Touchdowns: 6
Field goals: 3
PATS: 5
Step-by-step explanation:
6*6 = 36
3*3 = 9
5*1 = 5
9+5+36 = 50 points
6+3+5 = 14 scored times
Answers:
6 touchdowns (TD)
3 field goals (FG)
5 points after touchdown (PAT)
===============================================
Explanation:
Acronyms used in football
PAT = point after touchdownTD = touchdownFG = field goalDefine the following variables
x = number of TDsy = number of FGsz = number of PATs"They had 3 more touchdowns than field goals", so,
TD = FG + 3
x = y + 3
They scored 14 times which means we can say
x+y+z = 14
Let's look at the point breakdown per type of score
TDs give 6 points each. Scoring x of them gives 6x pointsFGs give 3 points each. Scoring y of them gives 3y pointsPATs give 1 point each. Scoring z of them gives 1z pointsThen we can add up those expressions to get us to 6x+3y+1z = 50 points total. This is the same as saying 6x+3y+z = 50.
--------------------------
Here's our system of equations
x = y+3
x+y+z = 14
6x+3y+z = 50
Let's replace each x with y+3 in the second equation. Then solve for z.
x+y+z = 14
y+3+y+z = 14
2y+z = 14-3
2y+z = 11
z = 11-2y
Now replace every x with y+3 in the third original equation
6x+3y+z = 50
6(y+3)+3y+z = 50
6y+18+3y+z = 50
9y+z = 50-18
9y+z = 32
Then plug in z = 11-2y and solve for y
9y+z = 32
9y+11-2y = 32
7y+11 = 32
7y = 32-11
7y = 21
y = 21/7
y = 3 is the number of FGs scored
Use this to find z
z = 11-2y
z = 11-2(3)
z = 11-6
z = 5 is the number of PATs scored
Now let's find x
x = y+3
x = 3+3
x = 6 is the number of TDs scored
--------------------------
Checking the answers:
x+y+z = 6+3+5 = 9+5 = 14 times they scored
6x+3y+z = 6*6+3*3+5 = 36+9+5 = 50 points scored
There are 3 more TDs than FGs since x = y+3 leads to 6 = 3+3 which is a true statement.
All three original equations we set up for the system of equations are true. Therefore, the final answers are confirmed.
The difference of two numbers is 16. The greater number is 4 times the smaller
number minus 5. Find the numbers.
After using the linear equation - The smaller number is 7, and the greater number will be 23.
what is the substitution method?
Mathematicians frequently use the substitution method to resolve an equation system. With this method, you solve the equation for the first variable first, and then plug the answer into the second equation.
what is a linear equation in two variables?
When an equation is written in the form axe + by + c=0 and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero and the greater of the two numbers is four times the smaller number minus 5, that equation is said to be linear in two variables.
Let's assume that "x" is the smaller number, making "4x-5" the greater number. The requirement that the difference between the two numbers be 16 is also included.
thus,
4x - 5 - x = 16
3x -5 = 16
3x = 16 +5
3x =21
x = 21/3
x = 7
for the second number
4x-5
=4(7)-5
=28-5
=23
hence the smaller number is 7, and the greater number will be 23.
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Curtis has a part time job working for a video game store. He is paid a wage of $8 per hour plus 2% commission of his total sales each week. Write a linear equation that represents his weekly salary S.
Let H = Hours Worked
Let C = Commission earned on total sales
The linear equation which can be used to represents Curtis weekly salary is S = 8H + 0.02C
Linear equation that represents weekly salaryCurtis wage per hour = $8Percentage commission = 2%H = Hours WorkedC = Commission earned on total salesS = weekly salaryWeekly salary = Curtis wage per hour(Hours Worked) + Percentage commission(Commission earned on total sales)
S = 8(H) + 2%(C)
S = 8H + 0.02(C)
S = 8H + 0.02C
So therefore, Curtis linear equation for his weekly salary is S = 8H + 0.02C
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Rachel got a prepaid debit card with $30 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 21
cents per yard. If after that purchase there was $20.97 left on the card, how many yards of ribbon did Rachel buy?
43 yards because she spent 9.03 cents on ribbon 9.03 divided by 0.21=43
12. Write the equation of a line that is perpendicular to y = -x - 6 that goes through
the point (3,-8).
