Doomtown is 300 miles due west of Sagebrush and Joshua is due west of Doomtown. At 9 a.m. Mr. Archer leaves Sagebrush for Joshua. At 1 p.m. Mr. Sassoon leaves Doomtown for Joshua. If Mr. Archer travels at an average speed 20 mph faster than Mr. Sassoon and they each reach Joshua at 4 p.m., how fast is each traveling?
Mr. Archer was going at a speed of approximately 67 mph and Mr. Sassoon was going at a speed of 47 mph (rounded to the nearest whole number).
Explanation:This problem is a typical distance-rate-time problem. Firstly, we can infer based on the travel times for Mr. Archer and Mr. Sassoon that Mr. Archer traveled for 7 hours (from 9 am to 4 pm) and Mr. Sassoon traveled for 3 hours (from 1 pm to 4 pm) to reach Joshua.
Equalizing the distance travelled by both individuals, we have: its clear that 20 mph * 7 hours = Mr. Sassoon's speed * 3 hours. From this, we can easily infer that Mr. Sassoon's speed is [tex]20*7/3 = 46.67[/tex] mph
Since Mr. Archer travelled 20 mph faster than Mr.Sassoon, Mr.Archer's speed was [tex]46.67 + 20 = 66.67[/tex] mph. Therefore, Mr. Archer was going at a speed of approximately 67 mph and Mr. Sassoon was going at a speed of 47 mph (rounded to the nearest whole number).
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A semiconductor manufacturing company employs 1,000 people. The average weekly salary of each employee is $750.
Select the graph that correctly shows the total cost to the company of paying its employees during a year.
Answer:
Graph A is the correct choice.
Step-by-step explanation:
Let x be the number of weeks.
We have been given that a semiconductor manufacturing company employs 1,000 people. The average weekly salary of each employee is $750.
Let us find the weekly salary for 1000 employees by multiplying 1000 by $750.
[tex]\text{The weekly salary for 1,000 employees}=1,000\times \$750[/tex]
[tex]\text{The weekly salary for 1,000 employees}=\$750,000[/tex]
Let us find amount of salaries after 52 weeks as 1 year equals 52 weeks.
[tex]\text{The amount of salaries after 52 weeks for 1,000 employees}=52*\$750,000[/tex]
[tex]\text{The amount of salaries after 52 weeks for 1,000 employees}=\$39000000[/tex]
Since at week 0, the salaries for 1000 employees will be also 0, so point (0,0) will be on the line of our graph.
Now let see which of our given graphs has point (0,0) and (52,39000000).
We can see that graph A has y-value 39 million on x equals 52, therefore, Graph A is the correct choice.
Which theorem or postulate justifies that angle HEF~angle HGE ?
A. AA similarity postulate
B. SAS similarity theorem
C. SSS similarity theorem
D. SSA similarity theorem
Answer:
Option A is correct.
AA similarity postulate justifies that [tex]\triangle HEF \sim \triangle HGE[/tex]
Step-by-step explanation:
The sum of the measures of a angles in a triangle add up to 180 degree.
In the triangle HGE:
[tex]\angle EHG+\angle EGH+\angle GEH = 180^{\circ}[/tex]
Substitute the given values;
[tex]90^{\circ}+37^{\circ}+\angle GEH = 180^{\circ}[/tex]
[tex]127^{\circ}+\angle GEH = 180^{\circ}[/tex]
Simplify:
[tex]\angle GEH = 180 -127 = 53^{\circ}[/tex]
In triangle HEF and triangle HGE
[tex]\angle FHE = \angle GHE = 90^{\circ}[/tex] [Angle]
[tex]\angle EFH = \angle GEH = 53^{\circ}[/tex] [Angle]
AA (Angle-Angle) similarity postulates states that two triangle are similar if they have two corresponding angles that are congruent or equal.
by AA similarity postulates;
[tex]\triangle HEF \sim \triangle HGE[/tex]
Grammy's Apple Orchard is selling apple cider in 34.7 ounce bottles for $2.09. Grammys competitor is selling 24.6 ounce bottles of cider for $1.99. Who is selling at the lower price?
Divide 4/5 by 2/3.
a. 8/15b. 5/6c. 1 1/5d. 1 7/8
The graph of a sinusoidal function intersects its midline at (0,5) and then has a maximum point at (\pi,6)
Write the formula of the function, where x is entered in radians.
f(x)=
The sinusoidal function described in the question is a cosine function that has been shifted vertically by 5 units. This can be written in the form f(x) = cos(x - π) + 5.
Explanation:In the given question, we are told that a sinusoidal function intersects its midline at (0,5) and has a maximum point at (π,6). Since the function reaches its maximum at π, it implies that this is a cosine function which shifted 5 units up on the y axis.
