The value of the expression 3(4) can be expressed as 12 with the help of a title diagram or a number line and the explanation for this same can be done easily if we take into consideration a number line.
What does the math number line mean?A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics. It can also be assumed that every point present on a number line corresponds to a real number, and that every real number also corresponds to a point.
To solve this expression, we can deduce as follows:
As per the number line, for the expression 3(4).
Since it is absolutely positive, thus we will get the final answer in positive that means on the side of the number line lying right to zero.
To express this expression,
3 (4) means we have to move towards the right side of the number line from zero for 4 times and each time covering a total of 3 units each.
Thus, we start from zero, first time we reach 3 then 6, then 9 and then finally 12.
Thus, the value of the expression is received as 12.
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8. A baseball is thrown from a height of 40 feet and goes up at a rate of 2.5 feet per second. A football is
thrown from a height of 25 feet and goes up at a rate of 3 feet per second. After how many seconds
would the two reach the same height?
The time taken depends upon velocity and distance so the time taken by both balls to reach the same height will be 30 seconds.
What is velocity?Velocity is the rate of distance covered per time. Velocity could be average or instantaneous.
Units of velocity are given by ⇒ meter/second
For example, if a car drives 50 meters for 10 seconds and it is constant then 50/10 = 5 meters/second will be the velocity.
Difference between their initial height = 40 - 25 = 15 feet
It means if baseball cover x feet distance then football will cover x + 15 feet.
Now,
Time = distance covered / velocity
Since the time will be the same for both balls to meet them.
So,
Distance covered by baseball/velocity of baseball = Distance covered by football/ velocity of football
x/2.5 = (x + 15)/3
3x = 2.5x + 37.5
0.5x = 37.5
x = 75
So,
Time taken = 75/2.5 = 30 seconds.
Hence "After 30 seconds both balls will go to reach the same height".
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Two numbers have a sum of 195 and a difference of 45. What are the two numbers
Which is greater 8.391 or 8.371
Answer:
8.391
STEPS:1. Compare the first digit. If they are the same, move on to the next digit. In this case, we have to look at the hundredths place.
2. Check to see which number is bigger. We are looking at 9 and 7. 9 is the bigger number. this means that 8.391 is bigger.
What is the product of −17 • −5 • −12?
Answer:
-1020
Step-by-step explanation:
-17 x - 5 x - 12 =
- 17 x 60 =
- 1020
Samuel's family took a road trip to Mount Rushmore. Samuel fell asleep after they
had travelled 990 miles. If the total length of the trip was 1000 miles, what
percentage of the total trip had they travelled when Samuel fell asleep?
Answer:
99%
Step-by-step explanation:
Gasoline costs $3.79 per gallon.
Write an inequality that can be used to determine how many gallons of fuel can be
purchased for under $20. Clearly indicate what the variable represents.
Solve the inequality in part a, and write your answer in a complete sentence
fraction numerator 6 y plus 2 x over denominator 5 end fraction equals 18
The given statement fraction numerator 6 y plus 2 x over denominator 5 end fraction in numerical form 18 is 6y + 2x = 90.
What is a linear equation in two variable?A linear equation in two variables has the highest degree of 1 and contains two variables generally in x and y.
Given in numerator we have 6y + 2 and in the denominator, we have 5 and this fraction equals to 18, This can be numerically represented as
(6y + 2x)/5 = 18.
6y + 2x = 90.
This is a linear equation in two variables x and y and for every value of x we get a corresponding value of y or vice-versa and all (x,y) ∈ R.
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10.The table below shows the recorded temperature on a certain day starting at 6:00 a.m. time 6:00 6:45 7:30 8:30 9:00 9:45 10:30 11:00 temp 65° 67° 68° 72° 74° 75° 77° 80°
a) Find the regression equation.
b) Predict the temperature at 2:00 p.m.
From the temperatures given, we have that:
a) The regression equation is: y = 2.91x + 64.61.
b) The predicted temperature at 2 pm is of 88 ºF.
How to find the equation of linear regression?To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.
In the context of this problem, the input and the output are given as follows:
Input x: number of hours after 6 A.M.Output y: temperature.We have that an hour is 60 minutes, hence:
45 minutes = 0.75 hours.30 minutes = 0.5 hours.Thus the points are given as follows:
(0, 65), (0.75, 67), (1.5, 68), (2.5, 72), (3, 74), (3.75, 75), (4.5, 77), (5,80).
