Yes. The warehouse drivers deliver enough packages.
What is an expression?An expression is used to illustrate the information that's given.
In this case, the warehouse has 128 trucks. Each truck has 350 packages. The number of packages that van be delivered will be:
= Number of trucks × Amount in each package
= 128 × 350
= 44800
Since the drivers at a warehouse need to deliver 40,000 packages each day. this means they denied enough packages because 44800 is more than 40000.
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The janitor at a school discovered a leak in a pipe. The janitor found that it was leaking at a rate of 14 fl oz per hour. How fast was the pipe leaking in gallons per day?
Answer:
6.5625 gal per hour
Step-by-step explanation:
Since there are 60 minutes per hour, we need to multiply 14 by 60 to change per minute into per hour. Combining these: 14 fl oz / min x (1 gal / 128 fl oz) x (60 min / hr) = 6.5625 gal per hour. Written as a mixed fraction: 6 9/16 gal per hour.
If a and b are two events defined on the same sample space, given that p(a) = 0.28 and p(aub) = 0.51, find the p(b) such that a and b are mutually exclusive
P(B) such that a and b are mutually exclusive is 0.23
A group of potential results from a specific experiment is an event. Events that do not take place at the same time are said to be mutually exclusive. For instance, if a coin is tossed, the outcome will either be head or tail; we cannot obtain both outcomes. Since they do not occur at the same time, such occurrences are also known as disjunct events.
Given: P(A) =0.28
P(AUB) = 0.51
We know,
P(AUB) = P(A) + P(B) - P(A∩B)
Since A and B are mutually exclusive events, they cannot happen together.
So, P(A∩B) = 0
Then,
P(AUB) = P(A) + P(B)
0.51 = 0.28+ P(B)
P(B) = 0.51 - 0.28 = 0.23.
Hence, P(B) = 0.23
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If f (x) = 4x2 + 3x − 5, then the quantity f of the quantity x plus h end quantity minus f of x end quantity all over h is equal to which of the following?
4 times the quantity x plus h end quantity squared plus 3 times the quantity x plus h end quantity minus 5 minus 4 times x squared plus 3 times x minus 5 all over h
4 times the quantity x squared plus 2 times x times h plus h squared end quantity plus 3 times the quantity x plus h end quantity minus 5 minus the quantity 4 times x squared plus 3 times x minus 5 end quantity all over h
the quantity 4 times x plus 4 times h end quantity squared plus the quantity 3 times x plus 3 times h end quantity minus 5 minus the quantity 4 times x squared plus 3 times x minus 5 end quantity all over h
4 times the quantity x plus h end quantity squared plus 3 times x minus 5 minus 4 times x squared minus 3 times x plus 5 all over h
The difference quotient of f(x) is:[ f(x + h) - f(x)]/h = 8x + 4h + 3
How to get the difference quotient?Here we have the function:f(x) =4x^2 +3x - 5
And we want to get the difference quotient that can be written as:
[f(x + h) - f(x)]/h
Replacing the function we get:
[f(x + h) - f(x)]/h = [4*(x + h)^2 + 3*(x + h) - 5 - 4*x^2 - 3x + 5]/h
Solving further (open the brackets), we have
[f(x + h) - f(x)]/h = [4x^2 + 8*x*h + 4h^2 + 3x + 3h -5 - 4x^2 - 3x + 5]/h
Evaluate the like terms
So, we have
[f(x + h) - f(x)]/h = [8*x*h + 4h^2 + 3h]/h
Evaluate the quotients
[f(x + h) - f(x)]/h = 8x + 4h + 3
That is the difference quotient.
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Evaluate the function for the following values:
f(1) =
f(2)=
f(3) =
Answer: [tex]f(1)=1, f(2)=0, f(3)=2[/tex]
Step-by-step explanation:
[tex]0 \leq 0 \leq 1 \implies f(1)=1^2 =1\\\\1 < 1 \leq 2 \implies f(2)=-2+2=0\\\\2 < 3 \leq 3 \implies f(3)=3^2 -3(3)+2=2[/tex]
2. The height (cm) of a plant during a period can be described with a function where time is 24 hours after planting. y=3+34x
How tall is the plant after 4 days?
