The required the average speed must be at least 52.5 mph to travel 420 miles in 8 hours.
What is inequality?A difference between two values indicates whether one is smaller, larger, or simply not equal to the other. A B indicates that a and b are not equal. When a b, an is said to be less than b. A > B indicates that an is superior to b. These two constitute tight inequity.
According to question:Let the average speed of the trip "x" in miles per hour. To find out what the average speed must be, we need to write an inequality based on the given information and then solve it.
The formula for distance, speed, and time is:
distance = speed * time
So, the distance traveled can be written as:
distance = x * 8 hours
And the inequality based on the given information that the distance must be at least 420 miles is:
x * 8 ≥ 420
To solve for x, we need to divide both sides of the inequality by 8:
x ≥ 420 / 8
x ≥ 52.5
So, the average speed must be at least 52.5 mph to travel 420 miles in 8 hours.
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five friends equally shared 2 bottles of juice. Each bottle contains 1/3 liters of juice. What fraction of a bottle did each of them drink?
Answer:
2/5 bottle of juice
2/15L of juice
Step-by-step explanation:
We originally have 2 bottle of juice and each bottle contains 1/3 liter. From this, we can find that there are 2/3L of juice in total. Since five friends equally drink the juice, each of them drank 2/5 bottle of juice and 2/15L of juice.
I hope this makes sense to you. I am generally good with following up with additional questions. Feel free to leave a comment if you have any questions or you can also message me as well!
How do you convert grams to moles per gram?
To convert grams to moles per gram, you need to find the molar mass of the substance in grams per mole. Then, divide the number of moles by the given mass to get moles per gram.
To convert grams to moles per gram, you first need to determine the molar mass of the substance you are interested in. The molar mass is the mass of one mole of the substance, expressed in grams. Once you know the molar mass, you can use it to convert grams to moles, and then divide by the total mass to get moles per gram.
Here are the steps to follow:
Determine the molar mass of the substance. This is the sum of the atomic masses of all the atoms in the molecule, expressed in grams per mole. You can find the atomic masses on the periodic table.
Convert the given mass from grams to moles, using the formula:
moles = mass / molar mass
where mass is the given mass in grams, and molar mass is the calculated molar mass in grams per mole.
Divide the number of moles by the given mass, to get the moles per gram. This gives you the number of moles of the substance per gram of the sample.
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Trapezoid PQRS has vertices P(0, 0), Q(0, 6), R(8, 6), and S(14, 0). What is the length of the midsegment?
Using the trapezoid midsegment theorem, the length of the midsegment of trapezoid PQRS is 11 units,
What is the Midsegment of a Trapezoid?The Trapezoid Midsegment Theorem states that the length of the midsegment of a trapezoid is equal to the average of the lengths of the bases (the parallel sides). Mathematically, this can be expressed as:
length of midsegment = (length of base₁ + length of base₂) / 2
In the case of trapezoid PQRS, the bases are QR and PS.
The length of QR is 8 units and the length of PS is 14 units.
Therefore, the length of the midsegment can be calculated as:
length of midsegment = (8 + 14) / 2
length of midsegment = 22 / 2
= 11 units
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what does 2x - 2 ≥ -8 equal to
Answer: -3
Step-by-step explanation:
A triangle has vertices on a coordinate grid at
J(-7,−7) K(−7,3) and L(−1,3)
What is the length, in units, of JK ?
The requried measure of length JK on the coordinate plane is 10 units.
The distance between two points on the coordinate plane can be evaluated by the distance formula as,
D = √((x₂ - x₁)^2 + (y₂ - y₁)²)
Here,
The coordinates of the two points J(-7, -7) and K(-7, 3) suggest that they lie on a vertical line, where the x-coordinate is constant (-7) and only the y-coordinate changes. The distance between these points is equal to the difference in their y-coordinates.
Therefore, the length of JK is,
JK = |y-coordinate of K - y-coordinate of J|
= |3 - (-7)| = |3 + 7| = 10
So, the length of JK is 10 units.
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Write the word sentence as an inequality. Then solve the inequality.
225 is no less than 3/4 times a number w .
An inequality that represents this word sentence is.
