Final answer:
To determine how long Loretta's father drives, we deduct the distance Loretta drives (220 miles) from the total trip distance, then divide the remainder (390 miles) by her father's average speed (65 mph), resulting in 6 hours of driving time for her father. The total trip time is 10 hours.
Explanation:
The question is about calculating travel times and distances using average speed. Loretta and her family are traveling 610 miles with Loretta driving the first 4 hours of the trip at 55 mph and her dad driving the remainder at 65 mph. To calculate the distance Loretta drives, we multiply her driving time by her average speed (4 hours * 55 mph = 220 miles). Then, we subtract that distance from the total trip distance to find out how far her dad drives (610 miles - 220 miles = 390 miles). To calculate how long her dad drives, we divide his driving distance by his average speed (390 miles / 65 mph).
Now let's solve the dad's driving time:
390 miles / 65 mph = 6 hours. So, Loretta's dad would drive for 6 hours. The total driving time for the trip is the sum of both Loretta's time and her dad's time: 4 hours + 6 hours = 10 hours.
Let y be inversely proportional to x. if x doubles, what happens to y?
Final answer:
If x doubles and y is inversely proportional to x, then y will become half of its original value, as per the inverse proportionality relation y = k/x.
Explanation:
When variables y and x are inversely proportional, this means that as one value increases, the other value decreases. The relationship between y and x in this case is represented by the equation y = k/x, where k is the proportionality constant. If the value of x doubles, looking at the relationship expressed by the inverse proportionality equation, the value of y will decrease by half.
So, if x becomes 2x, then y becomes k/(2x), which is half the value of the original y if we assume that k is constant. This is reflective of the more-less relationship inherent to inverse proportionality, where increased values of one variable lead to decreased values of the other.
Tom has $10 that he wants to use to buy pens and pencils. However, he does not want to buy more pens than pencils. A pen costs $3, and a pencil costs $1. Which graph represents this scenario? (Here, x represents the number of pens and y the number of pencils.)
A)
B)
C)
D)
E)
Answer:
for plato it is graph A it goes with the first answers graph
Step-by-step explanation:
Show that the equation 2xcubed + 4x = 3 has a solution between 0 and 1
Find the volume of a rectangular prism with the following dimensions.
a length of 11 cm, a width of 4.2 cm, and a height of 7.1 cm
Answer:
441 cm
Step-by-step explanation:
Chris is in training for a bicycle race. He needs to ride 50 kilometers a week as a part of his training. He rode 18.23 kilometers on Monday and 13.94 kilometers on Tuesday.
How much more does Chris need to ride to complete his training for the week ?
A. 4.29 km
B. 17.83 km
C.31.77 km
D. 36.06 km
add how many he rode already:
18.23 + 13.94 = 32.17
now subtract that from 50:
50 - 32.17 = 17.83
answer is B. 17.83 km
PLEASE HELP!!! Write the equation that describes the simple harmonic motion of a particle moving uniformly around a circle of radius 8 units, with angular speed 5 radians per second
The equation that describes the simple harmonic motion of a particle moving uniformly around a circle is x(t) = Acos(wt + φ). In this case, the equation is x(t) = 8cos(5t + φ).
The equation that describes the simple harmonic motion of a particle moving uniformly around a circle can be derived using the concept of circular motion and trigonometry.
The equation for the position of the particle is given by x(t) = Acos(wt + φ), where A is the radius of the circle, w is the angular speed, t is the time, and φ is the phase shift.
In this case, the radius of the circle is 8 units and the angular speed is 5 radians per second. Therefore, the equation for the simple harmonic motion of the particle is x(t) = 8cos(5t + φ).
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Tamara earns her living as a salary plus commission employee. Her annual salary is $48,000, and she earns 4% commission on all sales she makes. If Tamara wants to make a total of $6,000 this month, how much in sales does she need to have?
Answer:
$5,000 in sales
Step-by-step explanation:
dividing the annual salary by 12 to find how much she makes in a month:
48,000/12 = $4,000
If she wants to make $6,000 this month, she needs
6,000 - 4,000 = $2,000 in comissions
$2,000 is the 4% of how much she made in sales.
denoting the total of sales by x:
4%x = 2,000
---> 0.04x = 2,000
this makes x = 2,000/0.04
--> x = $50,000
So to get a moth salary of $6,000 she needs to have $5,000 in sales
Use the formula to estimate the temperature when n = 20 chirps/min. Round to the nearest whole number, if necessary.