What does the value y=3 mean?
Here given ,
y = 3 + 34x
We have to find height of plant after 4 days,
so, x = 4,
by substituting x,
y = 3 + 34 x 4
= 3 + 136
= 139 cm
here y = 3 means,
The corresponding function when the value of y =3 .
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The difference between the two numbers is -1. Their sum is -27. Find the numbers. Let x represent the first number and y represent the second number. first number x = second number y =
Taking into account the definition of a system of linear equations, the first number is x= -14 and the second number y= -13.
System of linear equationsA system of linear equations is a set of linear equations (that is, a system of equations in which each equation is of the first degree) in which two or more unknowns are related.
Systems of linear equations have as a solution set all ordered pairs (x, y) that satisfy the equation, where x and y are real numbers. That is, solving a system of equations consists of finding the values of the unknowns, with which, when replaced in the equations, they must give the proposed solution.
This caseIn this case, a system of linear equations must be proposed taking into account that
"x" is the first number."y" is the second number.You know:
The difference between the two numbers is -1. Their sum is -27.The system of equations to be solved is
x-y= -1
x+y= -27
It is decided to solve the system of equations using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, isolating the variable "x" from the first equation:
x= -1 +y
Replacing this expression in the second equation:
-1 +y +y= -27
Solving:
y +y= -27 +1
2y= -26
y= (-26)÷2
y= -13
Remembering that x=-1 +y, you get
x= -1 -13
x= -14
Finally, the numbers are -13 and -14.
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The values of the first and second numbers are - 13 and - 14 respectively.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let us assume that the two numbers are x and y.
Given, The difference between the two numbers is -1.
∴ x - y = - 1...(i)
And, Their sum is - 27 which is,
x + y = - 27...(ii)
Now, if we add eqn (i) to eqn (ii)
x + y = - 27
+ x - y = -1
---------------------
2x = - 28
+ y and - y get canceled and we get
∴ 2x = 26.
x = - 13.
Now, substitute the value of x in any of the eqn(i). we get y = - 14.
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Is arc length equal to the measure of the radian?
For instance, if the arc length is 5 units, does it also mean that the measure of the radian is also 5 units, or can it vary??
The arc length is equal to the measure of the arc in radians only if the radius of the circle is 1 unit, for all the other circles this is false.
Is arc length equal to the measure of the radian?For a circle of radius R, if we have an arc defined by an angle of θ radians, then the length of that arc is:
L = R*θ
Particularly, the length is equal to the measure in radians only if the radius of the circle is R = 1:
L = 1*θ
So the statement is only true for the unit circle but is false for every other circle.
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Find the Factor Pairs (LOTS OF POINTS!)
The factor pairs which matches the number of tents to sleep exactly 40 boys with each tent having an equal number of boys are;
1 tent ===> 40 boys.2 tents ===> 20 boys each.3 tents ===> No match.4 tents ===> 10 boys each.5 tents ===> 8 boys each.6 tents ===> No match.7 tents ===> No match.What are the correct matches of factors such that each tent contains an equal number of students as the others?Since 40 students are to be equally distributed in each of the number of tents arrangement.
It follows that first, one must list the integer pairs whose products yield 40 as follows;
Hence, we have;
1 × 40.2 × 20.4 × 10.5 × 8.Hence, the factor pairs for each scenario of number of tents are as listed in the answer section above.
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an environmentalist wishes to conduct a hypothesis test on the percentage of cars driven in the city that are hybrids. is it sufficient for him to use a simple random sample of 172172 cars if hybrids currently account for 6%6% of the car sales in the country and he claims that the percentage of hybrids in the city is higher than that?
It is enough for him to use a simple random sample of 172 cars.
It is required that there are at least 10 successes and 10 failures to test a hypothesis that involves a proportion p in a sample of size n.
