Answer: 21 cups of sugar, 7 cakes
Solve the following proportion:
3/5=x/35
Cross multiply:
5x=35(3)
5x=105
x=21 cups of sugar
3 cups of sugar= 1 cake
21 cups of sugar= x cakes
Cross multiply:
3x=21
21/3
7 cakes
construct a rectangle so that the diagonal is 6 cm and angle between them is 30 degree
Answer:
Let the length of the rectangle be x and the width of the rectangle be y.
Then, we can use the Pythagorean Theorem to find the value of x and y:
x2 + y2 = 62
x2 + y2 = 36
We can use trigonometry to find the value of x and y:
x = 6 sin 30°
y = 6 cos 30°
Therefore, the length of the rectangle is 6 sin 30° cm and the width of the rectangle is 6 cos 30° cm.
Step-by-step explanation:
First of all
You should draw a straight line which is AC=6cm
Then you should take the centre of the line and draw
30 degree in centre. Then you should draw straight line from
30 degree to bisect center point. Then take 3 cm in compass
and join their point.
Name the marked angle in 2 different ways.
J, K, I
Answer: Where is the image?
Step-by-step explanation:
alan's camping troop is raising money for a camping trip. the camping troop is selling boxes of popcorn, b, for $3.75 each. each camper starts with a credit of $25. to make the first deposit on the camping trip, alan total sales, f(b), needs to be at least $1100. write an inequality to represent the problem:
Answer:
$3.75b + $25 >= $1100
Step-by-step explanation:
10 points will be given
Answer : n⁸
:)
QUESTION 1
If we enter 6 debits of $25 each, the net effect on our account is how many
dollars (indicate if this is negative or positive amount by using a negative sign if the answer is negative).
Andariel went for a ride on her dune buggy in the desert. She rode east for 6 km, then turned 125° to the left for the second stage of her ride. After 5 minutes riding in the same direction, she turned to the left again, and from there travelled the 5.5 km straight back to her starting position.
How far did Andariel travel in the second section of her ride, correct to 2 decimal places?
Applying the laws of cosine, in the second section of her ride, Andariel traveled about 3.012 km, as rounded to 2 decimal places.
What is the law of cosines?The law of cosines is a mathematical formula used to determine the unknown length or angle of a triangle when two sides and an angle or all three sides are known.
Hence, we can think of it as trying to know Andariel's travel distance around a big triangle.
Thus to calculate, using the law of cosines, we have:
[tex]c^2 = a^2 + b^2 - 2ab*cos(C)[/tex]
Where in our case:
a = 6 km (distance traveled east)b = x km (distance traveled in the second section)C = 180 - 125 = 55 degrees (angle between a and b)c = 5.5 km (distance traveled straight back to the starting position)If we substitute the values above into the cosine formula, we get:
[tex](5.5)^2 = (6)^2 + (x)^2 - 2(6)(x)*cos(55)[/tex]
[tex]30.25 = 36 + x^2 - 12.0627x[/tex]
Simplifying and rearranging the equation further:
[tex]x^2 - 12.0627x + 5.75 = 0[/tex]
Applying the quadratic formula to simply:
[tex]x = (12.0627 ± sqrt(12.0627^2 - 415.75))/2[/tex]
x = 9.05 or x =3.012.
Remember, we are told Andariel turned left twice and ended up at her starting position, we know that she traveled in a closed loop.
Therefore, the distance she traveled in the second section of her ride must be less than 6 km (the distance she traveled east in the first section). Thus, the distance she traveled last or second section of her ride was 3.012 km.
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Express the trig ratios as fractions in simplest terms.
The trig ratios as fractions expressed in simplest terms is :cos(K) = 8 √(17)/17 , sin(L) = 9 √(17)/17
What are trigonometric ratios?Trigonometric ratios are mathematical relationships between the angles and sides of a right-angled triangle. They are ratios of the lengths of two sides of a right triangle in relation to one of its acute angles. The three primary trigonometric ratios are sine, cosine, and tangent, which are commonly denoted as sin, cos, and tan, respectively.