Which of these is a step in constructing an inscribed Equilateral triangle using technology?
A- Construct segment DB, segment BC, segment CE, segment EG, segment GI, and segment ID.
B- Create circle A with point B on the original circle.
C- Create circle E, which passes through points A and C.
D- Draw point E anywhere on segment DB.
Answer:
The answer is B,A
Step-by-step explanation:
In geometry, an equilateral triangle is a triangle in which all three sides have the same length
Divide. (5 1/4)÷(−2 1/2) Enter your answer as a mixed number, in simplified form, in the box.
Answer: [tex]-2\dfrac{1}{10}[/tex]
Step-by-step explanation:
The given expression to simplify : [tex]5\dfrac{1}{4}\div-2\dfrac{1}{2}[/tex] (i)
First we convert mixed fraction into improper fraction as :
[tex]5\dfrac{1}{4}=\dfrac{5\times4+1}{4}=\dfrac{20+1}{4}=\dfrac{21}{4}[/tex]
[tex]-2\dfrac{1}{2}=-\dfrac{2\times2+1}{2}=-\dfrac{4+1}{2}=\dfrac{-5}{2}[/tex]
Now , put them in (i) , we get
[tex]\dfrac{21}{4}\div\dfrac{-5}{2}[/tex]
[tex]=\dfrac{21}{4}\times\dfrac{-2}{5}=\dfrac{-21}{10}=-\dfrac{20+1}{10}=-2\dfrac{1}{10}[/tex]
Hence, the required answer is [tex]-2\dfrac{1}{10}[/tex].
If your speedometer reads 65 mph then you are actually traveling how many miles?
Can anyone figure this out for me?
3^4 = 3*3*3*3 = 81
3^2 = 3*3 =9
81/9 = 9
Answer is B. 9
Two pages that faces each other in a book have 333 as the sum of their page numbers what is the number of pages that come first
How many perfect cubes divide evenly into 13, 824?
A gumball machine contains 23 green gumballs, 52 red gumballs, 34 blue gumballs,61 yellow gumballs, and 30 pink gumballs. What percentage of the gumballs are red?
A paper hat is folded into the shape of a kite, as shown. What total length of ribbon is needed to line the two long sides of the hat? 10 in. 11 in. 20 in. 22 in.
Answer:
Step-by-step explanation:
your answer is d
A kite is a quadrilateral with four sides that may be divided into two adjacent pairs of equal-length sides. The total length of ribbon that is needed to line the two long sides of the hat is 22 inches.
What is a kite?A kite is a quadrilateral with four sides that may be divided into two adjacent pairs of equal-length sides. A parallelogram, on the other hand, has two sets of equal-length sides that are opposite each other rather than adjacent.
Since the two adjacent small and two adjacent long sides of a kite are always equal. Therefore, the length of the smaller sides can be written as,
(2x + 1) inches = 5 inches
2x + 1 = 5
2x = 4
x = 2
Now, the length of the longer side of the kite can be written as,
(3x + 5) inches
= 3(2) + 5
= 11 inches
As both the long sides are needed to be covered with the ribbon, therefore, the length of the ribbon needed is,
Ribbon needed = 11 inches × 2
= 22 inches
Hence, the total length of ribbon that is needed to line the two long sides of the hat is 22 inches.
The diagram of the question is mentioned in the below image.
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Terrell wants to drive his car at a speed of 50 miles per hour for 2.75 hours. His car has a fuel efficiency of 25 miles per gallon. How many gallons of fuel does Terrell need for his journey?
Answer:
5.5
Step-by-step explanation:
A circle whose area is 4 has a radius of x find the area of a circle whose radius is 3x
Answer:
Area = 36 units.
Step-by-step explanation:
Given : A circle whose area is 4 has a radius of x .
To find : find the area of a circle whose radius is 3x.
Solution: We have given
Area of circle = 4 units.
Radius = x .
Formula of area = pi (radius)².
Plug the values
pi (x)² = 4 -------(A)
If the radius = 3x .
