Each fraction must first be transformed into its simplest form.Hence, The problem can be solved in this way.
Second, improper fractions ought to be added to an integer and a proper fraction to get their original improper fraction. The second step is usually optional because it only improves the aesthetics of the situation. If you take this action, it is wise to add the expression's fractions and integers separately.After determining the lowest common multiple of each fraction's denominator, each fraction must then be represented by multiplying a suitable number by the denominator and numerator, ensuring that all fractions have the same denominator.The solution is a fraction with the sum of the numerators in the expression as the numerator and the L.C.M. as the denominator.To know more about Fractions here
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Two certificates of deposit pay interest rates that differ by 3%. For the first CD, the money is invested for a year and earns $50C interest. For the second CD the same amount of money invested earns $655 in a year. What is the interest rate of the first CD account (rounded to the nearest tenth)?
The rate interest of the first CD account is 5%.
What is the rate of interest?An interest rate tells you how high the cost of borrowing is, or high the rewards are for saving. So, if you're a borrower, the interest rate is the amount you are charged for borrowing money, shown as a percentage of the total amount of the loan.
Given that, two certificates of deposit pay interest rates that differ by 3%.
Let 1000 be the amount of principal invested. Let n/100 be the rate of interest on the first CD and n+3/100 be the amount paid on the second CD.
1000(n/100)=50
1000(n+3/100)=655
10n=50
n=5%
So, n+3= 8%
Therefore, the rate interest of the first CD account is 5%.
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(−∞,5]ก(−3, ∞)
simplify the following compound intervals
The solution of the interval will be;
⇒ (- 3, 5]
What is Number line?Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.
Given that;
The interval is,
⇒ (- ∞, 5] ∩ (- 3, ∞)
Now,
Since, The interval is,
⇒ (- ∞, 5] ∩ (- 3, ∞)
Hence, The solution of the interval is,
⇒ x ∈ (- ∞, 5] and x ∈ (- 3, ∞)
⇒ x ∈ (- 3, 5]
Thus, The solution of the interval = (- 3, 5]
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The captain of a ship must use extreme caution when approaching an iceberg, because only 0.125 of it is above the surface of the water. What percent of the iceberg is NOT visible above the water?
The percent of the iceberg which is not visible above the water could be 12.5%.
What is percentage ?
percentage can be defined as the product of ratio of value and total value and 100 .
Given, the captain of a ship must use extreme caution when approaching an iceberg, because only 0.125 of it is above the surface of the water
so the percent of the iceberg which is not visible could be
0.125 * 100 = 12.5 %
Hence , the percent of the iceberg which is not visible above the water could be 12.5%.
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Bright Blocks toy company sells sets of building blocks. The Beginner Builder set has 40 large blocks and 25 small blocks. The Mega Maker set has the same ratio of large blocks to small blocks, but it comes with 100 small blocks.
How many large blocks are in the Mega Maker set?
There are approximately 63 large blocks in the Mega Maker set.
What is a Ratio?
Ratio is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division. In ratios the dividend is called the 'antecedent' and the divisor is called the 'consequent'.
The ratio of large to small is 40 to 25
To find the ratio of the big block for the the mega maker will be;
40 : 25 in its simplest form 8 : 5
100 : X
X = (5 x 100) / 8
X = 500 / 8
X = 62.5
62.5 is not a whole number so it can be approximated to the nearest whole number which is 63.
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Answer: 160
Step-by-step explanation:
A shopkeeper bought rice at 42₹ and sold them at ₹ 45 . If he sold 15 kg of rice . Find his profit
The profit is 45 ₹ if he sold 15 kg of rice.
Cost of rice for the shopkeeper, c = 42 ₹
Price of the rice sold, p = 45₹
hence, the profit per kg of rice, P = p - c = 45 - 42
P = 3₹ per kg of rice
therefore, the profit of 15kg
= 15 × 3 ₹
Total profit = 45 ₹
Therefore, the profit is 45 ₹ if he sold 15 kg of rice.
