Step-by-step explanation:
Let the other rational number be represented by "x". We know that the difference of the two rational numbers is 17/28, which can be written as:
x - (-9/14) = 17/28
Simplifying the left-hand side:
x + 9/14 = 17/28
Multiplying both sides by the least common multiple of 14 and 28, which is 28, we get:
28(x + 9/14) = 28(17/28)
Simplifying:
4(2x + 9) = 17
Expanding:
8x + 36 = 17
Subtracting 36 from both sides:
8x = -19
Dividing by 8:
x = -19/8
Therefore, the other rational number is -19/8.
There are 50 athletes signed up for a neighborhood basketball competition. Players can select to play in the 6-player games ("3 on 3") or the 2-player games ("1 on 1").
All 50 athletes sign up for only one kind of game. Complete the table to show different combinations of games that could be played
If 13 matches are played in total then, 7 2-player matches and 6 6-player matches are played.
Here we see that the table has two columns- 6 player Athletes and 2 player athletes. It is given that no athlete participates in both the type of games. Hence we can say that
If one match for 2 player game is held then 2 players are employed there.
Hence we have 48 players left
hence we will have 48/6 = 8 6-player matches.
Similarly, if 1 6-player match is played then 44 players applied for the 2-player match, hence, we have 44/2 = 22 2-player matches
If 4 2-player matches are held then we will have 8 players booked. Hence 42/6 = 7 6-player matches were held.
If 4 6-player matches were held then, we have 26/2 = 13 2-player matches.
Hence the table will be
Number of 6 Player Games Number of 2-player games
8 1
1 22
7 4
4 13
b)
Let the total 2-player games played be x and 6-player games be y
we have,
x + y = 13
2x + 6y = 50
or, 2(x + y) + 4y = 50
or, 26 + 4y = 50
or, 4y = 24
or, y = 6
Hence x = 7
Therefore, in total 7 2-player matches and 6 6-player matches are played.
To learn more about Equations visit
https://brainly.com/question/22591166
#SPJ4
Using the formulas, answer the question.
A = P(1 + =)nt
A = Pert
Ted invests $500 in an account that compounds interest quarterly with a 3.5%
rate. How much money will he have after 15 years? Round to the nearest
dollar.
Answer:
First, convert R as a percent to r as a decimal
r = R/100
r = 3.5/100
r = 0.035 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 500.00(1 + 0.035/4)(4)(15)
A = 500.00(1 + 0.00875)(60)
A = $843.30
A = $843 (round-off)
Determine the critical points and the linearizations for the following systems: = (a) x' = (1 + x) sin y, y' = 1 – X – cos y (b) x = 1 - xy, y' = 2 - 43 x – =
a) The critical points are x = -1 and y = nπ, where n is an integer. The linearization of the system near the center is x' = ky, y' = -kx
b) The critical points are (1, 1) and (-1, -1). The linearization of the system near the degenerate critical point is x' = y, y' = 2x + 2y
(a) To find the critical points of the system, we need to solve the equations:
1 + x = 0 and sin y = 0 for x and y, respectively. This gives us x = -1 and y = nπ, where n is an integer. We can also find the linearizations near each critical point by computing the Jacobian matrix:
J(x, y) = [cos y, (1 + x)cos y - sin y; -1, sin y]
At the critical point (-1, nπ), the Jacobian matrix becomes:
J(-1, nπ) = [(-1)^n, 0; -1, 0]
The eigenvalues of this matrix are 0 and (-1)^n, which means that we have a center at (-1, nπ) when n is even, and a saddle point when n is odd. The linearization of the system near the center is:
x' = ky, y' = -kx
where k is a constant determined by the Jacobian matrix. The linearization near the saddle point is:
x' = -y, y' = -x
(b) To find the critical points of the system, we need to solve the equations:
1 - xy = 0 and x - y^3 = 0 for x and y, respectively. This gives us two critical points: (1, 1) and (-1, -1).
We can find the linearizations near each critical point by computing the Jacobian matrix:
J(x, y) = [-y, -x; 1, 3y^2]
At the critical point (1, 1), the Jacobian matrix becomes:
J(1, 1) = [-1, -1; 1, 3]
The eigenvalues of this matrix are -1 - √5 and -1 + √5, which means that we have a saddle point at (1, 1). The linearization of the system near the saddle point is:
x' = (-1 - √5)x - y, y' = x + (3 - √5)y
At the critical point (-1, -1), the Jacobian matrix becomes:
J(-1, -1) = [1, 1; 1, 3]
The eigenvalues of this matrix are 2 and 2, which means that we have a degenerate critical point at (-1, -1). The linearization of the system near the degenerate critical point is:
x' = y, y' = 2x + 2y
This system has infinitely many solutions, since the eigenvalues are equal.