Sine: The sine of a right triangle angle seems to be the ratio of the length of the opposite side towards the length of the hypotenuse.
Cosine: The cosine of an angle in a right triangle is the ratio of the length of the adjacent side to the angle towards the length of the hypotenuse.
Tangent: In a right triangle, the tangent of an angle is really the ratio of the length of the side opposite the angle to the length of the adjacent side.
Given: A right angle triangle JKL, with angle J = 90 degrees, JL = sqrt(17), JK = 8, LK = 9
We can use the following trigonometric ratios:
To find the values of sin(L) and cos(K), we need to identify the opposite, adjacent and hypotenuse sides of the angles L and K.
For angle K:
cos(K) = adjacent/hypotenuse = JK/JL = 8/√(17)
To make the fraction easier to understand, multiply the numerator and denominator by √(17):
cos(K) = (8/√(17)) x (√(17)/√(17)) = (8 √(17))/17
Therefore, cos(K) = 8 √(17)/17
For angle L:
sin(L) = opposite/hypotenuse = LK/JL = 9/√(17)
To make the fraction easier to understand, multiply the numerator and denominator by √(17):
sin(L) = (9/√(17)) x (√(17)/√(17)) = (9 √(17))/17
Therefore, sin(L) = 9 √(17)/17
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hi i need help checking 12x + 9 = - 15
i know the answer ( x = 2) i just need help checking!!
well actually, your answer is -2
not positive 2
you have to take the 9, and subtract it from the other side (the -15), giving you -24
then you divide -24 by 12, giving you x=-2
this is true because when you plug it back in, you get 12 x -2 = -24
-24 + 9 = -15
The Position Vectors of points A,B,C with respect to the origin are 8i-10j, 2i+6j and -10i +4j respectively. If ABCN is a parallelogram find The Position Vector of N. /AN/ and /AB/. Acute angle between AN and AB
Answer:
The Position Vectors of points A,B,C with respect to the origin are 8i-10j, 2i+6j and -10i +4j respectively. If ABCN is a parallelogram find The Position Vector of N. /AN/ and /AB/. Acute angle between AN and AB
I NEED HELP ON THIS ASAP! PLEASE IT'S DUE TODAY!!!
a. Midpoint of AB, BC, CD, DA is (4,4), (0,-4), (-4,-4),(-4,4) respectively. b. polygon formed by connecting the consecutive midpoints. c. get a smaller square inside the square.
Describe Midpoint?In geometry, the midpoint refers to the point that is exactly halfway between two given points, lines, or line segments. It is the point that divides a line segment into two equal parts. The midpoint is also known as the half-way point.
The midpoint can be found using a variety of methods, but the most common one is by using the midpoint formula, which is:
Midpoint = [(x1 + x2)/2, (y1 + y2)/2]
Where (x1, y1) and (x2, y2) are the coordinates of the two points.
The midpoint is an important concept in many mathematical and scientific fields, including physics, engineering, and computer graphics. It is often used to determine the center of mass, the point of balance, or the halfway point in a process or journey.
a. We can use the midpoint formula to find the midpoint of each side of the square:
Midpoint of AB: ((0+8)/2, (8+0)/2) = (4,4)
Midpoint of BC: ((0+0)/2, (-8+0)/2) = (0,-4)
Midpoint of CD: ((-8+0)/2, (0-8)/2) = (-4,-4)
Midpoint of DA: ((-8+0)/2, (0+8)/2) = (-4,4)
b. Connecting the consecutive midpoints of each side of a square creates a smaller square inside the original square. We can see this by observing that the midpoints of opposite sides of a square form the vertices of a smaller square.
The polygon formed by connecting the consecutive midpoints of each side of the square is a square.
c. If we repeat the process of connecting consecutive midpoints one more time, we will get a smaller square inside the square formed in part (b). This smaller square will have vertices at the midpoints of the sides of the square formed in part (b). We can see this by observing that the midpoints of the sides of a square form the vertices of a smaller square inside that square.