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How many numbers can you make by using the digits 2 5 and 3?
There are six possible numbers that can be made by using the digits 2, 5, and 3: 253, 325, 235, 352, 523, and 532.
1. 253: This number is formed by using the digits 2, 5, and 3 in that order.
2. 325: This number is formed by rearranging the digits 2, 5, and 3 to form a new number.
3. 235: This number is formed by rearranging the digits 2, 5, and 3 to form a new number.
4. 352: This number is formed by rearranging the digits 2, 5, and 3 to form a new number.
5. 523: This number is formed by rearranging the digits 2, 5, and 3 to form a new number.
6. 532: This number is formed by rearranging the digits 2, 5, and 3 to form a new number.
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Count the significant digits in each of these measurements: measurement number of significant digits 90500 kg 7.1 x 10 ml - 3.0 x 10 moi 0.004300
The number of significant figures that the digits given have are;
1) 3
2) 2
3) 4
What are the significant digits?Significant figures are defined as the number of digits in a value, which is often a measurement, that contributes to the degree of accuracy of the value.
Some of the rules for counting significant figures are;
- All non-zero digits and any zeros contained between non - zero digits count e.g 300042 has 6 significant digits
- Leading zeros don't count e.g 0.000254 has only 3 significant figures.
- Trailing zeros count if there is a decimal point e.g 0.0002500 has 4 significant figures.
- Trailing zeros will not count if there is no decimal point e.g 180000 has only 2 significant figures.
1) 90500 Kg; This has only 3 significant figures when applying rule 1 and 4 above.
2) 7.1 x 10 ml = 71 ml; This clearly has 2 significant figures.
3) 0.004300; Applying rule 3 above, this has 4 significant figures.
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Mrs. Malatlian selects a simple random sample of 28 seniors from the 300 seniors at her school and finds that 20 of
them are planning to participate in the school's annual capture the flag game. She wants to construct a confidence
interval for p= the proportion of all seniors who plan to participate in the game. Which condition has she failed to meet,
if any?
a) The sample was selected at random.
b) np ≥ 10
c) n(1-p) ≥ 10
d) The sample size is less than 10% of the population size.
e) All conditions are met.
Mrs. Malatlian has failed to meet the condition that np ≥ 10.
What is meet?Meet is an event or gathering of people who have come together for a common purpose or to discuss specific topics. It typically involves a group of people who come together in person or virtually to exchange ideas and information. Meetings are often used as a platform for brainstorming, collaboration, problem solving, decision-making, and/or making plans. They can also serve as a platform for networking, team building, and connecting with others. Meetings can also be used to disseminate information or provide updates to a group.
Specifically, the sample size (n) is 28 and the proportion of those who plan to participate in the game (p) is 20/28 = 0.71.
Thus, np = 28(0.71) = 19.88 which is less than 10.
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After donovan gives mabel 6 pears, she has (x 6) pears. if mabel gives one-third of her pears to nelson, how many pears, in terms of x, does nelson have?
Nelson has 2+x/3 pears.
Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in every area of mathematics, including coordinate geometry, calculus, and trigonometry.
In algebra, symbols are used, and operators are used to connecting the symbols to one another. It is more than just a mathematical idea; it is a skill that we all utilize on a regular basis without even being aware of it.
After Donovan gives Mabel 6 pears, she has 6+x pears. If Mabel gives one-third of her pears to Nelson, he gets (1/3) * (6+x) pears = (2+x/3) pears. Therefore, Nelson has 2+x/3 pears.
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GEOMETRY PLEASE HELP ME
Answer:
4
Step-by-step explanation:
This is a right triangle.
To find the value of x we can use Pythagoras theorem:
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
a and b are the legs which are given as 3 and √7 respectively and c is the hypotenuse.