Answer:
y = x - 11
Step-by-step explanation:
Find the equation of the line that contains the given point and is parallel to the given line. Write the equation in slope-intercept form, if possible. (1.-3): y=-2
The equation of the line is y = -3x + 8.
What exactly is slope?
The slope of a line, or angle between it and the horizontal, is stated numerically. The slope of a line, ray, or line segment in analytical geometry is the ratio of its vertical to horizontal distance between any two locations ("slope equals rise over run").
Given,
x1 = 1
y1 = 5
m = -3
From,
y-y1 = m(x-x1) (x-x1) (x-x1)
y - 5 = -3(x - 1) (x - 1) (x - 1)
y-5 = -3x + 3
y = -3x + 8
As a result, the equation for the line is y = -3x + 8.
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Each student read 41 pages in December How many total pages did the students read by the end of December? and there are
27 students!
data:
september: chapter 1, 35 pages.
october: chapter 2, 38 pages
november: chapter 3, 35 pages
december: 41 pages.
total 4023 pages the 27 students read by the end of December
Step-by-step explanation:
35 + 38+35+41 = 149
27 students
149 × 27
4023 pages 27 students reads in this given four month
64 pens cost £5.76.
How much would 80 of these pens cost?
Answer: £7.20
Step-by-step explanation: £5.76/64 = £0.09 So one pen is £0.09. If you need 80, then £0.09 x 80 = £7.20
Not sure what to do here.
The trigonometric ratios of the right triangle are as follows:
sin E = 12 / 13cos E = 5 / 13tan E = 12 / 5sin F = 5 / 13cos F = 12 / 13tan F = 5 / 12How to find the angles of right triangle?A right triangle is a triangle that has one of its angles as 90 degrees.
The side and angles of a right triangle can be solved using trigonometric ratios.
The ratios of the sides of a right triangle are called trigonometric ratios.
A right angle triangle has the opposite side, adjacent side and hypotenuse side depending on the angles location.
Using ratios,
sin ∅ = opposite / hypotenuse
cos ∅ = adjacent / hypotenuse
tan ∅ = opposite / adjacent
Therefore,
sin E = 12 / 13cos E = 5 / 13tan E = 12 / 5sin F = 5 / 13cos F = 12 / 13tan F = 5 / 12learn more on right triangle here: https://brainly.com/question/15284655
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Find an angle in each quadrant with a common reference angle with 41°, from 0°≤θ<360°
The angles in each of the four quadrants with a common reference to the acute angle 41° are as follows;
For 2nd quadrant; 139°.For 3rd quadrant; 221°.For 4th quadrant; 319°.Which angles in each quadrant have a common reference angle with 41°?It follows from the task content that the angles which have a common reference to the angle 41° in each quadrant he determined.
On this note, the angles can be determined from custom formulas for reference angles in each quadrant as follows;
For 2nd quadrant; θ = (180 - θ) = (180 - 41) = 139°.For 3rd quadrant; θ = (180 + θ) = (180 + 41) = 221°.For 4th quadrant; θ = (360 - θ) = (360 - 41) = 319°.Ultimately, the angles in each quadrant with a common reference alongside 41° are; 139°, 221° and 319°.
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a random sample of size is selected from a population with . a. what is the expected value of (to decimals)? b. what is the standard error of (to decimals)? c. show the sampling distribution of . (to decimals) (to decimals) d. what does the sampling distribution of show? - select your answer -
a. The expected value is 0.40
b. The standard error is 0.0024
Given that:
Sample size, n=100
Population proportion, p=0.40
a) The expected value of the sample proportion is defined as:
E(^p)=p
now,
E(^p)=0.40
b) The standard error of the sample proportion is defined as:
SE(^p) = √p(1-p)/n
SE(^p) = √0.40(1-0.40)/100
SE(^p) = 0.0024
c) The sampling distribution of the sample proportion is normally distributed with the expected value of the sample proportion of 0.40.
Therefore,
E(^p) = 0.40
d) The central limit theorem states that the sample statistic (sample proportion) tends to the population parameter (population proportion) as the sample size tends to infinity (OR n→∞).
^P~N(p, p(-p)/n) as n→∞
Hence we get the required answers.
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EASY! SHAPES! (points, brainliest, stars)
Ratio and rates pls help me
Answer:
Step-by-step explanation:
5 parts blue
yellow: 3 parts
WE SHOULD HAVE DONE EQUAL COLOURS FOR A GOOD RESULT?