To learn more about critical points click on,
https://brainly.com/question/29991963
#SPJ4
Which unique sequence of rigid motions maps quadrilateral abcd to quadrilateral efgh?
s
а
ib
4
d
ll2_3 4 5 6
e
f
h
g
a a reflection over the x-axis followed by a translation of (,y) → (, y - 4).
b. a reflection over the y-axis followed by a translation of (1,y) → (, y-6).
c a translation of (+,y) → (2, y - 3) followed by a reflection over the y-axis.
a translation of (cv) (1-6, y) followed by a reflection over the x-axis.
d.
The correct answer is option B, a reflection over the y-axis followed by a translation of (1,y) → (1, y-6).
To solve this problem, we need to find the sequence of rigid motions (i.e., transformations that preserve distance and angle) that maps quadrilateral ABCD to quadrilateral EFGH.
First, we need to identify the corresponding vertices of the two quadrilaterals. Let's assume that vertex A maps to vertex E, vertex B maps to vertex F, vertex C maps to vertex G, and vertex D maps to vertex H.
Now, we can apply different transformations to map each vertex of quadrilateral ABCD to the corresponding vertex of quadrilateral EFGH. We can try each option provided and check if it maps all the vertices correctly.
Option A involves a reflection over the x-axis, followed by a translation of (0,y) → (0, y - 4). This transformation does not map vertex A to vertex E correctly.
Option B involves a reflection over the y-axis, followed by a translation of (1,y) → (1, y - 6). This transformation maps vertex A to vertex E, vertex B to vertex F, vertex C to vertex G, and vertex D to vertex H, which is the correct mapping.
Option C involves a translation of (+,y) → (2, y - 3) followed by a reflection over the y-axis. This transformation does not map vertex A to vertex E correctly.
Option D involves a translation of (1-6, y) followed by a reflection over the x-axis. This transformation does not map vertex A to vertex E correctly.
Therefore, the unique sequence of rigid motions that maps quadrilateral ABCD to quadrilateral EFGH is a reflection over the y-axis followed by a translation of (1,y) → (1, y-6), which is option B.
To know more about reflection refer here:
https://brainly.com/question/30270479
#SPJ11
50 POINTS AND BRAINLYEST Triangle NMO has vertices at N(−5, 2), M(−2, 1), and O(−3 , 3). Determine the vertices of image N′M′O′ if the preimage is reflected over x = −1.
N′(5, −2), M′(2, 1), O′(3, 3)
N′(−5, 5), M′(−2, 3), O′(−3, 7)
N′(3, 2), M′(0, 1), O′(1, 3)
N′(−5, −2), M′(−2, −1), O′(−3, −3)
Answer:
N'(3, 2), M'(0, 1), O'(1, 3)
Step-by-step explanation:
Please sketch the graphs of the two triangles and the line of reflection to confirm my answer.
Since NMO is reflected over the line
x = -1, the y-coordinates of N'M'O' will remain the same. Since the x-coordinate of N is at -5, which is 4 units to the left of the line of reflection, the x-coordinate of N' is at -1 + 4 = 3. Since the x-coordinate of M is at -2, which is 1 unit to the left of from the line of reflection, the x-coordinate of M' is at -1 + 1 = 0. Since the x-coordinate of O is at -3, which is 2 units to the left of the line of reflection, the x-coordinate of O' is at -1 + 2 = 1. So the vertices of N'M'O' are at (3, 2), (0, 1), and (1, 3).
I…. NEEDDDD… HELPPP
According to the information, the customer would save $492 in the first year by switching to Intellivision; the customer would save $207 in the second year by using Intellivision; ElectroniSource would be cheaper in the third year.
How to calculate the annual cost for both companies?a. To calculate the annual cost for ElectroniSource: $42/month for phone service x 12 months = $504/year, $35/month for internet service x 12 months = $420/year, and $59/month for cable television x 12 months = $708/year.
So the total annual cost with ElectroniSource would be $504 + $420 + $708 = $1,632.