[tex] {3}^{2} + ( { \sqrt{7} )}^{2} = {c}^{2} [/tex]
Calculate the square value of expressions[tex]9 + 7 = {c}^{2} [/tex]
Add the numbers[tex]16 = {c}^{2} [/tex]
Find the root for both sides4 = c
Answer:
Answer is written in the link
Step-by-step explanation:
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When ABC is dilated by a scale factor of 2?
If we perform a dilatation by a scale factor of 2 on triangle ABC and resulting in triangle A’B’C’ where A’(-4,4), B’ (-4,6), and C’ (2,4), then the original coordinates of triangle ABC are A(-2,2), B(-2,3), C(1,2)
A coordinate plane is a system that graphs and describes the position of points and lines. It consists of horizontal (x) and vertical (y) axes.
We can perform dilatation for a point or line in a coordinate plane system based on specific criteria.
Dilation is a form of image transformation that produces a new image, which is larger, or smaller, based on a certain scale factor.
The rule of dilatation:
[tex]D_{k}[/tex](x,y) = (kx, ky)
where [tex]D_{k}[/tex] is the resulting point and k is the scale factor.
Now take a look at the vertices of triangle A’B’C’ and apply the rule:
A'(x,y) = (kx, ky)
(-4,4) = (2x, 2y)
so x = -2, and y = 2 ⇒ A (-2,2)
B'(x,y) = (kx, ky)
(-4,6) = (2x, 2y)
so x = -2, and y = 3 ⇒ B (-2,3)
C'(x,y) = (kx, ky)
(2,4) = (2x, 2y)
so x = 1, and y = 2 ⇒ C (1,2)
Thus, the original coordinates of triangle ABC are A(-2,2), B(-2,3), C(1,2)
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Geometry find length of third side
Answer:=4
Step-by-step explanation:√(√7)²+3²
√7+9
√16
=4
Which expression is equivalent to (32−4x)44(32−4x)?
a)x+32
b)-x-8
c)-4x-8
d)-x+8
e)28x-1
Answer:
b
Step-by-step explanation:
Which statement is true of all equilateral triangles?
Every equilateral triangle is an isosceles triangle.
The sides of an equilateral triangle are all different
the length of the legs of the triangle is always different
An equilateral triangle has equally long sides.
An equilateral triangle is a special type of triangle where all three sides are equal in length. This means that all three angles of the triangle measure 60 degrees each. This also means that all three sides of the triangle are of equal length, and that the triangle is also an isosceles triangle (since two of the sides are equal). Therefore, the statement "All sides of an equilateral triangle are equal in length" is true for all equilateral triangles.
All equilateral triangles have three sides of equal length, with all three angles measuring 60 degrees each, and they are also isosceles triangles.
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The right triangle on the right is a scaled copy of the right triangle on the left. Identify
the scale factor. Express your answer as a fraction in simplest form.
A scaled-down version of the right triangle on the left, where the fraction is 54, is shown on the right.
What is fraction in simplest form ?A scaled-down version of the right triangle on the left can be seen in the right triangle on the right. The scaling factor should be recognised as a whole integer or simplest possible fraction. In order to relate these two sides, we will choose the number 15 since it is a finer number than 254 and is therefore the longer of the two sides that correlate to the number 12.
And since we're moving in this direction and getting bigger, the scale factor needs to be greater than 1 . Consider the difference between the original corresponding length of 12 and the new length of 15, which is 15. Because 15 is three times the original length of 12, the difference between 15 and 12 may be simplified. Though your response is 54.
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Here scale factor is 33/25
33/25 = 1.32
How do you calculate scale factor?The ratio between comparable measurements of an object and a representation of that object is known as a scale factor in mathematics. The copy will be larger if the scaling factor is a whole number. A fractional scaling factor means that the duplicate will be smaller. The scale factor is the ratio of the length of a side of one figure to the length of the corresponding side of the other figure. Here larger triangle side is 33 smaller triangle side is 25Then scale factor = larger triangle measurement / smaller triangle measurementThen answer is 33/25The fractional value of 33/25 = 1.32To learn more about scale factor refer to:
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The area of a rectangle is x2+4x-5, and the with is x-1. Find the rectangle's length
The length of the rectangle is, (x + 5).
