Answer:
x = 17/32
Step-by-step explanation:
Firstly, you want to simplify by combining like terms:
4x(3+5)—10 = 4 · 3 + 5 – 10
32x—10 = 7
Add ten to both sides:
32x - 10 = 7
+10 +10
32x = 17
Divide both sides by 32:
32x = 17
/32 /32
32 divided by 32x makes x
so we get x = 17/32
(we dont divide 17/32 since we would get an irrational number (0.53125))
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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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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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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What happens when a distribution is skewed to the right?
Answer:
Step-by-step explanation:
A distribution is said to be skewed to the right (also known as positively skewed) if it has a longer tail on the positive side of the mean or median, indicating that the majority of the data values are on the lower end and there are a few large values on the higher end. This results in a mean that is larger than the median.
In other words, the right skew occurs when the tail of the distribution is located to the right side of the peak, which pulls the mean to the right as well. The presence of outliers or extreme values on the right side of the distribution can cause right skew.
Right-skewed distributions are common in data sets that represent measurements or quantities that have a minimum value of zero or a natural lower limit, but can increase without bound, such as income, wealth, and height.
In summary, when a distribution is skewed to the right, it has a higher mean and lower median compared to a symmetrical distribution, and the majority of the data is concentrated on the left side.
Does someone mind helping me with this problem? Thanks!
By evaluating the linear equation we can see that the complete table is:
x| -4 -2 0 2 4
y| 17 13 9 5 1
How to compete the table?Here we have a linear function:
y = -2x + 9
And we want to complete the given table, to do so, we just need to evaluate the linear function in the given values of x.
if x = -2
y = -2*-2 + 9 = 4 + 9 = 13
if x = 0
y = -2*0 + 9 = 9
if x = 2
y = -2*2 + 9 = 5
if x = 4
y = -2*4 +9 = 1
Then the complete table is:
x| -4 -2 0 2 4
y| 17 13 9 5 1
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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 ?*
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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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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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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Independent Practice
Graph the following function. Then, write the domain and range.
f(x)=3*
*HINT: Make a table first
Based on the graph of this exponential function, the domain and range are as follows;
Domain = {-∞, ∞}.
Range = {0, ∞}.
What is a domain?In Mathematics, a domain is the set of all real numbers for which a particular function is defined.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-∞, ∞}.
Range = {0, ∞} or {y|y > 0}.
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Ruby says that a quadrilateral is a square if and only if it is a rectangle. Is this a true biconditional statement?.
The statement "a quadrilateral is a square if and only if it is a rectangle" made by Ruby is a true biconditional statement in mathematical terms.
A quadrilateral is a four-sided shape that can have different properties based on its sides and angles.
Ruby says that a quadrilateral is a square if and only if it is a rectangle. This statement can be written as:
(Q is a square) if and only if (Q is a rectangle)
To understand if this statement is a true biconditional statement, we need to examine the definition of a square and a rectangle and how they relate to each other.
A square is a type of quadrilateral where all four sides are equal in length and all four angles are equal (90 degrees). In other words, a square is a rectangle that has four equal sides.
A rectangle is a type of quadrilateral where all four angles are equal to 90 degrees. This means that the opposite sides are parallel and equal in length.
Based on the definitions, we can conclude that the statement "a quadrilateral is a square if and only if it is a rectangle" is a true biconditional statement.
This means that if a quadrilateral is a square, it is also a rectangle and vice versa. If a quadrilateral is not a square, it cannot be a rectangle.
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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
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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Use the rules of equations and Inverse operations to solve the equation.
3x² = 48
04
0 +4
0 -4
0+2
Answer:
Below
Step-by-step explanation:
3 x^2 = 48 divide both sides of the equation by 3 to get
x^2 = 16 Now, sqrt both sides
x = + 4 or -4
The change in the number of students at a high school in Naples was the same from 2007 to 2013 as it was from 2013 to 2019.
Which type of function best models the data?
Answer: The type of function that best models the data would depend on the actual change in the number of students and the specific data points for each year. However, if the change in the number of students was the same for each time period, a linear function would be a good candidate for modeling the data. This function would have the form y = mx + b, where m represents the rate of change (the change in the number of students over a certain time period) and b is the y-intercept (the number of students at the starting year).
Step-by-step explanation:
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
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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lines as you need to collect the stars
Answer:
Step-by-step explanation:
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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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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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!
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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Show that the quadrilateral with the vertices $H(1,\ 9),\ J(4,\ 2),\ K(5,\ 2),\ L(8,\ 9)$H(1, 9), J(4, 2), K(5, 2), L(8, 9) is a trapezoid. Then decide whether it is isosceles.