So the polygon that would result from connecting the consecutive midpoints of each side of the polygon determined in part (b) is another square.
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please solve question with explanation *TEST REVISION*
Answer:
Step-by-step explanation:
You roll one die. What is the probability that you roll a 6?
Each rectangle is 16% longer than the original. Complete the table with the length of each new rectangle.
It seems that the table has not been provided in the question. However, I can provide a general method to complete the table based on the given information.
If each rectangle is 16% longer than the original, we can calculate the length of each new rectangle by adding 16% of the original length to the original length.
Let L be the original length of the rectangle. Then, the length of the new rectangle would be L + 0.16L = 1.16L.
Using this formula, we can calculate the length of the new rectangle for any given original length. For example, if the original length is 10 cm, then the length of the new rectangle would be:
1.16 x 10 cm = 11.6 cm
Similarly, we can calculate the length of the new rectangle for any other original length and complete the table accordingly.
Amari gathered a random sample of oranges in her town. She calculated data on different variables. For one of the variables that she collected, she constructed a bar graph.
Which of the following variables did she use?
Type of orange
Diameter of the oranges
Number of navel oranges
Price per pound of oranges
Answer:
no. four
Step-by-step explanation:
Price of the oranges per pound..
Answer:
Step-by-step explanation:
Type of orange
witch shapes have atleats one right angle ?? please anwser fluently
Answer:
top left and top right
Step-by-step explanation:
a right angle is 90⁰
during certain periods of time at an airport, passengers arriving at a security checkpoint have waiting times that can be modeled by a uniform distribution on the interval from 0 to 15 minutes. find the probability that a randomly selected passenger has to wait more than 10 minutes during one of these time periods.
There is a 1/3 chance, or around 0.333, that a randomly chosen passenger will have to wait longer than 10 minutes during one of these times.
What is probability?
Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.
Since waiting times follow a uniform distribution on the interval from 0 to 15 minutes, the probability density function (PDF) is:
f(x) = 1/15, for 0 ≤ x ≤ 15
The probability that a randomly selected passenger has to wait more than 10 minutes is:
P(X > 10) = ∫10¹⁵ f(x) dx
P(X > 10) = ∫10¹⁵ 1/15 dx (since f(x) = 1/15 for 0 ≤ x ≤ 15)
P(X > 10) = [x/15]10¹⁵
P(X > 10) = (15 - 10)/15
P(X > 10) = 5/15
P(X > 10) = 1/3
Therefore, there is a 1/3 chance, or around 0.333, that a randomly chosen passenger will have to wait longer than 10 minutes during one of these times.
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7+3p2Write the polynomial in standard form. Identify the degree and leading coefficient of the polynomial. Then classify the polynomial by the number of terms.
The degree of the polynomial is 2, and the leading coefficient is 3. The polynomial has two terms, so we classify it as a binomial.
What is the polynomial equation?
A polynomial equation is an equation in which the variable(s) are raised to non-negative integer powers and the coefficients are constants. In other words, it is an equation in which the terms involve only addition, subtraction, multiplication, and positive integer exponents.
The expression is 7 + 3p²
To write the polynomial in standard form, we need to arrange the terms in descending order of degree:
3p² + 7
hence, The degree of the polynomial is 2, and the leading coefficient is 3. The polynomial has two terms, so we classify it as a binomial.
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Part A: The line of best fit for this data is y = 5. 3x + 23. Use this equation to make a conjecture about the temperature of the water in the beaker if heated for 6 minutes. Explain your thinking
The line of best fit suggests that the temperature of the water in the beaker after 6 minutes will be approximately 91.8°C. This is because when x = 6, the equation gives us y = 91.8.