Following conditions are required for it:
1) np ≥ 10
2) n (1-p) ≥ 10
p = 6% = 0.06
n = 172
np = 172x0.06 = 10.322 ≥ 10172 (1-0.06) = 161.68 ≥ 10So, there are at least 10 successes and 10 failures in the 172 cars sample, it is enough for him to use a simple random sample of 172 cars.
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cenario 2: the directors of an annual community concert want to learn the musical preferences of the audience. the directors choose 2 and 6 from a random number generator and place a survey card on every sixth seat beginning with the second seat. all the cards are returned as the audience leaves. they are using
The sampling method used here is systematic sampling.
What is systematic sampling?
To generate a representative sample from a population, systematic sampling is a probability sampling technique.An advantage of systematic sampling is that it does not necessitate a comprehensive population list in advance. A sort of probability sampling technique called systematic sampling involves choosing individuals from a broader population using random beginning points and defined intervals.Random systematic samples, linear systematic samples, and circular systematic samples are the three primary categories of systematic samples.Here , this scenario is systematic sampling since it entails choosing n at random and selecting every nth person in the audience starting at a random point.To learn more about systematic sampling , refer:
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-5< x < 5Graph the solution set on a number line
- 5 < x < 5
Number line:
Which of the following best describes the slope of the line below?
Answer:
D. Negative
Step-by-step explanation:
Always read the graph from left to right
The graph is going down thus it is negative
Answer: Negative.
Step-by-step explanation: The graph of the line falls from left to right which makes it negative.
What is x in this equation -7(x+-2)=-63
A construction crew has just built a new road. They built the road at a rate of 18.75 kilometers per week. They worked for 3 weeks. How many kilometers of road did they build?
Answer:
6.25 weeks
Step-by-step explanation:
Take 18.75 ÷ 3. The construction crew finishes 3 km per week. You should receive 6.25 by solving the equation. So, this is the answer.
can you please answer work the math problem the easiest quick way please
Given: the three points are plotted on graph.
For the first point it is observed that,
For the x =3/2 the value is y=6/2
For second point ,
For x= 9/2 the y value is y=12/2
For the third point ,
For x= 15/2 the y value is y=18/2
According to obtained information it matched to option J)
Answer: Option J)
betty and karen have been hired to paint the houses in a new development. working together, the women can paint a house in two-thirds the time that it takes karen working alone. betty takes 4 h to paint a house alone. how long does it take karen to paint a house working alone?
Betty takes 6 hours to paint a house alone, that indicates she can paint 1/6 of the house in 1 hour then Karen working alone will paint a house in 3 hours.
How long does it take paint a house working alone?Since Betty takes 6 hours to paint a house alone, that indicates she can paint 1/6 of the house in 1 hour.
Karen can even paint 1/x in 1 hour
Both of them will paint the house in 3/2 hours.
We then add them together which gives:
1/6 + 1/x = 3/2x
The lowest common multiple is 6x
1x/6x + 6/6x = 9/6x
We then leave out the denominators
1x + 6 = 9
simplifying the above equation, we get
x = 9 - 6
x = 3
Therefore, the value of x = 3.
Karen working alone will paint a house in 3 hours.
The complete question is:
Betty and Karen have been hired to paint the houses in a new development. Working together, the women can paint a house in two-thirds the time that it takes Karen working alone. Betty takes 14 h to paint a house alone. Betty takes 6 h to paint a house alone.
Required:
How long does it take Karen to paint a house working alone?
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Paula measured the auditorium and made a scale drawing. The stage, which is 56 feet long in real life, is 84 inches long in the drawing. What scale did Paula use?
3 inches= blank feet
Based on the number of inches in the drawing and the number of feet in real life, the scale that Paula used was 3 inches = 2 feet
What scale did Paula use?The scale that Paula used was such that the stage was 56 feet long in real life but 84 inches long on the drawing.
The scale can therefore be shown by the ratio:
56 feet : 84 inches
If the number of inches is 3 then the number of feet in the scale would be:
56 feet : 84 inches
x feet : 3 inches
Cross-multiplying gives:
84x = 168
x = 168 / 84
x = 2 feet
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Find the area of the region that is inside the square and outside the circle. The circle has a diameter of 8 inches. Round to the nearest tenth.
