The value of the expression 2/3 x -4/5 is -8/15.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
An expression,
2/3 x -4/5.
Here, we have to multiply the fraction.
So,
2/3 x -4/5,
= -8/15
Therefore, -8/15 is the value.
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A company fee pays a fee to use a song in their advertisement. There are 3 people in the band: the writer gets 4/12 of the fee, the singer gets 1/12 of the fee and the guitarist gets 1/12 of the fee.
What fraction of the fee does the whole band get??
Can u please help me I really need answers by this evening!!!
The whole band gets 1/2 of the fee.
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
The writer gets 4/12 of the fee, the singer gets 1/12 of the fee and the guitarist gets 1/12 of the fee, so the total fraction of the fee that the band members get is 4/12 + 1/12 + 1/12 = 6/12.
So, the whole band gets 6/12 or 1/2 of the fee. This means that half of the fee paid by the company goes to the band members, while the other half goes to other costs or expenses.
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Luke melts 200 grams of dark chocolate that contains 60% cocoa and mixes it with 200 grams of milk chocolate that contains 30% cocoa.
There are 180 grams of cocoa in the resulting mixture.
When the 200 grams of dark chocolate and the 200 grams of milk chocolate are mixed together, the amount of cocoa in the mixture is found by adding the amount of cocoa in each type of chocolate.
First, the amount of cocoa in the dark chocolate is calculated by multiplying the total weight of the dark chocolate by its cocoa percentage:
200 grams(0.60) = 120 grams
Next, the amount of cocoa in the milk chocolate is calculated in the same manner:
200 grams(0.30) = 60 grams
Finally, the total amount of cocoa in the mixture is found by adding the amount of cocoa in each type of chocolate:
120 grams + 60 grams = 180 grams
Therefore, the total amount of cocoa in the resulting mixture is 180 grams.
The problem seems incomplete, it must have been...
"Luke melts 200 grams of dark chocolate that contains 60% cocoa and mixes it with 200 grams of milk chocolate that contains 30% cocoa. How many grams of cocoa are in the resulting mixture?"
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Given sin x= 3/5 and sin y= 2/3 , where x and y are both in first quadrant ' Evaluate sin(x + y)
With the values sin x= 3/5 and sin y= 2/3 , where x and y are both in first quadrant, then after calculation sin(x + y) = (3 * √(7/9)) / 5 + 1/2.
To evaluate sin(x + y), we can use the identity sin(a + b) = sin a cos b + cos a sin b.
Given that sin x = 3/5 and sin y = 2/3, we have:
sin(x + y) = sin x cos y + cos x sin y
= (3/5) * √(1 - (2/3)^2) + (√(1 - (3/5)^2)) * (2/3)
= (3/5) * √(7/9) + (4/5) * (2/3)
= (3 * √(7/9)) / 5 + (8/15)
= (3 * √(7/9)) / 5 + (8/15)
= (3 * √(7/9)) / 5 + (16/30)
= (3 * √(7/9)) / 5 + (1/2)
= (3 * √(7/9)) / 5 + 1/2
So, sin(x + y) = (3 * √(7/9)) / 5 + 1/2.
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Satvik plans to take piano lessons. He has two payment options : He can pay $3 per lesson plus $18 per month or he can pay $60 for the a month of unlimited lessons. For what number of lessons is it cheaper for Satvik to pay $60 for the month? Write and solve the inequality that represents the situation.
The inequality that represents the situation when the number of lessons would mean that it is cheaper for Satvik to pay $60 for the month is x ≥ 15.
What is inequality?Inequality is a mathematical statement that two mathematical expressions are unequal.
Inequality is represented as either:
Greater than (>)Less than (<)Greater than or equal to (≥)Less than or equal to (≤)Not equal to (≠).Payment Plans:
Plan A = $18 + $3 per lesson
Plan B = $60
Let each lesson = x
Solving Equations:18 + 3x = 60
3x = 42
x = 14
x ≥ 15
Thus, if the number of lessons is greater than or equal to 15, it is cheaper for Satvik to pay under Payment Option B.