Inserting these points into the calculator, the equation is:
y = 2.91x + 64.61.
2 pm is 8 hours after 6 am, hence x = 8 and the predicted temperature, in ºF, is given by:
y = 2.91(8) + 64.61 = 88 ºF.
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If the parent function f(x) = |x| is transformed to g(x) = |x + 5|, what transformation occurs from f(x) to g(x)?
Function g (x) horizontal shift left with 5 units.
What is Transformation?
The act or process of changing completely is called transformation.
Given that;
The parent function is;
f (x) = |x|
and , After transformed the function is g(x) = |x + 5|
Now, Compare the function to the parent function we get;
The transformation occur from f (x) = |x| to g (x) = |x + 5|.
Function g (x) = |x + 5| horizontal shift left with 5 units.
So, Function g (x) horizontal shift left with 5 units.
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Write down all the whole numbers that are between 25 and 50 and have a difference of 4 between their digits. please and thanks
these are the only ones i can find
26 37 40 48
The maximum weight an apartment elevator can hold is 1615 pounds weighs 240 pounds and he needs to carry boxes that weigh pounds each Use the equation 55b 240 1615 to find the greatest number of boxes Bill can carry in the elevator in one trip
Answer: Bill weighs 230 pounds and he needs to carry boxes that weigh 75 pounds each. Use the equation 75b+230< =1805 to find the greatest number of boxes Bill can carry in the elevator in one trip.
Step-by-step explanation:
Solve for the value of r.
(9r+2)°
70°
90°
Answer:
If they all had to equal 360 when put together then the answer would be 22. If they All had to equal 180 when put together, then the answer would be 2.
Step-by-step explanation:
The directions are not quite clear but I have two answers just in case.
if a polynomial is prime, then it cannot be factored. 5x + 13y is prime.
5x + 13y is prime , it cannot be factored.
A polynomial with integer coefficients that cannot be factored into polynomials of lower degree , also with integer coefficients, is called an irreducible or prime polynomial .
Some trinomials cannot be factored. If none of the pairs total b, then the trinomial cannot be factored.
Given equation is 5x + 13y
If a polynomial is prime, then it cannot be factored. 5x + 13y is prime.
In this regard,
The law of detachment states that
1) If p happens, then q happens;
2) p is true;
Then, a there is a third statement that is
3) q is also true.
In this question,
If a polynomial is prime, then it cannot be factored.
The statements in the question can be represented as:
(1) If 5x + 3y is a polynomial and is prime then it cannot be factored
(2) It cannot be factored
Using the above representations of p and q, as an illustration; the third statement would be:
(3) 5x + 3y is a polynomial and is prime then we can conclude that
5x + 13y cannot be factored.
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During one year, the Larsons' real estate bill included $401 for local schools. Of this amount, $145 went to the high
school district. What percent did the Larsons pay to the high school district?
According to the solving the percent Larsons pay to the high school district 63.8%.
Describe percentage:A % is a relative figure that represents one-tenth of a quantity. One percent (symbolized 1%) is the hundredth part; consequently, 100 percent denotes the complete amount and 200 percent specifies twice the supplied number.
How do you write percentages?In scientific and engineering writing, use the symbol% to denote percent, except when expressing numerals at the beginning of a phrase. When writing the word, use the form percent as opposed to the archaic version percent. During the test period, just 3% of the systems crashed.
According to the given data:Bill included $401 for local schools
$145 went to the high school district
Amount Remaining = $ 401 - $145
= $ 256
Percent Larson's pay to the high school district is:
256/401
.638 x 100
= 63.8%
According to the solving the Larsons pay to the high school district 63.8%.
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The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 51 minutes of calls is $17.24 and the monthly cost for 95 minutes is $22.52. What is the monthly cost for 68 minutes of calls?
With respect to the linear function, the monthly cost for 68 minutes of calls is $19.28 if 51 minutes and 95 minutes cost $17.24 and $22.52 respectively.
What is the slope of the cost function?The slope of the cost function which is the same as the variable charge per minute of call is determined by:
(the total costs of the highest activity - the total cost at the lowest activity) /the difference between the number of call minutes slope (cost per minute)
= ($22.52-$17.24)/(95-51)
Slope (cost per minute) =$0.12y
=a+bxy
=total cost
=$22.52
Note that:
a = fixed charge = unknown
b = slope = $0.12x = number of minutes = 9522.52
= a+(0.12*95)22.52
= a+11.40a =22.52-11.40a
=11.12y
= 11.12+0.12x
when x = 68y
= 11.12+(0.12*68)y
= total cost for 68n minutes
=$19.28
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The monthly cost for 68 minutes of calls is $19.28
What is the equation of straight-line?