The area of the region within the square and without the circle is equal to 13.7 square inches.
What is the area of a region generated by a square and a circle?In this problem we find the case of figure generated by a square and an inscribed circle. Then, the area of the region is found by subtracting the area of the circle from the area of the square. Then, the area is:
A = L² - 0.25π · D²
Where:
L - Side length, in inches.D - Diameter, in inches.A - Areas, in square inches.If we know that D = L = 8 in, then the area of the region is:
A = (8 in)² - 0.25π · (8 in)²
A = 64 in² - 50.265 in²
A = 13.735 in²
The area of the region is equal to 13.7 square inches.
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Given the polynomial f(x)=x⁴+3x³-3x²-x, which of the following is true?
a) (x+1) is a factor since f(-1)=0.
b) (x-1) is a factor since f(-1)=0.
c) (x+1) is a factor since f(1)=0.
d) (x-1) is a factor since f(1)=0.
Part of the graph of the function f(x) = (x + 4)(x - 6) isshown below.Which statements about the function are true? Selecttwo optionsThe vertex of the function is at (1,-25).6The vertex of the function is at (1,-24).The graph is increasing only on the interval -4
The vertex of the function is (1, -25) Correct
Because
f(x) = (x + 4)(x - 6)
Substitution
-25 = (1 + 4)(1 - 6)
Simplification
-25 = (5)(-5)
Result
-25 = -25 As both sides of the equation are equal this option is true
5) The graph is negative on the entire interval - 4 < x < 6 because the graph is below the x-axis
Mr. Webster sells vacation rentals and
earns a 3.5% commission on every
vacation rental he sells. How much
commission would he earn on a vacation
rental that sold for $4,200?
Answer:
$134.50
Step-by-step explanation:
4200 x .035 = 134.50
3.5% Percent means per 100
3.5/100 when you divide by 100, you move the decimal two places to the left.
The commission amount is $147
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Mr. Webster sells vacation rentals and earns a 3.5% commission on every vacation rental he sells.
He sold $4200.
So, 3.5% of commission:
4200 x 3.5 / 100
= 147
Therefore, the commission is $147.
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12/-3 Enter your answer as a number, like this: 42
Answer:
-4
Step-by-step explanation:
12/-3=-4
f (x)=(x-3)^2 + 4 when is f increasing
Answer:
(3,∞)
Explanation:
Given the function:
[tex]f(x)=\mleft(x-3\mright)^2+4[/tex]The graph of f(x) is attached below:
The interval when f(x) is increasing is therefore: (3,∞)
Beth is planning a playground and has decided to place the swings in such a way that they are the same distance from the jungle gym and the monkey bars. if beth places the swings at point d, how could she prove that point d is equidistant from the jungle gym and monkey bars? if segment ad ≅ segment cd, then point d is equidistant from points a and b because congruent parts of congruent triangles are congruent. if segment ad ≅ segment cd, then point d is equidistant from points a and b because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects. if m∠acd = 90° then point d is equidistant from points a and b because congruent parts of congruent triangles are congruent. if m∠acd = 90° then point d is equidistant from points a and b because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.
The angle bisector theorem states that a triangle's opposite side is divided into two halves by an angle bisector that is proportional to the triangle's other two sides.
A point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects, therefore if mACD = 90°, point D is equidistant from points A and B.
Any point on the perpendicular bisector is simply equal distance from both endpoints of the line segment on which it is drawn, according to the perpendicular bisector theorem.
The answer is that point is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it makes up. Therefore, if a pillar is stationed at the middle of a bridge at an angle, all the points on the pillar will be equidistant from the end points of the bridge intersects.
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What is the distance between the points (−7, −3) and (−7, −9) ? Responses
Find the measure of
Answer: ∠BDG = 50°
Step-by-step explanation:
We know that a straight line is equal to 180°, meaning that line CDF is 180°.
Next, we know that angle CDB, angle BDG, and angle GDF should all add up to be 180°, since we know CDF is equal to 180°.