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Find the x intercept and the y intercept of each line. Express the answers as ordered pairs
Y=5x-10
The x-intercept and the y-intercept of each line include the following ordered pairs:
x-intercept = (2, 0).
y-intercept = (0, -10).
What is the x-intercept?In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).
What is y-intercept?In Mathematics, the y-intercept is sometimes referred to as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).
In this exercise, we would use an online graphing calculator to plot the linear function in order to determine the x-intercepts and y-intercepts as shown in the image attached below.
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a pin can contain 3 numerical digits. however, no digit can be repeated. how many pins are possible?
There are 720 possible pins, as no digit can be repeated. This is calculated by taking 3! (3 factorial) which is 3x2x1, which equals 6, and then multiplying it by 10, as there are 10 digits, 0-9.
A pin can contain 3 numerical digit and no digit can be repeated. To calculate the amount of pins possible, we use 3! (3 factorial), which is 3x2x1, equaling 6. Then, we multiply this by 10, as there are 10 digits, 0-9. Therefore, 6x10 = 720. In order to calculate 3! (3 factorial) we start by multiplying 3x2x1. This is because each digit has to be multiplied by the number of digits before it, as no digit can be repeated. The first digit has no digits before it, so it stays as 3. The second digit has one digit before it, so it is multiplied by 2. The third digit has two digits before it, so it is multiplied by 1. Therefore, 3x2x1 = 6. Then, we multiply 6 by 10, as there are 10 digits, 0-9. 6x10 = 720, which means there are 720 possible pins with no digit being repeated.
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Find the equation of the line parallel to -3x+2y=4 and passing through (-1,1)
The equation of the line parallel to the given line is 3x - 2y + 5 = 0.
What is the equation of a line?
The set of points that make up a line in a coordinate system is represented algebraically by a line's equation.
A straight line's equation is y=mx+c, where m denotes the gradient and c, commonly known as the y-intercept, is the height at which the line crosses the y-axis.
The given line is -3x+2y = 4
Then, [tex]y = \frac{3}{2}x + 2[/tex]
Slope [tex](m_1) = \frac{3}{2}[/tex] and [tex]c_1[/tex] = 2
Now, the slope of the parallel line [tex]m_2[/tex] = [tex]m_1[/tex] = 3/2
and passes through a point (-1,1)
Then,
the equation of the parallel line is
[tex]or, y-y_1=m(x-x_1) \\\\or, y-1=\frac{3}{2}(x+1) \\\\ or, 2y-2=3x+3\\\\or, 3x-2y+5=0[/tex]
Hence, the required equation of the line is 3x - 2y + 5 = 0.
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Abby is creating a stained glass windowpane that will be 6 inches by 8 inches. To make the
rectangular windowpane, Abby fuses together two triangles of colored glass. What is the
perimeter of one triangle?
In inches
The perimeter of the triangles will be 24 inches.
What is the perimeter of one of the triangles?
With two triangles she forms a rectangle of 6in by 8 in.
Then the triangles will have legs with these dimensions, and the last side (the hypotenuse) has a length equal to the diagonal of the rectangle:
diagonal = √( (6in)² + (8in)²) = 10in
Then the perimeter of te triangle is:
P = 10in + 8in + 6in = 24in
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Describe how to graph a point on the coordinate axis. Be as clear and specific as possible.
cross section math
i need help assap
Answer:
Step-by-step explanation: is half cut up so therefore the shape thats cut is a trapeziod
a square that is 10in. on a side is placed inside a rectangle that has a width of 13in. and a length of 19in. what is the area of the region inside the rectangle that surrounds the square?
The area of the region inside the rectangle that surrounds the square is 147 square in.
The side of square is 10 in
Area of square is = side x side
A = 10 x 10
A = 100 square in.
Therefore, Area of square is 100
The length of rectangle is 19 in and width of rectangle is 13in
area of rectangle = l x w
A = 19 x 13
A = 247 square in.
Area of rectangle is 247 square in.
To calculate area of the region inside the rectangle that surrounds the square,
= A[rectangle] - A[square]
= 247 - 100
= 147 square in.
Therefore, The area of the region inside the rectangle that surrounds the square is 147 square in.