The general form for a cosine function is f(x) = A cos(Bx - C) + D, where: A is the amplitude of the wave, B determines the period of the wave, C is the phase shift, and D is the vertical shift. Given that we reach a maximum at (π,6), the amplitude is 1 (since it rises 1 unit above the midline). The vertical shift is 5, as the function crosses at (0,5).
Considering these factors and that the function hits a maximum (as opposed to a minimum) at x = π, we can say that the cosine's phase shift is π. Thus, the function does not need to be horizontally shifted. Therefore, the function is f(x) = cos(x - π) + 5.
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2/5, 9/10, 7/5, 19/10, 12/5
Find the common difference between the terms of the following arithmetic sequence. ...?
the diameter of a cone-shaped container is 4 inches, and its height is 6 inches .How much grater is the volume of a cylinder-shaped container with the same diameter and height?
Answer:The radius r used in below equations would equal 2in because it is half the given diameter of 4in.
The volume of the cone would be
The volume of a cylinder with the same dimensions would be
The cylinder is 24 - 8 = 16 cubic inches greater.
Step-by-step explanation:
How many thirds are in 3 hours?
There are 9 thirds in 3 hours, since each hour is made up of 3 thirds.
Explanation:To find out how many thirds are in 3 hours, we consider that 1 hour is equal to 3 thirds (since 1 divided by 1/3 equals 3). Therefore, if 1 hour equals 3 thirds, then 3 hours would contain 3 times as many thirds. We calculate this as follows:
1 hour = 3 thirds
3 hours = 3 hours × 3 thirds/hour = 9 thirds
Thus, there are 9 thirds in 3 hours.
5/16 = x/160 solve the proportion
A convenience store sells 1/3 pound of one brand of trail mix for $1.50 and 1/2 pound of another brand of trail mix for $2.15. which brand has a lower price per pound? explain your reasoning.
convert the fractions to decimals.
3/20
7/50
9/25
4/15
1/9
9/40
5/16
7/9
13/20
37/50
11/30
19/40
Every ten years, the bureau of the census counts the number of people living in the united states. in 1790, the population of the u.s. was 3.93 million. by 1800, this number had grown to 5.31 million.
solve for m : -3(m-2n)= 5m
-3(m-2n)=5m (distribute the negative 3)
-3m+6n=5m (add 3m to both sides)
6n= 8m (now divide by 8 to solve for m)
6n/8=m you can simplify
3/4n=m
1.An object falls from rest on a high tower and takes 5.0 s to hit the ground. Calculate the object’s position from the top of the tower at 1.0 s intervals. Make a position-time graph for the object’s motion. In your response, show what you are given, the equation that you used, any algebra required, a table of data, and your graph.
g = 9.8 m/s2
Answer:
Position of ball from top of tower after 1 second is 4.9 m
Position of ball: [tex]y=-4.9t^2+122.5[/tex]
Step-by-step explanation:
An object falls from rest on a high tower and takes 5.0 s to hit the ground.
Initial speed, u = 0Height of tower, [tex]h_0[/tex]Acceleration due to gravity, [tex]g=9.8\ m/s^2[/tex]Let position of object from top of tower be y
Using formula, v =u - gt
[tex]v=0-9.8\times 5[/tex]
[tex]v=49\ m/s[/tex]
Speed of object when hit the ground.
Height of tower, H₀
[tex]H_0=\dfrac{49^2-0}{2\times 9.8}=122.5\ m[/tex]
Velocity of ball after 1 s
[tex]v=0-9.8\times 1[/tex]
[tex]v=-9.8\ m/s[/tex]
Using formula, [tex]s=\dfrac{v^2-u^2}{2g}[/tex]
[tex]y=\dfrac{9.8^2-0^2}{2\times 9.8}[/tex]
[tex]y=4.9\ m[/tex] From top of tower
Now find position of ball from top of tower.
[tex]y=-\dfrac{1}{2}\times 9.8\times t^2+122.5[/tex]
[tex]y=-4.9t^2+122.5[/tex]
Please find the attachment for graph.
How many zeros does the function f(x) = 2x14 − 14x6 + 27x3 − 13x + 12 have?
An Airplane travels about 1500km in a straight line between Toronto and Winnipeg . However, the plane must climb to 10 000 m during the first 200km. Then it must descend 10 000 m during the final 300km
1. How much Distance do the climb and desent add to the flight? ...?
Answer:
Climbing and descending add to the flight 416 m
Step-by-step explanation:
The plane must climb to 10 km during the first 200 km. This forms a right triangle, where 10 and 200 are its legs and the hypotenuse is the distance travelled by the airplane. From Pythagorean theorem, that distance is:
√(10² + 200²)
The plane must descend 10 km during the final 300km. This forms a right triangle, where 10 and 300 are its legs and the hypotenuse is the distance travelled by the airplane. From Pythagorean theorem, that distance is:
√(10² + 300²)
If the airplane climbed during 300 km and descended during 200 km, then during 1500 - 200 - 300 = 1000 km it doesn't climb or descend.