The equation of straight-line considers the fixed charge of using phone plan per month plus the total variable cost of minutes of call, I mean the cost per minute of the plan can be determined by computing the slope of the straight-line equation
slope=(total cost for 95 minutes-total cost of 51 minutes)/(95-51)
total cost for 95 minutes=$22.52
total cost of 51 minutes=$17.24
slope=($22.52-$17.24)/(95-51)
slope= variable cost per minute=$0.12
We can determine the fixed charge per month using the straight-line equation and cost for 95 minutes
y=a+bx
y=total cost=$22.52
a=fixed charge per month=unknown
b=cost per minute=$0.12
x=number of minutes=95
$22.52=a+($0,12*95)
$22.52=a+$11.40
a=$22.52-$11.40
a=$11.12
total cost(68 minutes)=a+bx
a=$11.12
b=$0.12
x=68
total cost=$11.12+($0.12*68)
total cost=$19.28
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100POINTS100POINTS100POINTS100POINTS
The data set shows the fuel efficiencies, in miles per gallon, of the vehicles featured in a car-buying guide.
27 30 41 27 20 22 36 37 44 45 29 29
(a) What is the five-number summary of the data set? Show your work.
(b) What is the range of the data set? Show your work.
(c) What is the interquartile range (IQR) of the data set? Show your work
The five number summary are as follows:
minimum = 20maximum = 45Q₂(median) = 29.5Q₁(first quartile) = 27Q₃(third quartile) = 39The range of the data sets is 25.
The interquartile range of the sets is 12.
How to find five number summary?The five number summary describes where data values occur, their central tendency, variability, and the general shape of their distribution.
The five number summary includes minimum number, maximum number, median(Q₂), first quartile(Q₁) and third quartile(Q₃).
Therefore, the five number summary are as follows:
27, 30, 41, 27, 20, 22, 36, 37, 44, 45, 29, 29
Arrange the data in ascending order.
20, 22, 27, 27, 29, 29, 30, 36, 37, 41, 44, 45
There are as follows;
minimum = 20maximum = 45Q₂(median) = 29 + 30 / 2 = 29.5Q₁(first quartile) = 27 + 27 / 2 = 27Q₃(third quartile) = 37 + 41 / 2 = 39Therefore,
Range of the data sets = 45 - 20 = 25
Interquartile range (IQR) = Q₃ - Q₁ = 39 - 27 = 12
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Lisa works as a tutor at Springfield high school. She can work up to 20 hours a week and gets paid $15 dollars an hour. Find a reasonable domain and range for Lisa’s possible weekly earnings.
What is the number in scientific notation? 0.000000000093
Check the picture below.
Write the expanded form of the expression.
y(0.5 + 5)
Answer:5.05y
Step-by-step explanation:
Therefore, the expanded form of the expression y (0.5 + 8) is 0.5y + 8y
Using this example we can find out that 0.5y+5 y=5.05 y thats the answer
please kindly give me brainiest thank you
Find the center of dilation.
• Triangle B is a dilation of A with approximately what scale factor?
• Triangle A is a dilation of B with approximately what scale factor?
• Triangle B is a dilation of C with approximately what scale factor?
Answer:
Triangle B is a dilation of A with approximately what scale factor
Triangle B is a dilation of A with approximately a scale factor of 8.
Triangle A is a dilation of B with approximately a scale factor of 1/8.
Triangle B is a dilation of C with approximately a scale factor of 3/4.
We have,
In mathematics, dilation refers to the transformation of a shape, object, or figure by uniformly scaling it up or down.
When the constant factor is greater than 1, the dilation results in an enlargement of the shape, making it larger.
Conversely, when the constant factor is between 0 and 1, the dilation leads to a reduction of the shape, making it smaller.
Now,
Triangle B is a dilation of A with approximately by a scale factor of:
Since triangle B is greater than A.
The scale factor is greater than 1.
Triangle B looks 8 times of triangle A.
So,
The scale factor is 8.
And,
Triangle A is a dilation of B with approximately by a scale factor of:
Since triangle B is smaller than A.
The scale factor is less than 1.
Triangle A looks like 12.5 % of triangle C.