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
We have to given that;
The area of a rectangle is (x² + 4x - 5).
And, The width of rectangle = (x - 1)
Now, We know that;
In a rectangle;
⇒ Area of rectangle = Length × Width
Substitute given values,
⇒ (x² + 4x - 5) = Length × (x - 1)
⇒ (x² + 5x - x - 5) = Length × (x - 1)
⇒ x(x + 5) - 1 (x + 5) = Length × (x - 1)
⇒ (x + 5) (x - 1) = Length × (x - 1)
⇒ (x + 5) (x - 1) / (x - 1) = Length
⇒ Length = (x + 5)
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Find all points where the function is discontinuous.
A) x=0, x=2
B) x=-2, x=0. x=2
C) x=-2, x=0
D) x=2
E) x=-5
F) x=-6, x=0
G) x=10
The function is discontinuous at x=-2, x=0, x=2. The correct answer is B.
A function is said to be discontinuous at a point if it does not have a well-defined value at that point or if the left-hand limit and the right-hand limit at that point are not equal. Discontinuity can be classified as removable or non-removable. Without knowing the specific function, it is not possible to determine exactly where it is discontinuous. However, From the options provided B) x=-2, x=0, x=2 is the only option that lists all possible discontinuous points.
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Please I need help
I will mark u the brainliest
a) The equation in the form of x is x + x+2 + x+4 = 648.
b) The three consecutive even integers are 214, 216 and 218.
What is an integer?
The number zero (0), a positive natural number (1, 2, 3, etc.), or a negative integer denoted by a minus sign (1, 2, 3, etc.) are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.
It is given that the sum of three consecutive even integers is 648.
The smallest integer is taken to be x.
Since, the numbers are consecutive and even then the numbers will be x, x+2 and x+4
So, according to the question the equation will be -
x + x+2 + x+4 = 648
Solve the equation to get the value of x -
3x+6 = 648
3x = 648 - 6
3x = 642
x = 214
Hence, the three numbers are x = 214,
x+2 = 214+2 = 216
x+4 = 214+4 = 218.
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Which table represents a direct variation function
Table 4 represents a direct variation function.
What is the direct variation?
A pair of variables that are related when one is a constant multiple of the other. For instance, two variables are said to be in proportion when one affects the other. b = ka is the equation if b is directly proportional to a. (where k is a constant).
Here,
We have given a table and we have to determine which table represents a direct variation function.
A function of direct variation fulfills the following form:
y = kx<br/>
Where,
x: independent variable
y: dependent variable
k: proportionality constant (k> 0)
The value of k is given by:
k = (y₂ - y₁)/(x₂ -x₁)<br/>
Now, we substitute value
k = (12.5 - 5)/(5 -2)<br/>
k = 2.5>0
Hence, table 4 represents a direct variation function.
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Analysis of data from a statistical study shows a linear relationship in the data with a correlation coefficient of -0.524. Which statement best summarizes this result? O There is a strong positive correlation between the variables. O There is a strong negative correlation between the variables. O There is a moderate positive correlation between the variables.O There is a moderate negative correlation between the variables.
The best summarizes for the result is:
O There is a moderate negative correlation between the variables.
CORRELATION COEFFICIENTA correlation coefficient measures the strength and direction of the relationship between two variables. The coefficient ranges from -1 to 1, with -1 indicating a perfect negative correlation, 0 indicating no correlation, and 1 indicating a perfect positive correlation.
In this case, the correlation coefficient of -0.524 indicates a moderate negative correlation between the variables. This means that as the value of one variable increases, the value of the other variable decreases, and vice versa. The negative sign indicates that the relationship is negative, and the absolute value of the coefficient (0.524) indicates that the relationship is moderate in strength.