With Intellivision, the flat monthly fee for all three services is $95, so the total annual cost would be $95 x 12 months = $1,140.
Therefore, the customer would save $1,632 - $1,140 = $492 in the first year by switching to Intellivision.
How to calculate the best rate for the second year?b. After the first year, Intellivision raises the rates by 25%, so the new monthly fee would be $95 x 1.25 = $118.75.
The total annual cost in the second year would be $118.75 x 12 months = $1,425.
Using the same services, the annual cost with ElectroniSource would still be $1,632.
Therefore, the customer would save $1,632 - $1,425 = $207 in the second year by using Intellivision.
How to calculate the best rate for the third year?c. If Intellivision raises the rates by 16% in the third year compared to the second year, the new monthly fee would be $118.75 x 1.16 = $137.95.
The total annual cost in the third year would be $137.95 x 12 months = $1,655.4.
The annual cost with ElectroniSource would still be $1,632.
Therefore, ElectroniSource would be cheaper in the third year.
Learn more about fee in: https://brainly.com/question/28498239
#SPJ1
Without using a protractor, estimate the measure of the angle below. Explain how you made your estimate.
Answer:
The approximated measure of this angle is 90°, so this may be a right angle.
Place a sheet of paper so that the corner corresponds to the angle. You will notice that the lines will closely align with the edges of the paper.
An electronics retailer offers an optional protection plan for a mobile phone it sells. Customers can choose to buy the protection plan for \$100$100dollar sign, 100, and in case of an accident, the customer pays a \$50$50dollar sign, 50 deductible and the retailer will cover the rest of the cost of that repair. The typical cost to the retailer is \$200$200dollar sign, 200 per repair, and the plan covers a maximum of 333 repairs.
Let X be the number of repairs a randomly chosen customer uses under the protection plan, and let F be the retailer's profit from one of these protection plans. Based on data from all of its customers, here are the probability distributions of X and F:
X=\# \text{ of repairs}X=# of repairsX, equals, \#, start text, space, o, f, space, r, e, p, a, i, r, s, end text 000 111 222 333
F=\text{ retailer profit}F= retailer profitF, equals, start text, space, r, e, t, a, i, l, e, r, space, p, r, o, f, i, t, end text \$100$100dollar sign, 100 -\$50−$50minus, dollar sign, 50 -\$200−$200minus, dollar sign, 200 -\$350−$350minus, dollar sign, 350
Probability 0. 900. 900, point, 90 0. 70. 070, point, 07 0. 20. 020, point, 02 0. 10. 010, point, 01
Find the expected value of the retailer's profit per protection plan sold
Note that the expected value of the retailers profit is - $114. This means he made a loss.
How did we arrive at this ?To find the expected value we must proceed as follows
Expected Value - E(F) is
Probability of F - P(F)
= 100 x ($100 - $200) + (P(F) = $50) x ($50 - $200) + (P(F) = $ -200) x ( $ - 200 - $200) + (P(F) = $- 350) x ($ -350 $ 200)
= (0.9) x (-100) + (0.07 ) x (-150) + (0.01) x (-550) + (0.02) x (-400)
= - 90 - 10.5 - 5.5 -8
E(F) = $ -114
So it is right to state that the expected value of the retailer's profit per protection plan sold is -$114, which is a loss.
Learn more about expected value:
https://brainly.com/question/29574962
#SPJ4
Full Question:
An electronics retailer sells mobile phones with an optional protection plan for $100. In case of an accident, the customer pays a $50 deductible and the retailer covers the rest of the repair cost, which is typically $200 per repair. The protection plan covers a maximum of 333 repairs.
Let X be the number of repairs a randomly chosen customer uses under the protection plan, and let F be the retailer's profit from one of these protection plans. The probability distributions of X and F are:
X = number of repairs: 0 1 2 3
Probability: 0.90 0.07 0.02 0.01
F = retailer profit: $100-$50-$200-$350
Probability: 0.90 0.07 0.02 0.01
The task is to find the expected value of the retailer's profit per protection plan sold.
You have decided to purchase a car for $25,625. The credit union requires a 10% down payment and will finance the balance with a 9% annual interest loan for 36 months. The sales tax in your city is 7. 5%, and the license and title charges are $175. 13. What is the total purchase price of the car including tax, license, and title? Round your answer to the nearest cent. A. $24,949. 80 c. $27,722. 01 b. $24,967. 32 d. $27,735. 14.