The midpoints of the given quadrilateral, AB = CD and AD = BC, are equal.
What is meant by quadrilateral vertices?Vertices are the angular intersections of two sides or edges. The four vertices of a quadrilateral are A, B, C, and D. (iii)Angles. A quadrilateral's angle is the inclination between its two sides.A closed quadrilateral is a form of polygon with four sides, four vertices, and four angles. Four non-collinear points are joined to create it. Quadrilaterals' interior angles add up to a constant 360 degrees.A polygon's vertex is a point where the sides or edges of the object or two rays or line segments meet. Vertices is the plural of a vertex.Let P represent the quadrilateral's vertices (-4,2) Q (2,6): Let A, B, C, and D be the midpoints of P(-4,2) and Q. R(8,5) and S (9,-7) (2,6)
Consequently, A's coordinates are
[tex]$\left(\frac{-4+2}{2}, \frac{2+6}{2}\right)=\left(\frac{-2}{2}, \frac{8}{2}\right)=(-1,4)$[/tex]
Coordinates of B are
[tex]$\left(\frac{2+8}{2}, \frac{6+5}{2}\right)=\left(\frac{10}{2}, \frac{11}{2}\right)=\left(5, \frac{11}{2}\right)[/tex]
Coordinates of c are
[tex]$\left(\frac{8+9}{2}, \frac{5-7}{2}\right)=\left(\frac{17}{2}, \frac{-2}{2}\right)=\left(\frac{17}{2},-1\right)[/tex]
coordinates of D are [tex]$\left(\frac{9-4}{2}, \frac{7+2}{2}\right)=\left(\frac{5}{2}, \frac{-5}{2}\right)$[/tex]
Distance between A and B
[tex]$& d(A, B)=\sqrt{(-1-5)^2+\left(4-\frac{11}{2}\right)^2}=\sqrt{36+\frac{9}{4}}=\sqrt{\frac{153}{4}} \\[/tex]
Simplify,
[tex]$& d(C, D)=\sqrt{\left(\frac{17}{2}-\frac{5}{2}\right)^2+\left(-1+\frac{5}{2}\right)^2}=\sqrt{36+\frac{9}{4}}=\sqrt{\frac{153}{4}} \\[/tex]
Then,
[tex]$& d(A, D)=\sqrt{\left(-1-\frac{5}{2}\right)^2+\left(4+\frac{5}{2}\right)^2}=\sqrt{\frac{49}{4}+\frac{169}{4}}=\sqrt{\frac{218}{4}} \\[/tex]
We get,
[tex]$& d(B, C)=\sqrt{\left(5-\frac{17}{2}\right)^2+\left(\frac{11}{2}+1\right)^2}=\sqrt{\frac{49}{4}+\frac{169}{4}}=\sqrt{\frac{218}{4}}[/tex]
As a result, the given quadrilateral's midpoints, AB = CD and AD = BC, are equal.
It is a parallel gramme as a result.
The complete question is :
A quadrilateral has the vertices at the point (−4,2),(2,6),(8,5) and (9,−7). Show that the mid-point of the sides of this quadrilateral are the vertices of a parallelogram.
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what does 2x - 2 ≥ -8 equal to
Answer: -3
Step-by-step explanation:
A rectangle with side lengths y and z has perimeter 2y+2z. Elizabeth bought a rectangular painting of the seashore and wants to decorate the edges with sky-blue ribbon. The painting is 2 feet long and 1.5 feet wide.
What is the perimeter of the painting?
The perimeter of the painting 7 feet.
What is Perimeter?Perimeter is the distance around the edge of a shape. To find the perimeter by adding up the side lengths of various shapes.
Given:
A rectangle with side lengths y and z has perimeter 2y+2z.
Elizabeth bought a rectangular painting whose length = 2 ft and width = 1.5 ft.
So, the perimeter of the painting
= 2l+ 2w
= 2(2)+ 2(1.5)
= 4 + 3
= 7 feet
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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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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.
Which one of these ordered pairs show a combination of 12 coins from the graph?
Which one of these ordered pairs show a combination of 12 coins from the graph?
(10, 2)
(5, 5)
(10, 5)
(10, 10)
The ordered pair that show a combination of 12 coins from the graph is (10, 2)
How to determine the ordered pairfrom the question, we have the following parameters that can be used in our computation:
The graph
The purple line represents the combination of 12 coine
Using the above as a guide, we have the following:
The equation is
x + y = 12
From the list of options, we have
(10, 2): 10 + 2 = 12
Hence, the ordered pair is (10, 2)
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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:
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