A large gym with hundreds of members offers yoga classes. Members are free to take these
classes at no charge, but not all members are interested, and some never take advantage of the
yoga classes. Non-members can also take these classes, but they must pay a fee for each class.
A manager at the gym is curious about overall satisfaction with these yoga classes, so they
survey a large random sample of anyone who has taken a yoga class at the gym in the past year.
They find that 78% of those surveyed are "very satisfied" with the yoga classes.
For which population is 78% a legitimate estimate of the percent of people that are "very
satisfied" with the yoga classes?
Choose 1 answer:
only those surveyed
All members who have taken a yoga class at the gym in the past year, but not non-
members
All non-members who have taken a yoga class at the gym in the past year, but not
members
anyone who has taken a yoga class at the gym in the past year but not before that
anyone who has ever taken a yoga class at the gym
The population for which 78% is a legitimate estimate of the percent of people that are 'very satisfied" with the yoga classes is C. anyone who has taken a yoga class at the gym in the past year but not before that.
What is an estimate?An estimate is a rough calculation that may not be based on real figures or it may be based on rounded-off or appropriated facts and figures.
Estimates enable the decision-maker to make a quick guess or decision that cannot wait for all the facts to be collected.
Thus, the population of interest for the estimate includes members and non-members who have participated.
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Answer:
D
Step-by-step explanation:
What is x/3 + 6 - 2x = -6?
Answer: 7.5
Step-by-step explanation: 2 x 7.5 = 15
3 + 6 - 15
9 -15
-6
how many packages of diapers can you buy with 40$ if one packages cost 8$. this is a one step equation
In order to determine how many packages of diapers you can buy, it is only necessary to divide the total money you have, between the price of each package.
You have:
available money = 40$
package cost = 8$
Then, you calculate the quotient between available money and package cost:
[tex]\frac{40}{8}=5[/tex]Hence, you can buy 5 packages of diapers with 40$
The table below shows the average price of a Miami Marlins baseball ticket between 2006 and 2021.
The equation y=1.67x−3338.5 models this relationship, where x is the year and y is the average ticket price.
Use the model to predict the ticket price for a Miami Marlins baseball ticket in 2030.
$=
By evaluating the equation in x = 2030, we can estimate the price to be $51.60.
How to use the model?We know that the equation:
y = 1.67*x - 3338.5
Models the relationship between the year, x, and the average ticket price of a Miami Marlins baseball ticket.
We know that this relationship works for the years 2006 to 2021, but can be used to estimate the price for years after and before that.
if we use x = 2030, we will get:
y = 1.67*2030 - 3338.5 = 51.6
This will be the price, in dollars, of a game in the year 2030.
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the admission fee at an amusement park is $3.50 for children and 13.00 for adults. on a certain day, 240 people entered the park, and the admission fees collected totaled $1,980.00. how many children and how many adults were admitted?
120 children and 120 adults were admitted to the amusement park if the admission fee collected was $1980.00
The number of children and adults that entered the park can be calculated using linear equations.
Considering x to be the number of adults and y to be the number of children;
As 240 people entered the park, therefore;
x + y = 240
As the fee for children is $3.50 and for adults is $13, therefore;
13x + 3.50y = 1980
Determining the value of y in the first equation;
x + y = 240
y = 240 - x
Putting this value of y in the second equation;
13x + 3.50y = 1980
13x + 3.50(240 - x) = 1980
13x + 840 - 3.50x = 1980
9.5x = 1980 - 840
9.5x = 1140
x = 1140 / 9.5
x = 120
To determine the value of y, we Substitute this value of x in the first equation;
y = 240 - x
y = 240 - 120
y = 120
Hence, 120 children and 120 adults entered the park if the admission fee for children was $3.50 and for adults was $13.00
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Help I neee help asap
Based on the information given, below statements are true
A. Feldman & Sons have a greater hourly rate.
B. The graph of the function for Strong Arm Movers has a greater y-intercept than the graph of the function for Feldman & Sons.
Feldman and Sons have a higher hourly rate or slope (35 compared to 25), but Strong Arm. Movers have a higher y-intercept (50 compared to 30). Feldman and Sons charge more than Strong Arms for both 3-hour and 2.5-hour transfers.