The solution is
Answer:
Like the other solver, I believe they are correct because I arrived at the same solution:
3/4w <= 225
Multiplying both sides by 4/3 to isolate w:
w >= (225 * 4)/3
w >= 300
Solution is w >= 300. In order to meet the inequality, the value of w must be equal to or larger than 300.
On the coordinate plane below, plot and label each point.
The points are plotted and labeled in the graph.
What are coordinates?Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.
Given:
A graph of the coordinate plane.
The points are (0, 2), (-3, 4), (4, -6), (6, -2), (5, 5), (-3, -5), (0, -4), (4, 0), (5, 0), and (3, -6).
The points are plotted and labeled in the graph.
The required graph is given in the image below.
Therefore, all the coordinates are plotted in the graph.
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Find the value of each of the following :
(a) 6 1/5 % of 1.35 ml
(b) 56 7/8 % of 810m
(c) 0.56% of 15 000 L
(d) 2000% of 5￠
The value of each of the following:
(a) 0.0837 ml
(b) 460.68 m
(c) 84 L
(d) 100￠
What is percentage?The denominator of a percentage (also known as a ratio or fraction) is always 100. Ram, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test.
For 6 1/5 % of 1.35 ml
⇒ 6 1/5 % = 31/5 %
⇒ 31/5 % of 1.35 ml
= 31/(5×100) × 1.35 ml
= 0.0837 ml
For 56 7/8 % of 810 m
⇒ 56 7/8 % = 455/8 %
⇒ 455/8 % of 810 m
= 455/(8×100) × 810 m
= 460.68 m
For 0.56% of 15 000 L
⇒ 0.56% of 15 000 L
= 0.56/100 × 15 000 L
= 84 L
For 2000% of 5￠
⇒ 2000% of 5￠
= 2000/100 × 5￠
= 100￠
Hence, the answers are as follows:
(a) 0.0837 ml
(b) 460.68 m
(c) 84 L
(d) 100￠
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Determine the equation of the circle graphed below
The equation of the circle graphed is given as follows:
(x + 3)² + (y - 4)² = 41.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The center in this problem has the coordinates given as follows:
(-3,4).
Hence:
(x + 3)² + (y - 4)² = r².
x = -1 and y = 9 is a point on the circumference of the circle, hence the radius of the circle is obtained as follows:
r² = (-1 + 3)² + (9 - 4)²
r² = 41.
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Robert is painting a house. He has 35 cans of paint. He has used 30 kinds of paint on the walls perit now he needs to paint the trim. If each section of the trim takes 1/2 can of paint, how many sections of trim can he paint? Show your answer as an inequality with symbols, in words, and with a number line. Make sure your solution makes sense for this situation.
Answer: Robert has 35 cans of paint - 30 cans of paint that he has already used = 35 - 30 = 5 cans of paint left.
Since each section of trim takes 1/2 can of paint, Robert can paint 2 sections of trim with 1 can of paint.
Therefore, Robert can paint 5 cans of paint * 2 sections of trim per can = 10 sections of trim.
The inequality can be written as 10 <= sections of trim <= 10.
In words, the number of sections of trim that Robert can paint is less than or equal to 10.
On a number line, this solution can be represented as follows:
[9, 10, 11, ...]
^
|
sections of trim
The solution makes sense because Robert has only 5 cans of paint left, so it is not possible for him to paint more than 10 sections of trim.
Step-by-step explanation:
how to filled in a unit circle?
One needs to connect the points where these arcs intersect the circle to form the desired shape. Finally, the angles need to be labeled to complete the unit circle.
A unit circle is a circle with a radius of 1. It is a tool used in trigonometry to measure angles and lengths of arcs. To calculate the length of an arc, one needs to know the angle it subtends at the center of the circle. The formula for finding this length is L = rθ, where L is the length of the arc, r is the radius, and θ is the angle subtended at the center. To fill in a unit circle, one needs to first calculate the lengths of the arcs subtended by the angles in the circle. Then, one needs to connect the points where these arcs intersect the circle to form the desired shape. Finally, the angles need to be labeled to complete the unit circle.
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Pls helppp!!! Multiple choice questions
Answer:
Step-by-step explanation:
a
Pls help its due today at 1:30
Note that using relationship 1 where
A = 50°; and
Y = 110°
Angle b = 70°; and
Angle c = 60°
This means that the triangle is a scalene triangle.