Answer is 27,529.82
To calculate the total purchase price of the car including tax, license, and title, we need to add the down payment, the financed balance, the sales tax, and the license and title charges.
First, we calculate the down payment:
10% of $25,625 = $2,562.50
Next, we calculate the financed balance:
$25,625 - $2,562.50 = $23,062.50
Then, we calculate the sales tax:
7.5% of $23,062.50 = $1,729.69
Finally, we add the license and title charges:
$1,729.69 + $175.13 = $1,904.82
So the total purchase price of the car including tax, license, and title is:
$2,562.50 + $23,062.50 + $1,904.82 = $27,529.82
Rounded to the nearest cent, the answer is option D: $27,735.14.
To know more about rounding-off:
https://brainly.com/question/28128444
#SPJ11
a)cos 165 in terms of sine and cosine of acute angle
Cos 165 in terms of sine and cosine of acute angle would give cos(165) = -(1 + √3) / (2√2).
How to find the cosine ?To find the cosine of 165 degrees in terms of sine and cosine of an acute angle, we can use the cosine angle addition formula:
cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
Since 120 degrees is in the second quadrant, the cosine is negative, and the sine is positive:
cos(120) = -cos(60) and sin(120) = sin(60)
cos(165) = -cos(60)cos(45) - sin(60)sin(45)
Now we can plug in the values of the trigonometric functions:
cos(165) = - (1/2) x (1/√2) - (√3/2) x (1/√2)
cos(165) = -(1 + √3) / (2√2)
Find out more on cosine at https://brainly.com/question/12658311
#SPJ1
A corporation earned a profit of $ 2.5 × 1 0 4 $2.5×10 4 for 200 days in a row. What was the corporation’s total profit during this time period? Express your answer in scientific notation.
Answer: hopefully the image helps
Step-by-step explanation:
PLS HELP FAST I ONLY HAVE A LIL TIME LEFT! WILL MARK BRAINLIEST
Answer:
DStep-by-step explanation:
In this set,
the maximum is 35
the minimum is 6
So, we can cross out options A, B
the median is 14
The only option that works for this set is option D
Question 4
Question
What does the y-intercept of this relationship represent?
the initial height of the plant
the height of the plant at the end of the experiment
the amount of plant food Ryan uses each day
the average amount the plant grows each day
Answer:
Step-by-step explanation:
The correct answer is:
the initial height of the plant
The y-intercept represents the point where the graph intersects the y-axis. In the context of a relationship between plant growth and time, the y-intercept would represent the initial height of the plant, which is the height of the plant at the start of the experiment, before any growth has occurred.
You are going to run at a constant speed of 7.5
miles per hour for 45
minutes. You calculate the distance you will run. What mistake did you make in your calculation? [Use the formula S=dt
.]
The value of the distance you will run is 5.62500 miles
Calculating the value of the distance you will runFrom the question, we have the following parameters that can be used in our computation:
You are going to run at a constant speed of 7.5 miles per hour For 45 minutesThis means that
Speed = 7.5 miles per hour
Time = 45 minutes
The distance you will run is calculated as
Distance = Speed * Time
Substitute the known values in the above equation, so, we have the following representation
Distance = 7.5 miles per hour * 45 minutes
Evaluate the product
Distance = 5.62500 miles
Hence, the distance is 5.62500 miles
Read more about speed at
https://brainly.com/question/24571540
#SPJ1
WILL GIVE BRAINLIEST!!!
1.)
A composite figure is composed of a semicircle whose radius measures 4 inches added to a square whose side measures 11 inches. A point within the figure is randomly chosen.
What is the probability that the randomly selected point is in the semicircular region?
Enter your answer rounded to the nearest tenth in the box.
2.)
A circular spinner has a radius of 6 inches. The spinner is divided into three sections of unequal area. The sector labeled green has a central angle of 90°. A point on the spinner is randomly selected.
What is the probability that the randomly selected point falls in the green sector?
1/90
1/9
1/4
1/3
3.)
Question
A spinner is divided into 10 equally sized sectors. The sectors are numbered 1 to 10. A randomly selected point is chosen.
What is the probability that the randomly selected point lies in a sector that is a multiple of 3?
Enter your answer in the box.
4.)
Question
Two concentric circles form a target. The radii of the two circles measure 8 cm and 4 cm. The inner circle is the bullseye of the target. A point on the target is randomly selected.
What is the probability that the randomly selected point is in the bullseye?