The distance added by climbing and descending is:
1000 + √(10² + 200²) + √(10² + 300²) - 1500 = 0.416 km or 416 m
The set {0, 1} is closed under which operation? (Points : 3)
addition
multiplication
subtraction
none of the above
The set {0,1} is closed under both addition and multiplication, but not under subtraction. Closed means that any operation between any two elements in the set produces another element in the set.
Explanation:The set {0,1} is closed under both addition and multiplication. This means that if you perform either of these operations on any two numbers from the set, the result is a number that is also within the set.
For example if you add 0 and 1 (0+1), or multiply them (0*1), the result (1 and 0 respectively) is still within the set {0,1}. However, the set is not closed under subtraction, because 0-1 gives -1, which is not in the set.
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how many times is 2 bigger than 0.2
A bank account has a beginning balance of $560.00. After 6 months, the balance in the account has increased to $572.60. What interest rate is being earned annually on this account?
I need some help please. Write a function rule to describe each statement...
the cost in dollars of printing dollar bills when it costs 3.8cents to print a dollar bill.
the amount of money you earn mowing lawns at $15 per lawn.
the profit you make selling flowers at $1.50 each when each flower costs you $.80
A discount period is always greater than the credit period true or false ...?
Identify the missing symbol.
√31 ? √39
A. <
B. =
C. >
What number divide evenly into 125 ?
A salesperson at a furniture store earns a 3% commission on all sales. How much commission does the salesperson earn on a $1400 sale?
You just obtained a credit card. You immediately purchase a digital camera for $160. Your credit limit is $4000. Let’s assume that you make no payments and purchase nothing more and there are no other fees. The monthly interest rate is 1.42%.
Answer:
answer is b
Step-by-step explanation:
Students spend an average of $5.50 to buy materials for science olympiad if they each build three mouse trap cars what was the unit cost per car
The correct unit cost per car is $1.83.
To find the unit cost per car, we need to divide the total cost by the number of cars built. Since each student builds three mouse trap cars and spends an average of $5.50, the total cost for one student is $5.50.
Let's denote the unit cost per car as [tex]\( C \)[/tex]. The equation representing the total cost for one student is:
[tex]\[ 3C = \$5.50 \][/tex]
Now, we solve for [tex]\( C \)[/tex] to find the unit cost per car:
[tex]\[ C = \frac{$5.50}{3} \][/tex]
[tex]\[ C = $1.8333... \][/tex]
Rounding to two decimal places, the unit cost per car is approximately $1.83.
a line passes through the point (2, 3) and has a slope of -2. which is the equation of the line in point-slope form?
The equation of the line in point-slope form is y = -2x + 7.
To find the equation of the line passing through the point (2, 3) with a slope of -2, we can use the point-slope form of a linear equation:
[tex]\[y - y_1 = m(x - x_1)\][/tex]
where m is the slope and [tex]\((x_1, y_1)\)[/tex] is a point on the line.
Given that the point [tex]\((x_1, y_1)\)[/tex] is (2, 3) and the slope m is -2, we substitute these values into the point-slope form:
y - 3 = -2(x - 2)
Now, we can simplify the equation:
y - 3 = -2x + 4
Next, we can move the constant term to the other side:
y = -2x + 4 + 3
y = -2x + 7
So, the equation of the line in point-slope form is y = -2x + 7.
Valeriya wants to determine the likely voting outcome for the new town council election. Which sample is likely to yield the most biased results?
A. every tenth person working for the largest corporation in town
B. ten people chosen at random from each page of the town’s phone list
C. every tenth person walking down Main Street in town on a variety of days and times of the day
D. ten eligible voters chosen at random from each of the different neighborhoods in town
Answer:
A. Every tenth person working for the largest corporation in town
Step-by-step explanation:
We are given that,
'Valeriya wants to determine the likely voting outcome for the new town council election'.
It is required to find the most biased outcome.
Now, from the options, we see that,
'Every tenth person working for the largest corporation in town'.
will yield the most biased result, as the people working in the largest corporation may have different opinions and benefits.
So, it is most likely that the voting result for this sample may result in the outcome beneficial to only the people working in the large corporations and not for others.
Thus, sample A will yield a most biased result.
True or false? the length of time on the desk is a function of the temperature of the coffeewhich the longer coffee sits on a desk, the cooler it becomes