12.5% = 1/8
So,
The scale factor is 1/8.
Triangle B is a dilation of C with approximately by a scale factor of:
Since triangle B is smaller than A.
The scale factor is less than 1.
Let's say,
Triangle B looks 75% of triangle C.
So,
The scale factor is 3/4.
Thus,
Triangle B is a dilation of A with approximately a scale factor of 8.
Triangle A is a dilation of B with approximately a scale factor of 1/8.
Triangle B is a dilation of C with approximately a scale factor of 3/4.
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By eating 1 egg, 1 cupcake, and 1 slice of pizza, a child consumes 303 mg of cholesterol. If the child eats 3 cupcakes and 4 slices of pizza, he or she takes in 89 mg of cholesterol. By eating 2 eggs and 1 cupcake, a child consumes 571 mg of cholesterol. How much cholesterol is in each item?
If by eating 2 eggs and 1 cupcake, a child consumes 571 mg of cholesterol. The amount of cholesterol that is in each item are; 19 mg, 276mg, 8 mg.
Amount of cholesterolE + C + P = 303
Where:
Egg=E
Cupcake=C
Pizza=P
Hence,
3C + 4P =89
4P = 89-3C
P = (89-3C)/4
2E + C = 571
2E = 571-C
E = (571-C)/2
(571-C)/2 + C + (89-3C)/4 = 303
(571-C)2 + 4C + 89-3C = 303×4
(571-C)2 + 4C + 89-3C = 1212
1142 -2C + 4C + 89-3C = 1212
-C = 1212-89-1142
C =19mg (1 cupcake)
E = (571-C)/2
E= (571-19)/2
E=552/2
E= 276mg (1 egg)
P = (89-3C)/4
P = (89-3(19))/4
P = (89-57)/4
P=32/4
P=8 mg (1 pizza)
So,
Egg=E=19 mg
Cupcake=C=276 mg
Pizza=P=8 mg
Check:
19+276 + 8 = 303 mg
Therefore If by eating 2 eggs and 1 cupcake, a child consumes 571 mg of cholesterol. The amount of cholesterol that is in each item are; 19 mg, 276mg, 8 mg.
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1
A 13 km stretch of road needs repairs. Workers can repair 3 km of road per week.
1312/321
How many weeks will it take to repair this stretch of road?
weeks
The average time taken by workers to complete the repairing of the road is about the 4 and half weeks.
According to the statement
We have to find that the Time taken by the workers.
So, For this purpose, we know that the
Average time is a measurement that evaluates how long a works spends on repairing roads.
From the given information:
A 13 km stretch of road needs repairs. Workers can repair 3 km of road per week.
Then
If worker complete 3 km of the road in the 7 days
Then
Workers complete 13 km in the days = Total distance / Average distance
Then
Workers complete 13 km in the days = 13 / 3
Workers complete 13 km in the days = 4.33 weeks.
So, The average time taken by workers to complete the repairing of the road is about the 4 and half weeks.
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five sandwich rings are each cut into 4 pieces. you then cut each of the pieces into 3 servings . how many servings do you have.
The total number of servings is equal to the product of 5, 4 and 3. Thus, the required number of servings is 60.
A product is something that has undergone one or more multiplications. For instance, the mathematical formula "times equals" would be written with the terms "times," "multiplicand," and "product," respectively.
A number can be multiplied by another number to determine each of its products. For instance, 9 x 3 equals 27, so 27 is a product of 9 and 3. Each number has an infinite number of possible products because it can be multiplied by an infinite number of different numbers to produce an infinite number of results. When considering how to find the product of a number, there are some simple facts to understand. For instance, any whole number multiplied by two will always result in an even number.
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The owner of a ski resort estimates that a new 4-person ski lift will cost $5,000,000. The owner begins making payments on March 1 and every three months thereafter for 5 years into an account that earns 4% annual interest compounded quarterly. What payment amount must the owner make to have the cost of the ski lift in 5 years? Round your answer to the nearest cent.
The quarterly payment that the ski resort owner must make in 5 years to have the cost of the ski lift is $277,076.57.
How is the quarterly payment determined?The quarterly payment can be computed by determining the ski lift's total cost (future value).
Dividing the future cost or value by the number of periods (quarters) results in quarterly payments.