Explain about movers and packers ?Movers is an organization that helps people pack and move their belongings from one place to another. They take full responsibility for the items we have asked them to move and they also offer refunds if anything is broken or lost. That's what packers and movers mean. Movers and packers pack goods. Material load. Movement of goods and unloading of goods.
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LaTanya buys 6 yards of blue fabric and 9 yards of green fabric. The blue fabric costs $2 more per yard than the green fabric. She pays a total of $57. What would be the combined cost of 1 yard of blue fabric and yard of green fabric?
The price of 1 yard of blue fabric and 1 yard of green fabric is obtained by solving the system of linear equations and it is $8
Let
x = price of blue fabric per yard
y = price of green fabric per yard
"The blue fabric costs $2 more per yard than the green fabric" means:
x = y + 2 (Equation 1)
" LaTanya buys 6 yards of blue fabric and 9 yards of green fabric and pays $57" means:
6x + 9y = 57 (Equation 2)
Substitute equation 1 into equation 2:
6x + 9y = 57
6 (y + 2) + 9y = 57
6y + 12 + 9y = 57
15 y = 45
y = 3
Substitute y = 3 into equation 1
x = 3 + 2 = 5
Hence, the price of blue fabric is $5 per yard while the green fabric is $3 per yard.
The price of 1 yard of blue fabric and 1 yard of green fabric = x + y = 3 + 5 = $8
Complete question:
LaTanya buys 6 yards of blue fabric and 9 yards of green fabric. The blue fabric costs $2 more per yard than the green fabric. She pays a total of $57. What would be the combined cost of 1 yard of blue fabric and 1 yard of green fabric?
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the height, h meters, of a certain species of fir tree can be estimated from the formula h=35d2/3, where d meters is the diameter at the base. What is the approximate height of a fir tree with a base diameter of 3.2m
The approximate value of the height f the tree when the base diameter is 3.2 meters is 119.47 meters
How to approximate the height of the fir tree?From the question, the equation of the function of height is given as
h = 35d²/3
Also from the question, we have the base diameter of the fir tree to be
d = 3.2m
Next, we substitute 3.2 for d in the equation of the function of height given as
h = 35d²/3
So, we have the following equation:
h = 35 x 3.2²/3
Evaluate the exponent
So, we have
h = 35 x 10.24/3
Evaluate the product
So, we have the following equation:
h = 358.4/3
Evaluate the quotient
This gives
h = 119.47
Hence, the height is 119.47 meters
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Choose the point-slope form of the equation below that represents the line that passes through the point (6, -3) and has a slope of 1/2OPTIONS: A.) y-6 = 1/2(x+3)B.) y = 1/2x - 6C.) y+3 = 1/2(x-6)D.) y-2y = 12
ANSWER
B) y = 1/2x - 6
EXPLANATION
We have that the line passes through (6 -3) and has a slope of 1/2.
To find the point-slope form of the equation, we have to use the formula:
[tex]y-y_1=m(x-x_1)[/tex]where m = slope = 1/2
(x1, y1) = (6, -3)
So, we have:
y - (-3) = 1/2 (x - 6)
y + 3 = 1/2 x - (1/2 * 6)
y + 3 = 1/2 x - 3
=> y = 1/2x - 3 - 3
y = 1/2x - 6
The answer is Option B
Which is NOT a step when solving an equation using the distributive property?
Use the properties of equality to solve.
Check your work.
Solve for the variable using only the addition property of equality.
Distribute through the parentheses.
Answer:
use the property’s of equality to solve
Step-by-step explanation:
Use the properties of equality to solve, is not a step when we are solving an equation using distributive property.
Distributive property:- In general,
distribute means to divide something or give a share or part of something. According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
ex:- a(b+c)=ab+ac
a(b-c)=ab-ac ,also valid true for division
(b+c)/a = b/a + c/a
Steps involved while solving equations
1. If you see parenthesis, with more than one term inside, then distribute first.
2. Rewrite your equations with like terms together. Take the sign in front of each term.
3. Combine like terms.
4. Continue solving to get the answer.
Thus, Use the properties of equality to solve, is not a step involved in solving equation using distributive property.
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A food truck sells Mongolian ginger bowls for $14 per bowl. At a festival, 132 bowls are sold. About how much money does the food truck collect?
How many units the function y = |x| - 3 is translated from the parent function?3 units upwards from the origin3 units downwards from the origin3 units left from the origin3 units right from the origin
From the expression we can see that it is translated 3 units downwards from the origin.