Enter your answer as a simplified fraction in the boxes.
Answer:
1. 17.2
2. 1/4 or 0.25
3. 3/10 or 30%
4. 15/16
I hope this helped
Step-by-step explanation:
sets x y and z are defined below a number will be randomly selected from set x what is the probability that the selected number will be an element of set y and an element of set z.
x= (1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Y= (5, 10, 15, 20, 25)
Z= (1,5,25)
A. 0.1
B. 0.2
C. 0.5
D. 0.6
E. 0.8
When a number is chosen from set x, there is a 0.2 chance that the chosen number will also be found in sets y and z. The answer is option (B). 0.2.
What is Probability?The ratio of favourable outcomes to all possible outcomes of an event is known as the probability. The symbol x can be used to express the quantity of successful outcomes for a study with 'n' outcomes. The probability formula determines the likelihood that an event will occur.
It is the ratio of effective results to all effective results. The study of probability is a branch of mathematics that examines the likelihood that an event will occur. Probability, which expresses the likelihood that an event will occur, is calculated by dividing the total number of occurrences by the total number of positive events.
The number of elements of Both Y and Z answer is 5 and 25.
The probability of selecting a number from x that is an element of y and z
Intersection of y and z is (5, 25)
No.of elements in x is = 2/10
= 1/5
= 0.2
To know more about probability, visit:
brainly.com/question/29251004
#SPJ1
In an expansion of (2a-5b)^2 the coefficient of ab is
In the expansion of the given expression, (2a - 5b)², the coefficient of ab is -20
Determining the coefficient of a term in an expansion
From the question, we are to determine the coefficient of ab in the expansion of the given expression.
The given expression is
(2a - 5b)²
To determine the coefficient of ab, we will expand the expression
Expand the expression
(2a - 5b)²
(2a - 5b)(2a - 5b)
Applying the distributive property, we get
2a(2a - 5b) -5b(2a - 5b)
Distribute the expression outside
4a² - 10ab - 10ab + 25b²
Simplify the expression
4a² - 20ab + 25b²
Hence, the coefficient of ab is -20
Learn more on Determining the coefficient in an expansion here: https://brainly.com/question/30601451
#SPJ1
Orlando wants to borrow $3,000 for the purchase of a used car. He has to pay back the loan after 4 years. The two loan options are simple interest at a rate of 5. 8% each year, or interest compounded annually at a rate of 5. 2% each year. Which method should he choose , simple or compound , and how much less will he owe using that method?
Orlando should consider using simple interest and the amount he will have to pay is $696, under the condition that he wants to borrow $3,000 for the purchase of a used car. He needs to clear the loan after 4 years.
Orlando should apply the simple interest method.
The amount of interest he will pay using simple interest is evaluated
I = P × r × t
Here
I = interest paid
P = borrowed principal amount
r = rate of annual interest
t = time
In this case,
P = $3,000
r = 5.8%
t = 4 years
Therefore,
I = $3,000 × 0.058 × 4
= $696
So Orlando will pay $696 in interest using simple interest.
The amount of interest he will pay using compound interest is calculated as follows:
[tex]A = P * (1 + r/n)^{(n*t)}[/tex]
I = A - P
Here,
A = end term amount
n = count of interest that is compounded each year
In this case,
P = $3,000
r = 5.2%
t = 4 years
Interest is compounded annually so n=1
Therefore,
A = $3,000 × (1 + 0.052/1)⁴
= $3,697.47
I = $3,697.47 - $3,000
= $697.47
So Orlando will pay $697.47 in interest using compound interest.
Therefore, Orlando should choose simple interest method and he will owe $1.47 less using that method.
To learn more about simple interest
https://brainly.com/question/25845758
#SPJ4
1. the elevation of death valley, california is - 282 feet. the elevation of tallahassee, florida is 203
feet. the elevation of westmorland, california is -157 feet.
compare the elevations of death valley and tallahassee using < or >
fill in the blank:
death valley (-282 feet)
tallahassee, florida (203 feet)
Based on the elevations given, Death Valley (-282 feet) < Tallahassee, Florida (203 feet).
To compare the elevations of Death Valley and Tallahassee, we'll use the inequality symbols i.e., "<" or ">" . The symbol "<" indicate less than and ">" indicate greater than.
Death Valley, California has an elevation of -282 feet, while Tallahassee, Florida has an elevation of 203 feet. Since -282 is less than 203, we use the "<" symbol.