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What is the exact value of sin 165⁰? a. startfraction startroot 6 endroot startroot 2 endroot over 4 endfraction b. startfraction 2 startroot 2 endroot minus startroot 6 endroot over 4 endfraction c. startfraction startroot 6 endroot minus startroot 2 endroot over 4 endfraction d. startfraction startroot 2 endroot minus 2 startroot 6 endroot over 4 endfraction
Answer:
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
sin
(
15
)
Split
15
into two angles where the values of the six trigonometric functions are known.
sin
(
45
−
30
)
Separate negation.
sin
(
45
−
(
30
)
)
Apply the difference of angles identity.
sin
(
45
)
cos
(
30
)
−
cos
(
45
)
sin
(
30
)
The exact value of
sin
(
45
)
is
√
2
2
.
√
2
2
cos
(
30
)
−
cos
(
45
)
sin
(
30
)
The exact value of
cos
(
30
)
is
√
3
2
.
√
2
2
⋅
√
3
2
−
cos
(
45
)
sin
(
30
)
The exact value of
cos
(
45
)
is
√
2
2
.
√
2
2
⋅
√
3
2
−
√
2
2
sin
(
30
)
The exact value of
sin
(
30
)
is
1
2
.
√
2
2
⋅
√
3
2
−
√
2
2
⋅
1
2
Simplify
√
2
2
⋅
√
3
2
−
√
2
2
⋅
1
2
.
Tap for more steps...
√
6
−
√
2
4
The result can be shown in multiple forms.
Exact Form:
√
6
−
√
2
4
Decimal Form:
0.25881904
…
4) Randy can buy 6 gallons of gas for $18 or 7 gallons of gas for $21. How much do you think he would pay for 8 gallons of gas
Randy can buy six gallons of gas for $18. He would pay $24 for 8 gallons of gas.
We can see that he pays three dollars per gallon by dividing the per gallon. 18 dollars/6 gallons equals 3 dollars, and 21 dollars/7 gallons equals 3 dollars. So, if he pays the same $3 per gallon rate, he will pay $24.
Fuel costs can be estimated using this calculator based on trip distance, vehicle fuel efficiency, and gas prices in various units. Gas prices fluctuate, but for most drivers, it is always a significant expense.
If you use mpg (miles per gallon), the total gas consumption formula is as follows: as an example The total amount of fuel required is 500 / 20 = 25 gallons if the distance is 500 miles and the consumption rate is 20 miles per gallon
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which story can be represented by the equation y=x−2/3x? Select the correct choice. A Jada walked x miles. Priya walked 2/3 as far as Jada.Jada walked x miles. Priya walked 2 thirds as far as Jada. B Kiran worked x hours. Lin worked 2/3 more than that.Kiran worked x hours. Lin worked 2 thirds more than that. C Elena drank x ounces of water. Tyler drank 2/3 of that.Elena drank x ounces of water. Tyler drank 2 thirds of that. D Noah bought x pounds of cheese. Clare bought 2/3 less than that.
The story that can be represented by the equation y=x−2/3x is D. Noah bought x pounds of cheese. Clare bought 2/3 less than that.
How to illustrate the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
Since Noah bought x pounds of cheese. Clare bought 2/3 less than that. This will be:
x - 2/3x
Therefore, the correct option is D.
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What is the slope of this table
Answer: y+2.50
Step-by-step explanation:
Order the set of numbers (2.2, 2, 1/5, 2.25, v5) from greatest to least.
Answer:
2.25, v5, 2.2, 2 1/5, 2
Step-by-step explanation:
v5 = 2.24
I NEED HELP WITH THIS MATH EQUATION ASAP TYSM
Answer:
y = 2A - x
Step-by-step explanation:
Given equation,
→ A = (x + y)/2
Now the value of y will be,
→ A = (x + y)/2
→ (x + y)/2 = A
→ x + y = 2A
→ [ y = 2A - x ]
Hence, answer is y = 2A - x.
Find the surface area of the Rectangular Prism. 9 mm 3 mm 13 mm
Using the formula for the surface area of the rectangular prism and with the provided values, The answer is 366 [tex]mm^2[/tex].