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The center of a clock is at (0,0) in a coordinate system, and the minute hand is 10 inches long. Find the approximate coordinates of the tip of the minute hand at:
12:05 p.m.
12:45 p.m.
12:55 p.m.
Answer: At 12:00 p.m., the minute hand points straight up at (0,10).
At 12:05 p.m., the minute hand has rotated 30 degrees clockwise. The tip of the minute hand would be approximately:
x = 10 * cos(30) = 8.66
y = 10 * sin(30) = 5
So, the coordinates would be approximately (8.66, 5).
At 12:45 p.m., the minute hand has rotated 180 degrees. The tip of the minute hand would be approximately:
x = 10 * cos(180) = -10
y = 10 * sin(180) = 0
So, the coordinates would be approximately (-10, 0).
At 12:55 p.m., the minute hand has rotated 330 degrees clockwise. The tip of the minute hand would be approximately:
x = 10 * cos(330) = -5.77
y = 10 * sin(330) = -8.66
So, the coordinates would be approximately (-5.77, -8.66).
Step-by-step explanation:
find three consective integers if the sum of the first two is 51 more than the third integer
The three consecutive integers are 52, 53, 54, if the sum of the first two is 51 more than the third integer.
Consecutive Integer:
An integer is the number zero (0), a positive natural number (1, 2, 3, etc.), or a negative integer with a minus sign (−1, −2, −3, etc.). A negative number is the additive reciprocal of the corresponding positive number. In math language, the set of integers is often written as bold Z.
Consecutive integers are integers that follow each other in a regular counting pattern. When listing consecutive integers in a sequence, the difference between them is always fixed because there are no skipped digits between them. Consecutive integers are integers that follow each other in ascending order. The Sequential Integer Formula helps to find these integers for a given number or to determine whether a series of integers are consecutive.
According to the Question:
Let the three consecutive integers are
x , x+1, x+2
Since we have given that:
The sum of the first two is 51 more than the third,
Now,
(x + x + 1) - (x+2) = 51
⇒ 2x +1 -x - 2 = 51
⇒ x - 1 = 51
⇒ x = 52
So, the three consecutive integers are
52, 52+1, 52+2
Therefore,
52,53,54.
Hence, the integers are 52,53,54.
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in an emergency department, patients are assessed and placed in a categorical scale of 1, 2, 3, 4, or 5 based on the severity and urgency of their medical needs. how many dummy variables would be needed to include this categorical variable in a regression model?
Total 4 dummy variables would be needed to include this categorical variable in a regression model.
A regression analysis serves as the foundation for many types of forecasting and determining the effects on target variables. When you hear about studies in the news about fuel efficiency, pollution causes, or the effects of screen time on learning, a regression model is frequently used to back up their claims.
A dummy variable (also known as an indicator variable or simply dummy) in regression analysis is one that takes the values 0 or 1 to indicate the absence or presence of some classification impact that may be predicted to shift the result.
Total 4 dummy variables would be needed to include this categorical variable in a regression model.
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what is the probability that the first son of a woman whose mother's brother has lesch-nyhan syndrome will be affected?
If a woman's uncle has Lesch-Nyhan syndrome and her father carries the mutation, the probability of her first son being affected is 50%.
Lesch-Nyhan syndrome is an X-linked recessive genetic disorder, which means it is caused by a mutation on the X chromosome and is passed down through families primarily from affected fathers to their daughters. The probability that a son of a woman with an affected uncle (mother's brother) will be affected depends on the genetic status of the woman's father and the mother's X chromosome that she inherited from her mother.
If the woman's father does not carry the mutation, she will not carry the mutation herself and cannot pass it on to her children. In this case, the probability of her first son being affected is 0%.
If the woman's father carries the mutation, she has a 50% chance of inheriting the mutated X chromosome from her father and a 50% chance of inheriting a normal X chromosome from her mother. In this case, if the woman is a carrier of the mutation, her first son has a 50% chance of inheriting the mutation from her and being affected.
It's important to note that this is a simplified answer and that more complex genetic testing and counseling may be necessary to determine the specific risk in a particular family.
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Lynn works as a bus driver.