So, the comparison is as follows:
Death Valley (-282 feet) < Tallahassee, Florida (203 feet)
This means that the elevation of Death Valley is lower than or less than the elevation of Tallahassee.
Learn more about Inequality:
https://brainly.com/question/11457776
#SPJ11
A windshield wiper is 45 cm long and
creates a central angle of 120° in one
wipe. what is the sector area?
The windshield sector area is 706.86 cm².
To calculate the sector area of the windshield wiper, we need to use the formula for the area of a sector of a circle. The formula is:
A = (θ/360°) x πr²
where A is the area of the sector, θ is the central angle of the sector in degrees, and r is the radius of the circle.
In this problem, we are given that the windshield wiper has a length of 45 cm, which means that the radius of the circle traced by the wiper is 45 cm/2 = 22.5 cm.
We are also given that the wiper creates a central angle of 120° in one wipe. Substituting these values into the formula, we get:
A = (120°/360°) x π(22.5 cm)²
A = (1/3) x π x (22.5 cm)²
A ≈ 706.86 cm²
Therefore, the sector area of the windshield wiper is approximately 706.86 square centimeters.
To learn more about sector area refer here:
https://brainly.com/question/16367606
#SPJ11
Explain the role of the brackets, and how they effects the sum. Provide the answer for both sums. Sum 1 Sum 2 10 + 7 – 5 + 3 = 10 + 7 – (5 + 3) =
The role of the brackets, and how they effects the sum is given as the inside signs get changed after the opening of the bracket.
The associative property of addition is a mathematical statement that asserts that the arrangement of three or more integers does not affect their total. This indicates that no matter how the numbers are organised, the total of three or more integers remains the same.
The associative property of addition is a mathematical principle that asserts that when adding three or more integers, the amount obtained is constant regardless of how the numbers are grouped. Grouping here refers to where the brackets are positioned.
The sum for the 1st term is 10 + 7 – 5 + 3 = 15
The sum of the 2nd term is 10 + 7 – (5 + 3) = 17 - 8 = 9
Here, the bracket used made all the difference so after opening of the bracket the sign inside changed which impacted the summation of the terms above.
Learn more about Brackets:
https://brainly.com/question/31126413
#SPJ4
The function f(t)=350(1. 2)^{365t}f(t)=350(1. 2)
365t
represents the change in a quantity over t years. What does the constant 1. 2 reveal about the rate of change of the quantity?
The constant 1.2 in the function represents the rate of change of the quantity per year.
Specifically, it represents the factor by which the quantity grows or decays over a year.
Since 1.2 is greater than 1, the function describes an exponential growth, where the quantity is multiplied by 1.2 each year.
For example, after one year, the quantity is multiplied by 1.2, after two years it is multiplied by 1.2 squared, and so on.
To know more about exponential growth refer here:
https://brainly.com/question/12490064
#SPJ11
The radius of the moon is about 1. 738 mega meters. The formula for the volume of a sphere is v=4/3 nr3. Approximately what is the volume of the moon. Use 3. 14 as an approximation for pi
To calculate the volume of the moon, we can use the formula V = (4/3)πr^3, where r is the radius of the moon.
Given that the radius of the moon is about 1.738 mega meters (or 1,738,000 meters), we can substitute this value into the formula and simplify as follows: V = (4/3) × 3.14 × (1.738 × 10^6)^3 V ≈ 2.196 × 10^19 cubic meters Therefore, approximately, the volume of the moon is 2.196 × 10^19 cubic meters.
For more questions like radius visit the link below:
https://brainly.com/question/499103
#SPJ11
Solve for x and choose the correct solution: x-3<=-2
The solution of the given inequality, x - 3 ≤ -2, is solved as the possible value of x which is determined as: x ≤ 1.
How to Find the Solution of an Inequality?Given the inequality x - 3 ≤ -2, to find the solution, wr would have to solve for x as explained below:
x - 3 ≤ -2 [given]
Add 3 to both sides:
x - 3 + 3 ≤ -2 + 3 [addition property of equality]
x ≤ 1
This means that the values of x are less than or equal to 1, which is from 1 below.
Thus, the solution to the inequality is solved by finding the possible value of x, which is x ≤ 1.
Learn more about inequality on:
https://brainly.com/question/24372553
#SPJ1
You should always measure your following distance in.
You should always measure your following distance in seconds. The correct answer for measuring following distance is A.