What is the rationale for the above response?Since a = 50° - Given; and
y = 110° - Given
to determine the m∠b, you must use the concept of sum of angles on a straight line. Sum of angles on a straight line must always equal 180°
Thus,
b = 180 - y
b = 180 - 110
b = 70°
To determine the m∠c, we used the sum of angles in a Δ theorem. This states that all angles in Δ must equal 180°
Since
a = 50° - Given; and
b = 70° - as derived above,
c = 180 - (a + b)
c = 180 - (50 + 70)
c = 180 - 120
c = 60°
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t = A/4b-D
Single step literal equations solve for A
The equation for A is A=4b(t+D) from t = A/4b-D.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is t = A/4b-D
t equal to A by four times of b minus D
The variables in the equation are A, b and D.
The formula is given for the variable t.
We need to change the formula to find the value of A.
We need to solve for A.
Add D on both sides
t+D=A/4b-D+D
The positive and negative D on right side of the equation will be cancelled and left with A/4b.
t+D/1=A/4b
Now apply cross multiplication
A=4b(t+D)
Hence, the equation for A is A=4b(t+D) from the t = A/4b-D.
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Radio tower are used for transmitting a range of communication services including radio television .the tower will either act as an antenna itself or support one or more antennas on its structure, including microwave dishes .They are among the tallest human made structure. There are 2 main types guyed and self supporting structures.
a) Height of section A is 15.21 m, b) the length of the wire structure from the point O to the top of section A is 51 units and the length of the wire structure from the point O to the top of section B is 41.56 units
What is height and distance?Height is the measurement of an item in the vertical direction, whereas distance is the measurement of an object in the horizontal direction from a certain location.
Given that an arrangement of wires and tower, making it as two right triangles, Let us consider the foot of the tower be C (refer to image attached)
Using the concept of height and distance, we will find the asked measurements,
a) What is the height of the section A?
CA = tan 45° × CO [tan 45° = 1]
CA = 36 m
Similarly,
CB = tan 30° × CO [tan 30° = 0.577]
CB = 20.78
Height of section A = CA - CB
= 15.21 m
b) What is the length of the wire structure from the point O to the top of section A?
OA = AC / sin 45°
OA = 36 / 0.707
OA = 51
Therefore, the length of the wire structure from the point O to the top of section A is 51 units
c) What is the length of the wire structure from the point O to the top of section B?
OB = BC / sin 30°
OB = 41.56
Therefore, the length of the wire structure from the point O to the top of section B is 41.56 units
Hence, the answers are a) Height of section A is 15.21 m, b) the length of the wire structure from the point O to the top of section A is 51 units and the length of the wire structure from the point O to the top of section B is 41.56 units
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The complete question is :-
Radio towers are used for transmitting a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure, including microwave dishes. They are among the tallest human-made structures. There are 2 main types: guyed and self-supporting structures.
On a similar concept, a radio station tower was built in two sections A and 6. Tower is supported by wires from a point O. Distance between the base of the tower and point O is 36 m. From point O, the angle of elevation of the top of section B is and the angle of elevation of the top of section A is
On the basis of the above information, answer any three of the following questions
*(i) What is the height of the section A?*
*(ii)What is the length of the wire structure from the point O to the top of section A?*
*(iii) What is the length of the wire structure from the point O to the top of section B ?*
May i get some help Fast please
Mr. Fernandez deposits $60,000 into an account that pays 2.5% annual interest compounded quarterly. What will be the balance after 20 years? Round to the nearest cent
:Answer: $90000
i = prt (interest = principle x rate x time)
i = 60000 x 0.025 x 20
i = $30000 interest
b = p + i (balance = principle + interest)
b = 60000 + 30000
b = $90000 balance
how to calculate standard deviation using ti-84
The steps to calculate standard deviation using a TI-84 calculator:
1.Enter the data into a list
2.Calculate the mean
3.Calculate the standard deviation
Here are the steps to calculate standard deviation using a TI-84 calculator:
1.Enter the data into a list: Press STAT, then ENTER, and then use the arrow keys to move to a list (e.g., L1, L2, etc.) and press ENTER. Enter the data into the list by typing each value followed by ENTER.
