The solution of the inequality that determines how far Dev can travel over the weekend is -
x ≤ 400 miles.
What is a expression? What is a mathematical equation? What is Equation Modelling?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have Dave who is planning a car trip for weekend.
Assume that [x] represents the number of miles Dev can travel.
We can write the inequality as -
18 - 0.04x ≤ 2
0.04x ≤ 16
x ≤ 400 miles
Therefore, the solution of the inequality that determines how far Dev can travel over the weekend is -
x ≤ 400 miles.
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Estimate the answer to 4.8 x 47.1
Answer:
235
Step-by-step explanation:
When estimating the product of two decimals, first round the decimals to their nearest whole numbers.
If the number in the tenth place is less than 5, round down to the nearest whole number.If the number in the tenth place is 5 or more, round up to the nearest whole number.Therefore,
4.8 ≈ 547.1 ≈ 47So an estimate of the product of the two decimals is:
[tex]\implies 4.8 \times 47.1 \approx 5 \times 47[/tex]
Partition 47 into tens and units:
[tex]\implies 5 \times 47 = 5 \times (40 + 7)[/tex]
Apply the distributive property of multiplication over addition:
[tex]\begin{aligned}\implies 5 \times (40 + 7) &= (5 \times 40) + (5 \times 7)\\&=200+35\\&=235\end{aligned}[/tex]
Therefore:
[tex]\boxed{4.8 \times 47.1 \approx 235}[/tex]
HELP ME PLEASEEEEEEE
Answer:
[tex]{ \boxed{ \tt{ \sin( \theta) = \frac{opposite}{hypotenuse} }}}[/tex]
- \theta = 25°
- opposite = x
- hypotenuse = z
[tex]{ \tt{ \sin(25 \degree) = \frac{x}{z} }} \\ [/tex]
Answer: x/z
Step-by-step explanation:
sin25 uses soh from sohcahtoa
sin25 = opposite/hypotenuse = x/z
HELP the price of gasoline purchased varies directly with the number of gallons purchased if 10 gallons of gasoline are purchased for$23 what will be the price of 50 gallons be?
Answer:
Step-by-step explanation:
It will be 115$
Answer: the answer is $21.7391304348 or round to $21.74 is the cost for 50 gallons
Step-by-step explanation: I did the calculations and it costs $2.30 a gallon
two foods contain proteins, carbohydrates, and fats. food a costs $1 per pound and contains 30% protein, 10% fat, and 50% carbohydrates. food b costs $1.50 per pound and contains 20% protein, 4% fat, and 75% carbohydrates. what is a combination of x pounds of food a and y pounds of food b that provides at least 1 1 2 pounds of protein, 3 3 4 pounds of carbohydrates, and 1 5 pound of fat at the lowest cost? (x, y)
A combination of x pounds of food a and y pounds of food b that provides at least 1 1 2 pounds of protein, 3 3 4 pounds of carbohydrates, and 1 5 pound of fat lowest cost is at (x,y) is (3,2).
Define function.A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Given,
Function:
C = x + 1.5y
Subjected to:
30x + 20y ≥ 13/10 ×100 ≥ 130
10x + 4y ≥ 1/5 × 100 ≥ 20
50x + 75y ≥ 3 × 100 ≥ 300
Feasible region:
(0, 13/2), (3,2) (6,0)
C = x + 1.5y
(0, 13/2) ⇒ C = 0+ (1.5)(13/2)
(0.13/2) ⇒ C = 9.75
(3,2) ⇒ C = 3+ (1.5)(2)
(3,2) ⇒ C = 6
(6,0) ⇒ C = 6 + 0
(6,0)⇒ C = 6
A combination of x pounds of food a and y pounds of food b that provides at least 1 1 2 pounds of protein, 3 3 4 pounds of carbohydrates, and 1 5 pound of fat lowest cost is at (x,y) is (3,2).
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c) Which of these
numbers is a square number?
A: 4x10^5
B:9x10^4
C:4x10^3
D:9x10^3
Having trouble solving this
Answer:
[tex]r = 2279.41[/tex]
bob can do a job in 5 hours while bill can do the same job in 8 hours. how many hours would it take them, working together, to do this job?
Hours taken by Bob and Bill if they work together is 3 1/13.
Here it is given that Bob can do a job in 5 hours and Bill can do the job in 8 hours.
We have to find the time taken by both to do the work if done together.
Time ratio of Bob and Bill = 5: 8
Efficiency of Bob and Bill = 8: 5
Total amount of work done = 5× 8 = 8× 5 = 40
The total efficiency of Bob and Bill = 13
Hours took by both bob and bill to do the work if done together = 40/13
= 3 [tex]\frac{1}{13}[/tex]
Therefore the work done together is 3 [tex]\frac{1}{13}[/tex] hours.