It is important to keep a safe distance between vehicles on the road, which is known as following distance. Measuring following distance in seconds is a more reliable method than measuring it in car lengths or feet.
The recommended following distance is typically two to three seconds. This means that when the vehicle in front of you passes a fixed point on the road, you should not reach that same point before two to three seconds have elapsed.
Measuring in seconds is more effective as it takes into account the speed at which both vehicles are traveling. If you measure in car lengths or feet, it may not be accurate as the length of the cars may differ, and it does not account for the speed of the vehicles. By measuring in seconds, you can maintain a safe distance and reduce the risk of accidents or collisions.
The correct answer for measuring following distance is A.
To learn more about distance click on,
https://brainly.com/question/29461744
#SPJ4
Complete question is:
You should always measure your following distance in __________
A. seconds. B. car lengths. C. feet.
Green Frog Convenience Store supplies two types of protein bars. One protein bar has 320 calories in the 2-ounce size. How many calories are in the 3-ounce size of the bar? *
The number of calories in the 3 ounce bar is 480.
To solve this problem, we can use a proportion. If the 2-ounce protein bar has 320 calories, then we can set up the following proportion:
2 oz / 320 cal = 3 oz / x cal
where x is the number of calories in the 3-ounce protein bar.
We can solve for x by cross-multiplying and simplifying:
2 oz * x cal = 3 oz * 320 cal
2x = 960x = 480
Therefore, the 3-ounce protein bar has 480 calories.
To learn more about calories, click here:
https://brainly.com/question/22374134
#SPJ11
In Angle STU, the measure of U=90°, the measure of S=31°, and TU = 77 feet. Find the
length of US to the nearest tenth of a foot
If in Angle STU, the measure of U=90°, the measure of S=31°, and TU = 77 feet, then the length of US to the nearest tenth of a foot is approximately 39.4 feet.
In angle STU, we have a right triangle with U=90°, S=31°, and TU=77 feet. To find the length of US, we can use the sine function:
sin(S) = opposite side (US) / hypotenuse (TU)
sin(31°) = US / 77 feet
To find the length of US, multiply both sides by 77 feet:
US = 77 feet * sin(31°)
US ≈ 39.4 feet
Therefore, the length of US to the nearest tenth of a foot is approximately 39.4 feet.
More on angles: https://brainly.com/question/14378034
#SPJ11
Daniel read 77 pages in \frac{2}{5}
of an hour. if he continues reading at the same rate, how many pages will he read in an hour?
Daniel will read approximately 193 pages in one hour if he continues reading at the same rate.
How many pages will Daniel read in an hour?Since Daniel read 77 pages in $\frac{2}{5}$ of an hour, we can set up the proportion:
$\frac{77}{\frac{2}{5}} = x$
where $x$ is the number of pages he would read in 1 hour.
To solve for $x$, we can simplify the left side of the equation by multiplying both the numerator and denominator by 5, which gives:
$\frac{77 \times 5}{2} = x$
Simplifying this expression gives:
$192.5 = x$
Therefore, if Daniel continues reading at the same rate, he will read 192.5 pages in one hour. However, since the number of pages must be a whole number, we can round this answer to the nearest whole number to get:
$x \approx 193$
So, Daniel will read approximately 193 pages in one hour if he continues reading at the same rate.
Learn more about Daniel's reading pages
brainly.com/question/31902709
#SPJ11
Ink pens and pencils are substitutes. If demand of pen falls,what happens to demand, supply, quantity
Pen demand decrease reduces pen price, quantity supplied; increases pencil demand, price, and quantity supplied as a substitute.
How do pen demand changes affect supply?If the demand for ink pens falls, this would likely result in a decrease in the demand for pens and an increase in the demand for pencils, since they are substitutes.
As a result, the price of pens would likely fall, as producers try to entice buyers to purchase pens over pencils. This decrease in the price of pens would, in turn, lead to a decrease in the quantity supplied of pens, as producers shift their focus to producing other goods that are more in demand.
However, the quantity demanded of pencils would increase, leading to an increase in the price of pencils and an increase in the quantity supplied of pencils. Ultimately, the market for ink pens and pencils would adjust to reflect the changes in demand, resulting in changes in both price and quantity.
Learn more about demand
brainly.com/question/29703449
#SPJ11
What is the value of 1/4 (-4^3+10^2)
Answer:
The value of 1/4 (-4^3+10^2) is 9