The line of best fit for this data is y = 5.3x + 23. This equation can be used to make a conjecture about the temperature of the water in the beaker if heated for 6 minutes. To calculate this, substitute x = 6 into the equation: y = 5.3(6) + 23. Simplifying this equation, we get y = 31.8 + 23, which gives us y = 54.8. This is the temperature of the water in the beaker if heated for 6 minutes, which is approximately 91.8°C. hence, The line of best fit suggests that the temperature of the water in the beaker after 6 minutes will be approximately 91.8°C. This is because when x = 6, the equation gives us y = 91.8.
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A triangle has a 50° angle and two sides that are each 4 centimeters in
Select True or False for each statement about this triangle.
True False
0
One of the angles in the triangle might be 65º.
The triangle might be an equilateral triangle.
Two of the angles in the triangle must measure 50°.
One of the angles in the triangle might be 60°.
C
0
Answer:
1.True
2.False
3.True
4.False
What is the pattern of the numbers 1,3,6,10,15,21,28,36. What is the 5857th triangular number?
the pattern of the numbers 1,3,6,10,15,21,28,36. What is the 5857th triangular number: The unit digit of the 5857th triangular number is 8.
A series of numbers known as triangular numbers might be demonstrated as the amount of a series of positive whole numbers. The condition Tn = (n(n+1))/2 yields the nth triangular number. The initial not many triangular numbers, for example, are 1, 3, 6, 10, 15, etc. Numerous numerical and non-numerical applications exist for triangular numbers. They can be found, for example, in the investigation of math, combinatorics, and number hypothesis. They are used in calculations for information looking and arranging in fields like software engineering, where they have reasonable applications.
The nth triangular number is given by the recipe:
Tn = (n(n+1))/2
For the given arrangement 1,3,6,10,15,21,28,36, the units digit are:
1, 3, 6, 0, 5, 1, 8, 6, 5, 5, 6, 8, 1, 5, 0, 6, 3, 1, 0, 0, 1, 3, 6, 0, 5, ...
The worth of 5857 is compatible with 7 modulo 10.
Consequently, the unit digit is the seventh number in the cycle above, which is 8.
Thus, the unit digit of the 5857th triangular number is 8.
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the complete question is:
Here is the sequence of numbers called triangular numbers: 1,3,6,10,15,21,28,36, Notice the pattern -the numbers increase by one more each time. What is the unit's digit of the 5857th triangular?
Every year, Martha and her sister attend 'The Nutcracker' at the Greenpoint Ballet. Last year, orchestra seating cost $60 per ticket. This year, each ticket was 15% cheaper. What was the cost of each ticket this year?
Answer:119.7
Step-by-step explanation:60 divided by 15%
9,857 + 310 ÷ 2 - 10 = ?
Answer:
10002
Step-by-step explanation: I think this is correct
Answer:
10002
Step-by-step explanation:
9,857 + 310 ÷ 2 - 10 = 10002
p+13+q+27 prove that 6=p and q=20
I need help on my math work
The specified details of the triangle, obtained using the segments joining the midpoints of the sides of the triangle ΔADG and trapezoid ACFG indicates that we get;
4. [tex]\overline{CE}[/tex] is a midsegment of ΔBDF
[tex]\overline{BF}[/tex] is the midsegment of trapezoid ACFG
5. CE = 12 cm, AG = 36 cm
6. m∠2 = 116°, m∠3 = 32°, m∠4 = 58°, m∠5 = 58°, m∠6 = 64°
What is the midpoint of a segment?The midpoint of a segment or the side of a triangle is a point that divides the segment into two parts of the same length.