What is a rectangular prism?A rectangular prism is a three-dimensional geometric shape that has six rectangular faces. It has three pairs of parallel faces, with each pair being a rectangle of the same size and shape. The opposite faces of a rectangular prism are also parallel and congruent. It is also known as a cuboid. In addition to having three pairs of parallel, congruent rectangle faces, a rectangular prism also has three pairs of parallel edges and four pairs of congruent vertices. It can also be defined by its length, width, and height, which are the measurements of the three rectangular faces.
What do you mean by surface area?The surface area of a three-dimensional object is the total area of all of its faces or surfaces. It is the sum of the areas of all the faces of an object. For example, the surface area of a rectangular prism is the sum of the areas of all six of its rectangular faces. To find the surface area, you would add up the area of the length x width of each face. In a rectangular prism, the surface area can be calculated by:
Surface Area = 2lw + 2lh + 2wh
Where l is the length, w is the width and h is the height.
Surface Area = 2lw + 2lh + 2wh
l=9mm
w=3mm
h=13mm
surface area = 2·(3·9+13·9+13·3) = 366[tex]mm^2[/tex].
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m/ABC = 40°and BD is the angle
bisector of ZABC
B
3x-1
34-2x
A
3y+6
D
5y-18
m/ABD = [? ]°
The value of ∠ABD is 20°.
What is bisector of angle?In geometry, an angle bisector is a line that divides an angle into two equal angles. The term "bisector" refers to a device that divides an object or a shape into two equal halves. An angle bisector is a ray that divides an angle into two identical segments of the same length.
Given ∠ABC = 40°
and BD is angle bisector,
so ∠ABD = ∠DBC
∠ABD = 3x - 1
∠DBC = 34 - 2x
∠ABD = ∠DBC
3x - 1 = 34 - 2x
3x + 2x = 34 + 1
5x = 35
x =7
∠ABD = 3x - 1
∠ABD = 3(7) - 1
∠ABD = 20°
Hence value of ∠ABD = 20°.
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2x-3y 2 12
Line: Solid or Dashed?
Shade: Above or Below?
Are these points solution: (0,2)
(-2,-2)
For the given inequality: 2x - 3y ≥ 12.
m = 2
b = -4
Line: Solid
Shade: Below
(0, 2) is not the solution for the given inequality.
(3, 4) is the solution for the given inequality.
(-2, -2) is not the solution for the given inequality.
What is linear inequality?
An inequality is a mathematical statement comparing two values or expressions, usually involving one of the following relational operators: < (less than), > (greater than), <= (less than or equal to), >= (greater than or equal to), or != (not equal to). The solution to inequality is a set of values that make the inequality true.
The given inequality, 2x-3y>=12, is a linear inequality in two variables. The slope of the line represented by this inequality is the coefficient of x, which is 2. The y-intercept of the line is not explicitly given in the inequality, but we can find it by setting x = 0 and solve for y.
To find the y-intercept, we set x = 0 and substitute it into the inequality:
2(0) - 3y >= 12
-3y >= 12
y <= -4
and by observing the graph, we can say that
Line: Solid
Shade: Below
(0, 2) is not the solution for the given inequality.
(3, 4) is the solution for the given inequality.
(-2, -2) is not the solution for the given inequality.
Hence,
For the given inequality: 2x - 3y ≥ 12.
m = 2
b = -4
Line: Solid
Shade: Below
(0, 2) is not the solution for the given inequality.
(3, 4) is the solution for the given inequality.
(-2, -2) is not the solution for the given inequality.
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Crystal buys headphones that are on a sale with a 40% discount. If Crystal pays $24 for the headphones with the discount, what is the full price of the headphones
Answer:$40
Step-by-step explanation:
Find the price of the item after the discount was applied.
Find the discount percentage that was applied to the price.
Divide the discount percentage by 100.
Subtract that number from 1.
Divide the after-discount price by that number.
This number is the original price of the item, pre-discount.