2.Calculate the mean: Press STAT, then RIGHT ARROW to select the CALC menu, and then select 1: 1-Var Stats. This will display a list of variables. Type the list name that contains the data and press ENTER. The calculator will display the mean value.
3.Calculate the standard deviation: From the same list in step 2, look for "Sx" or "σx" in the output. Sx stands for the sample standard deviation, and σx stands for the population standard deviation.
That's it! Now you know how to calculate standard deviation using a TI-84 calculator.
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lines as you need to collect the stars
Answer:
Step-by-step explanation:
Felix is making a pattern with tiles shaped like parallelograms. He needs 5 black tiles and 5 white tiles. The tiles cost $0.50 per cm². What is the total area of the tiles Felix needs to buy? A = ? cm² 27 2.4 cm 2 cm 4 cm. How much would the tile pattern cost?
The total area for the parallelogram-shaped tiles Felix needs to buy exists 80cm² at the price of $40.
What is meant by the area of parallelogram?In calculating the area of a parallelogram, the base exists multiplied by the height, in an exact way as computing the area of a rectangle.
here, we have,
Given that, the base of one parallelogram-shaped tile exists 4cm with a height of 2 cm.
Area of one parallelogram shaped tile = 4cm × 2cm
Area of one parallelogram-shaped tile = 8cm²
Total area for the 5black and 5white tiles = 10 × 8cm²
Total area for the 5black and 5white tiles = 80cm²
Therefore, Felix must buy a total area of 80cm² of 10 parallelogram-shaped tiles.
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adding rational expressions with unlike denominators
The main step to add rational expressions with unlike denominators is to take least common multiple of denominator and make them like before applying the required operation.
To simplify rational expression of unlike denominators first take the least common multiple of all the denominators.Now make the unlike terms as like terms .Now add or subtract the numerator as per the given operation.For example : ( 1 / 5 ) + ( 2 / 3 )Take least common multiple of 5 and 3 is 15.( 1/ 5 ) = 3/ 15 and ( 2 / 3) = 10 / 15Add 3/15 + 10 /15 = ( 3 + 10 ) / 15Result is 13 / 15.Therefore, the addition of rational expressions with unlike denominators is simplified by taking least common multiple.
The above question is incomplete, the complete question is:
Write steps for adding rational expressions with unlike denominators with example ?
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Assume that we have two events, A and B; that are mutually exclusive Assume further that we know P(A) = 0.30 and P(B) = 0.70. If an amount zero, enter "0". What is P(AnB)? What is P(AIB)? student in statistics argues that the concepts of mutually exclusive events and independent events are really the same_ and that if events are mutually exclusive they must be independent; Do You agree with this statement? Use the probability information in this problem to justify your answer. Select your answer because P(AIB) Select your answer P(A). What genera conclusion would You make about mutually exclusive and independent events given the results of this problem?
P(A∩B) = 0 (the probability of both events occurring is zero).
P(A|B) = 0.
No. The student's argument that mutually exclusive events are independent is incorrect.
How to find P(AnB) and P(AIB) of the event?If events A and B are mutually exclusive, then by definition they cannot occur at the same time.
Thus, P(A∩B) = 0 (the probability of both events occurring is zero).
Since events A and B are mutually exclusive, they cannot be independent. In fact, if two events are mutually exclusive, it means that the occurrence of one event precludes the occurrence of the other event, so they are completely dependent on each other.
To calculate P(A|B), we can use the formula:
P(A|B) = P(A∩B) / P(B)
Since P(A∩B) = 0 and P(B) = 0.70, we have:
P(A|B) = 0 / 0.70 = 0
This means that if we know event B has occurred (i.e., P(B) > 0), then the probability of event A occurring (i.e., P(A|B)) is zero. Therefore, events A and B are not independent.
The student's argument that mutually exclusive events are independent is incorrect. Mutually exclusive events are by definition dependent events.
In general, the concept of mutually exclusive events and the concept of independent events are not the same. Mutually exclusive events are dependent events, while independent events are events that do not depend on each other.