She is paid £10.80 per hour for the first 38 hours she works each week.
She is paid 25% more per hour for each extra hour she works.
One week, Lynn was paid £491.40
In total, how many hours did she work that week?
You must show your working.
Answer:
44h
Step-by-step explanation:
money earned per extra hour worked=100+25/100×10.80=13.50
amount earned if working for 38 hours=10.80×38=410.40
remaining money=491.40-410.40=81
number of extra hours worked=81÷13.50=6
total hours worked=38+6=44h
I’m circle Y, what is m
In circle Y, the measure of m∠SZT is equal to: B. 94°.
What is a chord of circle?In Mathematics, a chord of circle can be defined as a line segment that typically join any two (2) points of a circle.
Generally speaking, the inscribed angle of a circle is equal to half of the central angle of a circle. Mathematically, this is given by this mathematical expression:
m∠STR = 1/2(SYR)
m∠STR = 1/2(50)
m∠STR = 50°.
m∠TSU = 1/2(TYU)
m∠TSU = 1/2(72)
m∠TSU = 36°.
For m∠SZT, we have the following:
m∠SZT = 180° - (m∠STR + m∠TSU)
m∠SZT = 180° - (50 + 36)
m∠SZT = 180° - 84°
m∠SZT = 94°
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Q1. The lines y=x+1 & x+2y =8 cut the y-axis at P and Q respectively.
(a) Find the y-coordinates at P and Q.
a recipe calls for of a cup of milk for 12 cookies. how many cups of milk are needed to make 108 cookies?
In a linear equation, 9 cups of milk are needed to make 108 cookies .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
1 cup of milk makes 12 cookies.
If you wanted to make twice as many cookies (24), then you would need 2 cups.
If you wanted to make three times as many cookies (36), then you would need 3 cups.
1 cup / 12 cookies = X cups / 108 cookies
1/12 = X/108
X = 9
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What is the solution to 56x−13>113 ?
Responses
x>2518
x is greater than 25 eighteenths
x<2518
x is less than 25 eighteenths
x>2
x is greater than 2
x<2
Answer:
x > 2
Step-by-step explanation:
To solve the inequality 56x - 13 > 113, you can start by isolating the variable on one side of the inequality. Subtract 113 from both sides:
56x - 113 > 0
Next, add 113 to both sides:
56x > 113
Finally, divide both sides by 56:
x > 2
So the solution is x > 2, meaning that x can be any value greater than 2.
Answer:
[tex]x > \dfrac{9}{4} \\\\[/tex]
or
x > 2.25
This does not fit any of the provided answer choices. Either the inequality is copied wrong or the answer choices are copied wrong
Step-by-step explanation:
The inequality is 56x - 13 > 113
Add 13 to both sides:
56x - 13 + 13 = 113 + 13
56x > 126
Divide by 56 both sides
[tex]\dfrac{56x}{56} > \dfrac{126}{56}[/tex]
Reducing the above fraction to lowest by dividing numerator and denominator by 14 to get:
[tex]x > \dfrac{126 \div 14}{56\div 14}\\\\x > \dfrac{9}{4}[/tex]
None of your answer choices fit. So not sure whether the inequality given is incorrectly copied/pasted or the answer choices are.
The closest this comes to is x > 2 but the inequality will not be satisfied for any value of x between 2(excluded) and 2.25(included)
The exterior angle of a regular polygon measures 8 ∘ . How many sides does the polygon have?
The number of sides in the regular polygon would be -
n{sides} = 360/K.
What is a polygon?In geometry, a polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.
The bounded plane region, the bounding circuit, or the two together, may be called a polygon.
The segments of a polygonal circuit are called its edges or sides.
Given is that exterior angle of a regular polygon measures {K°}.
In a regular polygon, the size of each exterior angle =
m∠E = 360° ÷ n{Sides}
m∠E = 360°/n{Sides}
n{sides} = 360°/m∠E
n{sides} = 360/K
Therefore, the number of sides in the regular polygon would be -
n{sides} = 360/K.
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What is the circumference if the radius is 8?
Also explain please.