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: the small town of west fremont has a population of 50,000. if the growth rate of west fremont is 2%, then how long will it take for the population of west fremont to double?
It takes 35 years for the population of West Fremont to double. We have the following condition;
West Fremont is a tiny town with 50,000 residents. If West Fremont experiences 2% growth. To solve the given case to get how long it takes for the population of West Fremont to double.
Here, we use the rule of 70 case. The rule of 70: By dividing the number 70 by the growth rate of the variable, the rule of 70 may be used to calculate how many years it will take for a variable to double.
According to the yearly rate of return, the rule of 70 is typically used to calculate how long it would take for an investment to double.
Doubling time = 70 / Growth rate
= 70 / 2
= 35 years
So, it takes 35 years for the population of West Fremont to double.
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Can anyone write the equation of the graph?
help meeeeeeeeeee pleaseeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
The dive lasted approximately [tex] \boxed{\sf 2.76} [/tex] seconds.
Step-by-step explanation:
Given formula: h = 16t²
Where, t is time in seconds and h is the distance in feet traveled by a free-falling body or object.
According to the question,
Height of the cliff from which diver dives (h) = 122 feet.
By substituting the value of height in the formula we get:
[tex]\rm \implies 122 = 16 {t}^{2} \\ \\ \rm \implies {t}^{2} = \dfrac{122}{16} \\ \\\rm \implies {t}^{2} = 7.625 \\ \\ \rm \implies t = \sqrt{7.625} \\ \\ \rm \implies t = 2.76 \: seconds[/tex]
Angles ABC and CBD are a linear pair. If m∠CBD=90°, what is m∠ABC in degrees?
NO LINKS OR FILES.
Measurement of ∠ ABC is 90°
What is Linear pair?A linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.
Given that ∠ CBD and ∠ ABC are linear pairs,
Therefore, m∠ CBD + m∠ ABC = 180°
m∠ ABC = 180° - 90° = 90°
Hence, Measurement of ∠ ABC is 90°
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1. in an experiment in which a six-sided dice is rolled twice, what is the probability that 4-dots side appears in at least one roll?
Answer:
11/36 = 0,305556 = 30,5556%
Step-by-step explanation:
5/6 * 5/6 = 25/36
36/36 - 25/36 = 11/36
Find the value of x. Then find the measure of each angle and write the answers in ascending order.
The measured interior angles of the triangle are 40°, 60°, and 80° in ascending order.
What is a Triangle?Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.
The triangle has interior angles are:
(2x)°, (3x)° and (4x)°
As we know that the sum of interior angles is 180 degrees in the triangle.
According to the given figure,
(2x)° + (3x)° + (4x)° = 180°
Apply the addition operation in the above equation,
9x = 180
x = 180/9
x = 20°
Thus, The triangle has interior angles are:
(2x)° = 2 × 20° = 40°
(3x)° = 3 × 20° = 60°
(4x)° = 4 × 20° = 80°
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Decrease 330 km by 54%.
Answer: 151.8
Step-by-step explanation:
330/100 x 54 = 178.2
330- 178.2 = 151.8
Can anyone write the equation of the graph?
The equation of the absolute value function graph is: y = |x - 3| + 5.
What is the Equation of the Absolute Value Function?The equation of the absolute value function can be written in the vertex form as y = a|x – h| + k, where:
The vertex of the graph = (h, k)The value of a is determined by whether the graph opens up or opens down.The horizontal translation factor, which determines how far left or right the parent function is translated = hThe vertical translation factor, which determines how far up or down the parent function is translated = k.From the given graph, we have the following:
(h, k) = (3, 5) [the vertex]
Substitute the values into the equation, y = a|x – h| + k:
y = a|x - 3| + 5
A point on the graph is (2, 6). To find the value of a, substitute (x, y) = (2, 6) into y = a|x - 3| + 5:
6 = a|2 - 3| + 5
6 = a|-1| + 5
6 = a + 5
6 - 5 = a
1 = a
a = 1
To write the equation of the graph, substitute a = 1 into y = a|x - 3| + 5:
y = 1|x - 3| + 5
y = |x - 3| + 5
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Please help with this
Step-by-step explanation:
remember, the circumference of a circle is
2×pi×r
and that is for the full 360° of a circle.
how long will the arc length of 1° be ?
well,
2×pi×r / 360
and how long will the arc length of 78° be ?
well,
78 × 1° = 2×pi×r × 78/360
you see ? that is the whole trick ...
now we only need to enter the value for r (radius).
and that is GH = 9 units.
so, the length of the arc GJ is
2×pi×9 × 78/360 = 2×pi × 78/40 = pi × 78/20 =
= 12.25221135... ≈ 12.25 units
The ordered pairs show the number of hours a student studied in a week, x, and that student’s exam score, y.