Data and Calculations:N (# of periods) = 20 quarters (5 x 4)
I/Y (Interest per year) = 4%
PV (Present Value) = $5,000,000
FV (Future Value) = $0
Results:
PMT = $277,076.57
Sum of all periodic payments = $5,541,531.49
Total Interest = $541,531.49
Thus, the quarterly payment that the ski resort owner must make in 5 years to have the cost of the ski lift is $277,076.57.
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2x−3y=−5 4x−4y=−4 Is (2,3)(2,3)left parenthesis, 2, comma, 3, right parenthesis a solution of the system?
(2,3) is a solution to the system of equations.
A collection of one or more linear equations containing the same variables is known as a system of linear equations (or linear system).
Consider the system of equations,
2x - 3y = - 5 --------(1)
4x - 4y = - 4 --------(2)
Multiplying equation (1) with 2.
4x - 6y = - 10
4x - 4y = - 4
Now, subtracting the above equations:
4x - 6y - ( 4x - 4y) = - 10 + 4
4x - 6y - 4x + 4y = - 6
- 2y = - 6
2y = 6
y = 3
Then,
4x - 4y = - 4
4x - 4 × 3 = - 4
4x - 12 = - 4
Adding 12 on both sides of the equation,
4x - 12 + 12 = - 4 + 12
4x = 8
x = ( 8/4 )
x = 2
Therefore, (x, y) = ( 2, 3) is a solution to the system of equations.
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Answer:
Yes
Step-by-step explanation:
7.You measure the diameter of a circular watch face
to be 3.2 centimeters. Estimate the area of the
watch face.
The estimated area of the circular watch face is: 8 cm².
How to Find the Area of a Circular Shape?The formula to use in determining or estimating the area of any shape that is circular is expressed as:
Area = πr², where the radius of the circular shape is represented as r.
Given the following:
Diameter of the circular watch face = 3.2 centimeters
The radius = 1/2(diameter) = 1/2(3.2)
Radius (r) = 1.6 centimeters
Plug in the value into πr² to find the estimated area of the watch face:
Area of the watch face = π(1.6²)
Area of the watch face ≈ 8 cm²
Therefore, the estimated area of the circular watch face is: 8 cm².
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i need help pleaseeeeee
A coefficient in the algebraic expression is: 5
The constant is: 12
A variable is: x
A term in the algebraic expression can be: 5x or 12.
What are the Parts of an Algebraic Expression?An algebraic expression consist of terms, which can be:
A variable in form of alphabetsA variable multiplied by a coefficientA constant, which is just a number.Thus, given the algebraic expression, 5x + 12, the following parts of the algebraic expression can be identified as shown below:
A coefficient in the algebraic expression is: 5 (tis is the number multiplied by the variable x)
The constant is: 12 (this is the number standing alone)
A variable is: x (this is the alphabet in the algebraic expression)
A term in the algebraic expression can be: 5x or 12.
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Suppose you go shopping for a new futon bed for your room. The model you really like happens to be on sale for $525. It's original price is $700. What percent of the original price will you save if you purchase it?
Round your percentage to one decimal place.
Do not include
%
sign with your answer.
25 percent of the original price was saved during the purchase of the futon bed
The percent of the original price that is saved can be calculated as follows
The original price is $700
The new price is $525
The first step is to calculate the percentage change
= 700-525
= 175
Therefore the percent saved can be calculated as follows
= 175/700 × 100
= 0.25 × 100
= 25
Hence 25 percent of the original price was saved
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If angle 2 = 6x + 5 and angle 4 = 4x + 14, what is the value of angle 2? Round your answer to the hundredths place.
Answer:
32°
Step-by-step explanation:
Angles 2 and 4 are vertical angles, so they are congruent. That means that their measures are equal.
First, we set their measures equal to each other.
Then we solve the equation for x.
Then, we use the value of x to find the angle measure.
m<2 = 6x + 5
m<4 = 4x + 14
Set the measures equal.
6x + 5 = 4x + 14
Subtract 4x from both sides.
2x + 5 = 14
Subtract 5 from both sides.
2x = 9
Divide both sides by 2.
x = 4.5
m<2 = 6x + 5
m<2 = 6 × 4.5 + 5
m<2 = 27 + 5
m<2 = 32
Answer: 32°
In the figure below, k || I and m || n. Find the values of z and y.
69°
N
m
zo
(4y - 29)
n
Answer:
y=35, z=111
Step-by-step explanation:
By the same-side interior angles theorem, z=111.
By the alternate interior angles theorem,
[tex]111=4y-29 \\ \\ 140=4y \\ \\ y=35[/tex]