Answer:
16π
Step-by-step explanation:
π is the ratio between the circumference and the diameter. 2x8xπ = 16π
Answer: 16π, or 50.2655
Step-by-step explanation:
Circumference is calculated using πd, where d is the diameter. Since d = 2r, where r is the radius, this can be rewritten as circumference = π2r. Plugging our radius, 8, into the equation gives us π(2)(8), which simplifies to 16π, or 50.2655.
A painter starts with a blank 30 inch by 18 inch piece of rice paper. The painter wants to leave a uniform border x inches wide along the outer edges so that the painting can be framed. Write a polynomial in standard form that represents the area of paper that can be painted
A polynomial in standard form that represents the area of paper that can be painted is equals to the x² - 48x + 540.
We have, a painter wants to painting on a paper. He starts with a blank piece of rice paper with dimensions 30 inch by 18 inch .
The total length of paper, l = 30 inch
Total width of paper , w = 18 inch
Area of paper = l× w = 18× 30
= 540 inch²
Now, painter wants to leave a uniform border.
The width of border = x inches
length of border = x inches
and paint the remaining paper. So, the length of paper which is painted = l - x
= (30 - x) inches
Width of paper which is painted = w - x = ( 18 - x) inches
Now, the painted area of paper, A = painted length × painted width
= (30 - x)( 18- x)
= 540 - 18 x - 30x + x²
= x² - 48 x + 540
which is a standard polynomial form of painted area.
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Help me please
Please help me i need help with this
Answer:
Please send a clearer image so I can answer question 1 and 3
Step-by-step explanation:
2: "One of the parallel lines can be translated so that it lands on the other line. After that, you would notice that the angles of the two lines have exactly the same measurement. Therefore, the interior and exterior angles of two parallel lines cut by transversal are equal."
5: The angles congruent to <8 are <6, <4, and <2
6: The value of m<6 = 70°
7: The equation to find <8 = 180 - <1
The measure m<8 = 85°
8: The value of x must be equal to 34
Please solve for all blanks
The blanks are filled as follows
coordinate key feature does the coordinate justification
make sense
(-7.565, 0) it is a key feature yes This is a zero
(0, 37) it is a key feature yes it is the y - intercept
(6, 46) it is a key feature yes it is the vertex
The constraint is that the range will always be
{y | y ∈ R ≤ 46}
What is vertex of quadratic function?The vertex of a quadratic function is the highest or lowest point of the parabolic graph of the function, which is also the turning point of the graph.
The vertex of a quadratic function in the form of y = ax^2 + bx + c is given by the coordinates
(x, y) = (-b/(2a), -(b^2 - 4ac)/(4a)).
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NO LINKS!! Please help me with this.
The value of the given ratio for triangle ACE and BCD include the following:
1.)25/16
2.)10/7
3.) 1
4.) 14/19
5.) 4/5
6.) 4/1
7.) 16/5
8.) 29/45
How to calculate the ratio of the given sides of the triangles?In order to calculate the ratio, the value of the missing parts of the triangle should be calculated such as line BD, and CE, by the use of Pythagorean formula.
The Pythagorean formula = c² = a² + b²
For first triangle:
BC = a = 20
CD = b = 14
BD = c = ?
C² = 20²+14²
c² = 400+196
c² = 596
C = √596
C = 24 = BC
The ratio of the given sides of the triangle include the following:
1.) = AC = 20+5 = 25; CE = 25/16
2.) BC:CD = 20/14 = 10/7
3.) BD:AE = 24/24 = 1
4.) CD:CE = 14/19
5.) BC:AC = 20/25 = 4/5
6.) BC:AB = 20/5 = 4/1
7.) CD:DE = 16/5
8.) perimeter of BCD = 20+14+24 = 58; perimeter of ACE =25+24+21 = 70
The ratio of perimeter of BCD:ACE = 58/70 = 29/45
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2. What is the product of -2x^3+x and x^3-3x-4 ?
(a) Show your work.
(b) Is the product of 2x^3+x-5 and x^3-3x-4 equal to the product of x^3-3x-4 and -2x^3+x-5 ? Explain your answer.