(1,70) (3,75) (5,80) (9,95) (12,98)
The equation y=2.7x+67 can be used to model the relationship between the number of hours a student studied in a week and their exam scores. Choose a number from each box to make the statement true.
The y-intercept shows that a student who studies____________
A: 0
B: 2.7
C: 67
D: 69.7
hours can expect to get a score of _______on the exam.
A: 0
B: 2.7
C: 67
D: 69.7
Answers:
1st box: 0
2nd box: 67
===============================================
Explanation:
The y intercept always occurs when x = 0. This is when the function curve either crosses or touches the vertical y axis. Therefore, the y intercept is when the student studies 0 hours
Plug x = 0 into the equation
y = 2.7x + 67
y = 2.7*0 + 67
y = 67
Or you can note that the equation is of the form y = mx+b
m = slope = 2.7b = 67 = y interceptThe y-intercept of 67 tells us that the person studying for 0 hours is estimated to get a score of 67
For this problem, write the numbers in scientific notation. 2,156 A. 21.56 × 102 B. 2.156 × 103 C. 2.156 × 102
Answer:
2,156 A. 21.56
Step-by-step explanation:
Suppose we want to choose 4 letters, without replacement, from 17 distinct letters. How many ways can this be done, if the order of the choices is not taken into consideration
Thus, the number of ways in which to choose 4 letters, without replacement, from 17 distinct letters is 57,120.
Define the term permutation?The term permutation applies to a mathematical computation of a number of possible arrangements of a given collection. Simply said, a permutation is a term that defines the amount of different ways something can be organized or arranged.Total distinct letters are 17.
There are 17 alternatives for the initial letter if there are 17 letters.
There are just 16 alternatives left once you remove the letter.
Each time you remove a letter, the bag contains one fewer letter.
Number of ways = 17 x 16 x 15 x 14
Number of ways = 57,120
Thus, if the sequence of the alternatives is irrelevant, there are 57,120 options.
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The fastest cheetah on record is Sarah who lives at the Cincinnati Zoo in Ohio. The fastest human on record is Usain Bolt. Sarah can
run 161 meters in the same time that Usain can run 100 meters. If Sarah's speed is 6.4 meters per second faster than Usain's, how
fast do Sarah and Usain run? Round values to one decimal place.
sarah’s speed:
usains speed:
Sarah can run = 100 metres.
Speed of usain bolt.It takes several steps to convert between the two rates of meters per second and miles per hour in this task.Since the units in this case are measured in meters per second, we do not know what this translates to in miles per hour. Since the speedometers in our cars utilize these numbers, the majority of us are accustomed to thinking of speeds in terms of miles per hour; therefore, it is advantageous for students to be able to convert between miles per hour and other units of speed that naturally arise.The first approach displays all units used in the calculations but waits until the very end to perform any calculations. The second option takes a step-by-step approach and offers anacc to our question=
Usain Bolt traveled 100 meters in 9.63 seconds. 1 meter is 3.28 feet, so 100 meters is.Usain Bolt traveled 1 foot in 0.02936 seconds. 1 mile is 5280 feet, so at this speed, he would travel 1 mile in 5280×0.02936=155 seconds.learn more about speed,distance,time click here:
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F(x)=x^2+1 what is f(f(x))?
Answer:
f(f(x)) = [tex]x^{4}[/tex] + 2x² + 2
Step-by-step explanation:
to evaluate f(f(x)), substitute x = f(x) into f(x)
f(f(x))
= f(x² + 1)
= (x² + 1)² + 1 ← expand factor using FOIL
= [tex]x^{4}[/tex] + 2x² + 1 + 1
= [tex]x^{4}[/tex] + 2x² + 2
Answer:
[tex]f[f(x)]=x^4+2x^2+2[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=x^2+1[/tex]
To find the composite function f[f(x)], substitute the function f(x) in place of the x in function f(x):
[tex]\begin{aligned}\implies f[f(x)]&=f(x^2+1)\\&=(x^2+1)^2+1\\&=(x^2+1)(x^2+1)+1\\&=x^4+x^2+x^2+1+1\\&=x^4+2x^2+2\end{aligned}[/tex]
simplify 1/x^-5 HELP ME PLEASE FIRST ANSWER GETS BRAINLIEST
Answer:
x^5
Step-by-step explanation:
cheyenne needs to cut a piece of paper so that she has exactly 1/3 of it. if the length of the paper is 11 inches, how long will be the piece that she cuts?