Then 4
Area = pi (3x)².
Area = pi (9)(x)².
Area = 9 pi (x)²-----(B) .
We can see from equation ( A) 4 = pi (x)²
Area = 9 * 4.
Area = 36 units.
Therefore, Area = 36 units.
I can't seem to understand the subject of converting scientific notation.
2.077×10^-4
Please explain how to solve this problem step by step.
~Thank you ♥︎
What are the side measures?
the shadow of an object varies directly as it height a man 1.8m tall cast a shadow 4.32m long if at the same time a flagpole cast a shadow 12.8m long how it is the flagpole?
ALGEBRA 2- Which property of addition is shown below?
If x = 1 + 2i and y = –1 – 2i, then x + y = 0.
A. commutative property
B identity property
C associative property
D inverse property
Answer:
D inverse property
Step-by-step explanation:
x=1+2i
y=-1-2i
Both x and y are complex numbers with both real and imaginary parts.
x+y = (1+2i) + (-1-2i)
= 1 + 2i - 1 - 2i
= (1 - 1) + (2i-2i)
= 0 + 0 = 0
Since the two given complex numbers add up to 0, this means that each number is the additive inverse of the other.
So x is the inverse of y and y is the inverse of x.
Among the given options, option D , namely, inverse property is the correct one.
QUICKK EXPERTS/ACE OR ANYONE WHO WANTS TO HELP!!
from the problem m = 1/2
point slope =
y -2 = 1/2(x+8)
If a circle has a diameter whose endpoints are (-5, 8) and (5, -8), then the circle has its center at the origin. True False
Answer:true
Step-by-step explanation:
As per an axiom in Euclidean geometry, if__ points lie in a plane, the___containing those points also lies in the same plane.
1. two or three
2. plane or line
Answer:
1. Two
2. Line
Step-by-step explanation:
Two out of the five axioms of the Euclidean Geometry are:
1. A straight line can be drawn between any two points.
2. Any straight line can be extended infinitely.
So, from the above axioms, we get that 'If two points lie in a plane, a straight line can be drawn between those points and that line can be extended indefinitely in that plane'.
Hence, 'If TWO points lie in a plane, the LINE containing those points also lie in the same plane'.
Lexi had planted seeds in 3/5 of the garden. She used 1/2 pound of seeds. How many pounds will she use for the entire garden?
Answer:
Lexi will use [tex]\frac{5}{6}[/tex] pounds of seeds.
Step-by-step explanation:
Lexi has planted seeds in [tex]\frac{3}{5}[/tex] of the garden. We know that to plant that part she used [tex]\frac{1}{2}[/tex] pound of seeds.
The entire garden is [tex]\frac{5}{5}=1[/tex].
Then if you multiply [tex]\frac{1}{2}[/tex] in [tex]\frac{5}{5}=1[/tex] and then divide the result in [tex]\frac{3}{5}[/tex] you will obtain how many pounds will she use for the entire garden. (It's a rule of three)
[tex](1).\frac{1}{2} :\frac{3}{5}=\frac{1}{2} :\frac{3}{5}=\frac{5}{2.3}=\frac{5}{6}[/tex]
Lexi will use [tex]\frac{5}{6}[/tex] pounds of seeds.
The mean score on a biology exam taken by all undergraduate students in a college in a particular year is 67.8 with a standard deviation of 11.5. The standard error of the mean for a sample of 70 students is , and the margin of error of the mean is . (Round off your answers to the nearest hundredth.)
The standard error of the mean for a sample of 70 students is 1.375 .
The margin of error of the mean is 2.69 .
[Round off your answers to the nearest hundredth]
Which expression can be used to determine the slope of the linear function represented in the table?
x
y
0
5
4
9
9-5/4-0
4-0/9-5
5-0/9-4
9-4/5-0
Answer:
9-5/4-0
Step-by-step explanation:
which is an equation in point-slope form of the line that passes through the points (4,5) and (-3,-1)?
A. y+1=6/5(x+3)
B. y-1=6/7(x-3)
C. y+1=6/7(x+3)
D. y+3=7/6(x+1)
What are the dimensions of the following matrix?
5 -6
0 1
3 5
-1 7
A. 2x4
B.4x2
C.3x2
D.none of these