Lastly, with all this information in mind, we will set up an equation and solve.
130° + BDG = 180°
∠BDG = 50°
A line has a slope of – 1 and includes the points (9,2) and (8,p). What is the value of p?
Answer:
p = 3
Step-by-step explanation:
y = mx + b They gave us the slope of -1. We need to find the y intercept. We will use the x of 9 and the y of 2 to find b. We will plug these numbers in to find b.
y = mx + b
2 = -1(9) + b
2 = -9 + b Add 9 to both sides
11 = b
y = -x +11
Now, plug in 8 for x
y = -1(8) + 11
y = -8 + 11
y = 3
In this case p is 3.
pulse rates of adult females are normally distributed with a mean of 74.0 beats per minute (bpm) and a standard deviation of 12.5 bpm. what is the percentage of adult females with pulse rates between 49.0 bpm and 86.5 bpm? what percentage of adult females have pulse rates below 90 bpm?
The percentage of adult females with pulse rates between 49.0 bpm and 86.5 bpm - 81.86%
The percentage of adult females have pulse rates below 90 bpm - 89.97%
a)
X ~ N ( µ = 74 , σ = 12.5 )
P ( 49 < X < 86.5 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 49 - 74 ) / 12.5
Z = -2
Z = ( 86.5 - 74 ) / 12.5
Z = 1
P ( -2 < Z < 1 )
P ( 49 < X < 86.5 ) = P ( Z < 1 ) - P ( Z < -2 )
P ( 49 < X < 86.5 ) = 0.8413 - 0.0228
P ( 49 < X < 86.5 ) = 0.8186 ≈ 81.86%
b)
X ~ N ( µ = 74 , σ = 12.5 )
P ( X < 90 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 90 - 74 ) / 12.5
Z = 1.28
P ( ( X - µ ) / σ ) < ( 90 - 74 ) / 12.5 )
P ( X < 90 ) = P ( Z < 1.28 )
P ( X < 90 ) = 0.8997 ≈ 89.97%
What is pulse rate ?
The pulse rate, or the number of times the heart beats each minute, is gauged by the pulse rate. The arteries enlarge and constrict with the flow of blood as the heart pumps blood through them. An elevated heart rate, or tachycardia, can occur for any reason. Exercise-induced or stress-related heart rate increases are two possible causes (sinus tachycardia). Sinus tachycardia is not seen as an illness but rather a symptom. Another factor contributing to tachycardia is an unsteady heartbeat (arrhythmia).
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The Mendez Family consists of two adults and two children. Their current monthly income is $4800. Calculate the percentage of the total budget for each category.
Percentage spent on transportation is 12%
Percentage spent on Property tax is 11%
Percentage spent on utilities is 9%
Percentage spent on food is 20%
Percentage spent on mortgage payment is 30%
Percentage spent on entertainment is 8%
Percentage spent on miscellaneous is 10%
What are the percentages?
Percentage is the fraction of a number expressed as a number out of 100. In order to convert a number of fraction to percentage, multiiply by 100. The sign that is used to represent percentage is %.
Percentage spent on transportation = (576 / 4800) x 100 = 12%
Percentage spent on Property tax = (528 / 4800) x 100 = 11%
Percentage spent on utilities = (432 / 4800) x 100 = 9%
Percentage spent on food = (960 / 4800) x 100 = 20%
Percentage spent on mortgage payment = (1440 / 4800) x 100 = 30%
Percentage spent on entertainment = (384 / 4800) x 100 = 8%
Percentage spent on miscellaneous = (480 / 4800) x 100 = 10%
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2/3×4/5 in fraction bar
Answer:
8/15
Step-by-step explanation:
Multiply the numerators:
2*4 = 8
Multiply the denominators:
3*5 = 15
Now we have 8/15.
This cannot be simplified, so this is our final answer.
[tex]\frac{2}{3} \times\frac{4}{5}[/tex]
Multiply numerator by numerator and denominator by denominator:
[tex]2*4=8\\3*5=15[/tex]
[tex]\frac{8}{15}[/tex] would be your final answer.