The lengths of the piece she should cut is = 3 2/3
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
1/3 of 11=1/3*11=11/3=3 2/3hence,The lengths of the piece she should cut is = 3 2/3
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Order from least to greatest 3.706, 3.76, 2.5991, 3.7
Answer:
2.5991 < 3.7 < 3.706 < 3.76
Step-by-step explanation:
At a party, 60 drank malt, 48 drank beer, 36 drank cocacola, 20 drank both beer and cocacola, 18 drank both cocacola and malt, 15 drank malt and beer and 12 drank all the three. If there are 100 in the party, is the data consistent?
Answer:
no because 60+48+36 is 144
Step-by-step explanation:
please mark brainliest
The total number of people is 144. The data is not consistent.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that at a party, 60 drank malt, 48 drank beer, 36 drank cocacola, 20 drank both beer and cocacola, 18 drank both cocacola and malt, 15 drank malt and beer and 12 drank all the three.
The total number of the people in the party,
60+48+36 is 144
But it is given in the question that there are 100 in the party.
Therefore, the total number of people is 144. The data is not consistent.
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p x 3,700=4,070
There was a % percent increase in the number of visitors.
There was 110% percent increase in the number of visitors.
Percent:
Basically, percentage refers the number or ratio that can be expressed as a fraction of 100.
Given,
p x 3,700=4,070
There was a % percent increase in the number of visitors.
Here we need to find the increase in the percentage.
While we looking into the given question we have identified that,
The Old population = 3700
And the new population = 4070
So, the value of P is calculated as,
=> p = 4070/3700
=> p = 1.1
When we convert this into percent then we get 110% as increase.
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A pediatrician prescribes 5 milliliters (ml) of a pain reliever for every 25 pounds of a child's weight. How many milliliters of
medicine will the doctor prescribe for a child who weighs 60 pounds?
If the child's weight is 60 pounds , then the doctor will prescribe 12 milliliter of medicine .
In the question, '
it is given that
the for every 25 pounds of weight 5 milliliter of pain reliever is required .
we need to find the amount of medicine for the child weighing 60 pounds
So , for 25 pounds = 5 milliliter is needed
for 1 pound = 5/25 ml is needed
hence for 60 pound = 60*(5/25) ml will be prescribed .
on simplifying further ,
we get
= 60*(5/25)
= 60*(1/5)
= 12 ml
Therefore , the doctor will prescribe 12 ml of medicines .
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Write an equation in slope-intercept form of the line that passes through $\left(-5,\ 19\right)$ and $\left(5,\ 13\right)$ .
Answer:
hmmm say 5)13
Step-by-step explanation:
i can't explain it
The equation of the line is y = (-3/5)x + 16
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The equation of a line is given by:
y = mx + c
The line passes through:
(-5, 19) and (5, 13)
So,
m = (13 - 19) / (5 + 5)
m = -6/10
m = -3/5
Now,
(5, 13) = (x, y)
13 = (-3/5) x 5 + c
13= -3 + c
13 + 3 = c
c = 16
Now,
y = mx + c
y = (-3/5)x + 16
Thus,
The equation of the line is y = (-3/5)x + 16
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how many cubes are added
The number of centimeter cubes to be added to make the cuboid is; 30 cubes.
How to Interpret the elevation of objects?From the given plan, side elevation and front elevation, we can see that the number of cubes needed to make the shape is 18 blocks.
From the front elevation, 12 blocks is required (4 * 3 blocks).
From the side elevation, 6 blocks are required which gives us a total of 18 blocks.
The number of blocks needed to make the given cuboid is;
Volume of cuboid = 4 * 4 * 3 = 48 cm cubes.
Therefore the number of cubes to be added = Volume cubes - Number of cubes from elevation
The number of cubes to be added = 48 cubes - 18 cubes
The number of cubes to be added = 30 cubes.
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Line ℓ has equation y=
–
x+5. Find the distance between ℓ and the point G(6,4).
Answer:
2.5√2 units
Step-by-step explanation:
The shortest distance between a point and a line is the length of the line segment perpendicular to the line and passes through the given point.
~~~~~~~~~~~~~~~~~~~~~
y = - x + 5 , slope m = - 1
Slope of perpendicular line is opposite reciprocal. In our case is 1 .
G ( 6 , 4 )
y - 4 = 1 × ( x - 6 )
y = x - 2
x - 2 = - x + 5 , x = 3.5
y = 1.5
Perpendicular line intersect the given line at the point O ( 3.5 , 1.5 )
OG = [tex]\sqrt{(6-3.5)^2 +(4-1.5)^2 }[/tex] = 2.5√2 units