4. The details of the diagram indicates that the segment [tex]\overline{CE}[/tex] is the midsegment of triangle ΔBDF
[tex]\overline{BF}[/tex] is the midsegment of trapezoid ACFG
5. [tex]\overline{CD}[/tex] is congruent to [tex]\overline{BC}[/tex] by the definition of the midpoint of [tex]\overline{BD}[/tex], similarly;
[tex]\overline{BC}[/tex] is congruent to [tex]\overline{AB}[/tex], by the definition of midpoint of [tex]\overline{AC}[/tex], therefore;
[tex]\overline{CE}[/tex] is the midsegment of triangle ΔBDF, therefore;
CE = (1/2) × BF
CE = (1/2) × 24 cm = 12 cm
CE = 12 cm
ΔBDF and ΔADG and ΔCDE are similar triangles, therefore;
[tex]\overline{BD}[/tex] = (2/3) × [tex]\overline{AD}[/tex]
Similarly, by the relationship between similar triangles we get;
[tex]\overline{BF}[/tex] = (2/3) × [tex]\overline{AG}[/tex]
BF = 24 cm, therefore;
24 = (2/3) × AG
AG = (3/2) × 24 = 36
AG = 36 cm
6. The length of a median of a right triangle, drawn from the right angled vertex, is half the length of the hypotenuse side.
Therefore; ΔACM and ΔABM are an isosceles triangles
m∠1 = m∠3 = 32°
m∠2 = 180° - (32° + 32°) = 116°
m∠2 = 116°
m∠3 = 32°
m∠4 = m∠5 = 90° - m∠1
m∠4 = m∠5 = 90° - 32° = 58°
m∠4 = 58°
m∠5 = 58°
m∠6 = 180° - (m∠4 + m∠5)
m∠6 = 180° - (58° + 58°) = 64°
m∠6 = 64°
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!!!TIMED!!! !!!Please help as fast as possible!!!
Find the value of a.
In right triangle LMN, angles L and M are complementary.
Find the mesure of angle L.
Answer:
Step-by-step explanation:
Select all the shapes below that show rotations of shape X
Answer:
A/C/E/F/G/H
Step-by-step explanation:
all of them have the same rotations there just have been turned around
What is the value of x?
Answer:
c
Step-by-step explanation:
Using what you know and learned about angles and triangles over the past few weeks, what is the measure of angle 6?
Answer:
158degrees
Step-by-step explanation:
2 = 68 ( vertically opposite)
4 = 90 (Vertically opposite)
6= 68 +90 = 158( exterior angle is sum of its opposite interior)
variable is normally distributed with mean and standard deviation . a. find the percentage of all possible values of the variable that lie between and . b. find the percentage of all possible values of the variable that are at least . c. find the percentage of all possible values of the variable that are at most .
The percentage of all possible values of the variable that lie between 10 and 16 is 97.71%, the percentage of all possible values of the variable that are at least 18 is 0.01% and the percentage of all possible values of the variable that are at most 8 is 0.01%.
Given that, variable is normally distributed with mean and standard deviation .
To find the percentage of all possible values of the variable that lie between and .
We can convert the given variable to standard normal variable using Z= (X- μ )/ σ
Therefore, we get, Z1 = (10- 12)/ 1 = -2 And Z2 = (16-12)/1 = 4
Thus, the probability of values that lie between 10 and 16 is given by
P(-2 ≤ Z ≤ 4) = P(Z ≤ 4) - P(Z ≤ -2) = 0.9999 - 0.0228 = 0.9771 = 97.71%.b)
To find the percentage of all possible values of the variable that are at least .Converting the given variable to standard normal variable using Z= (X- μ )/ σ, we get,
Z = (18-12)/1 = 6
The probability of values that are at least 18 is given by
P(Z ≥ 6) = 1- P(Z ≤ 6) = 1- 0.9999 = 0.0001 = 0.01%.c)
To find the percentage of all possible values of the variable that are at most .Converting the given variable to standard normal variable using Z= (X- μ )/ σ, we get,
Z = (8-12)/1 = -4
The probability of values that are at most 8 is given byP(Z ≤ -4) = 0.0001 = 0.01%.
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Notebooks at the school store were on sale for $3 off the regular price. Sam bought 4
notebooks on sale and paid a total of $28. Write an equation to find the regular
price of one notebook.
Answer: (28 / 4) + 3 = x; x = the regular price of a notebook not on sale.
Step-by-step explanation: The price of the notebook on sale is $7 and the price of a notebook regularly is $10 (not on sale). Therefore, the equation "(28 / 4) + 3 = x" explains how to come to that value.