(a) To find the product of -2x^3+x and x^3-3x-4, we can use the distributive property of multiplication:
(-2x^3 + x)(x^3 - 3x - 4)
= -2x^3(x^3) - 2x^3(-3x) - 2x^3(4) + x(x^3) - x(-3x) - x(4)
= -2x^6 + 6x^4 - x
= -2x^6 + 6x^4 - x
Therefore, the product of -2x^3+x and x^3-3x-4 is -2x^6 + 6x^4 - x.
(b) No, the product of 2x^3+x-5 and x^3-3x-4 is not equal to the product of x^3-3x-4 and -2x^3+x-5. This is because the order of the factors in a multiplication expression affects the outcome. When we expand both products using the distributive property, we get different expressions:
(2x^3 + x - 5)(x^3 - 3x - 4) = 2x^6 - 5x^3 - 3x^2 - 17x + 20
(x^3 - 3x - 4)(-2x^3 + x - 5) = -2x^6 + 11x^4 + 13x^3 - 3x^2 - x + 20
So the expanded expressions are not equal. Therefore, the two products are not equal.
Please help me find the value of x and y
The value of x and y are 25 and 25√3 respectively.
What are Trigonometric Functions?Trigonometric functions are defined as the real functions which are simply the functions of an angle of a triangle. They are basically the periodic functions which relate an angle in a right angled triangle to the ratios of the length of two sides.
Given a right angled triangle and an angle 30°.
Length of hypotenuse = 50 units
Sine of an angle in a right angled triangle is the ratio of opposite side to hypotenuse.
sin (30°) = x / 50
x = sin (30°) × 50
x = (1/2) × 50
x = 25 units
Cosine of an angle in a right angled triangle is the ratio of adjacent side to hypotenuse.
cos (30°) = y / 50
y = cos (30°) × 50
y = (√3 / 2) × 50
y = 25√3 units
Hence the value of x is 25 units and the value of y is 25√3 units.
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Find the perimeter of the area of the rectangle 15 cm and 12 CM
a) perimeter: 54 cm,area:180cm 2 (squared)
b)perimeter:54cm, area:108 cm 2 (squared)
c)perimeter: 42 cm, area 180 cm2 (squared)
d) perimeter: 42 cm, area:108 cm2 (squared)
(a) perimeter:54cm, area:108 cm 2 (squared)
The perimeter of a rectangle with length 15 cm and width 12 cm is 54 cm (2 * (15 + 12) cm).
The area of the rectangle is 180 square cm (15 * 12 cm^2).
Measure the length (l) and the width (w) of the rectangle. In this case, the length is 15 cm and the width is 12 cm.
To find the perimeter, calculate the sum of twice the length and twice the width. This is done by multiplying each measurement by 2 and then adding them together: 2 * l + 2 * w. In this case, the calculation is 2 * 15 + 2 * 12 = 30 + 24 = 54 cm.
To find the area, multiply the length and the width: l * w. In this case, the calculation is 15 * 12 = 180 cm^2.
The perimeter of the rectangle is the sum calculated in step 2. In this case, the perimeter is 54 cm.
The area of the rectangle is the product calculated in step 3. In this case, the area is 180 cm^2.
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Carlos can write 3 to 4 pages in his journal in 3/4 hour. If he writes for 5 hours, what's a reasonable number of pages he can write in that time?
A) between 10 and 15
B) between 15 and 20
C) between 20 and 25
D) between 25 and 30
A reasonable number of pages Carlos can write in 5 hours is between 20 and 25 pages.
Therefore the answer is C.
First, we need to find the average number of pages Carlos can write in one hour by dividing the number of pages he can write in 3/4 hour by 3/4:
(3 to 4 pages) / (3/4 hour) = 4 to 5.33 pages per hour
So, we can see that Carlos can write between 4 to 5.33 pages in an hour.
Next, we'll multiply that number by 5 to find the number of pages he can write in 5 hours:
(4 to 5.33 pages/hour ) * 5 hours = 20 to 26.65 pages
Since we can say that, he reads between 20 and 26 pages.
Therefore, the reasonable number of pages Carlos can write in 5 hours is between 20 and 25, which corresponds to option C.
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