In this problem, the fact that events A and B are mutually exclusive means that they are dependent events, and this is reflected in the probability calculation for P(A|B), which is zero. Therefore, we can conclude that mutually exclusive events are not independent events.
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Determine whether the graph of each function opens upward or downward.
y=-6x²
y = 11x²
Answer: y=6x^2 opens downward. y=11x^2 opens upward
Step-by-step explanation:
-6 is a negative so it opens downward. 11 is a positive number so it will open upward.
If 0° ≤ Θ≤ 360°, then find angle(s) Θ.
1) sec Θ = undefined
Answer:
The secant function is undefined for angles where the cosine function equals zero, because dividing by zero is undefined. Therefore, we need to find the values of Θ where cos Θ = 0.
The cosine function equals zero at 90° and 270° (or π/2 and 3π/2 in radians), so we have:
cos 90° = 0, cos 270° = 0
Therefore, the angles that satisfy sec Θ = undefined are:
Θ = 90° + 360°k, Θ = 270° + 360°k
where k is an integer (positive, negative, or zero) that allows us to generate all possible angles in the range 0° ≤ Θ ≤ 360°.
So, the solutions for Θ are:
Θ = 90° + 360°k, Θ = 270° + 360°k
where k is an integer.
Step-by-step explanation:
I need some help please
The simplified answer in improper fraction is -3 ¹/₅.
What is the simplified equation?To simplify the equation we will solve the equation and obtain the value of x as shown below.
7 ( x + 1 ) = 1 - 2( 5 - x )
open the bracket by multiplying by 7 and 2
7x + 7 = 1 - 10 + 2x
collect similar terms as shown below;
7x - 2x = 1 - 10 - 7
5x = -16
x = -16 / 5
x = -3 ¹/₅
Thus, the simplified answer in improper fraction is obtained by finding the value of x.
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what is (fxg)(x)
f(x)=x^3-4x+2
g(x)=x^2+2
Answer: x^6+6x^4+8x^2+2
Step-by-step explanation:
Since g comes after f then you will take g's equation and plug it into the f equation so it would turn out to be if you plugged it in
(x^2+2)^3-4(x^2+2)+2 which would equal x^6+6x^4+8x^2+2
100 points and brainliest!!!!! 2 multiple choice questions!!!!!!! you dont have to answer both if you dont want to
Answer: answer to 2nd mcq
Step-by-step explanation:
For (-6, 0): -6 + 3(0) = -6 + 0 = -6 ≥ -8 [true]
For (-1, -2): -1 + 3(-2) = -1 - 6 = -7 ≥ -8 [true]
For (-5, -1): -5 + 3(-1) = -5 - 3 = -8 ≥ -8 [true]
find the values of x , y and z
Answer:
y+75°=180°[co interior angle]
or,y=180-75
•°•y=105
again,
y=z(alternate angle)
•°•z=105°
now
z+x+68°=180(sum of angle of triangle is 180)
or,105+68+x=180
or,x+173=180
or,x=180-173
•°•x=7
Find the circumference of this circle using 3 for π.
The circumference of the circle is 30 cm.
What is circumference measured in?Any unit for measuring length can be used to calculate the circumference, including feet, miles, metres, millimetres, etc.
By substituting 3 for, we can use the following formula to determine the circle's circumference:
C = 2πr
where r is the radius and C is the circumference.
We can observe from the provided diagram that the circle's radius is 5 cm. Thus, by changing r = 5 cm and = 3 in the formula, we obtain:
C = 2(3)(5) = 30
The circle's circumference is 30 cm as a result.
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What is 45% in decimal?
45% in decimal form is 0.45.
Percentages are a way of expressing a fraction or proportion of a whole, with the whole being represented by 100%. To convert a percentage to a decimal, we simply divide by 100.
In this case, we have 45%. Dividing 45 by 100 gives us 0.45, which is the decimal equivalent of 45%.
Decimal numbers are a base-10 system that uses the digits 0 through 9 to represent all possible values. They are commonly used in mathematics, finance, and science for their precision and ease of calculation.
Converting percentages to decimals is an important skill to have when dealing with calculations involving percentages, such as taxes, discounts, and interest rates.
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What is SSS in geometry
SSS" is when we know three sides of the triangle, and want to find the missing angles