Answer:
The ratios for sin a and cos a is [tex]\frac{7}{24}[/tex] .
Step-by-step explanation:
As given the expression in the question be as follow .
[tex]sin\ a = \frac{14}{50}[/tex]
[tex]cos\ a = \frac{48}{50}[/tex]
Thus the ratio of the sin a and cos a .
[tex]\frac{sin\ a}{cos\ a} = \frac{\frac{14}{50}}{\frac{48}{50}}[/tex]
[tex]\frac{sin\ a}{cos\ a} = \frac{14\times 50}{48\times 50}[/tex]
[tex]\frac{sin\ a}{cos\ a} = \frac{14}{48}[/tex]
Simplify the above
[tex]\frac{sin\ a}{cos\ a} = \frac{7}{24}[/tex]
Therefore the ratios for sin a and cos a is [tex]\frac{7}{24}[/tex] .
What is the equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10?
Rewrite the given equation in slope intercept form:
5 y = 10 – 2 x
y = - 0.4 x + 2
Since the two lines are parallel, therefore they have similar slope which is – 0.4, so the equation is:
y = - 0.4 x + b
Given that x = 5, y = -4, find for b:
-4 = - 0.4 (5) + b
b = -2
So the answer is:
y = - 0.4 x – 2
or
2 x + 5 y = - 10
Find the interest for each loan. $252 at 8% for 2 years: ________ $400 at 2% for 6 months:________ $5,000 at 3.5% for 1 year:___________ $6,240 at 10% for 9 months: ___________
The interest for each loan is $40.32, $4, $175 and $468 respectively.
What is the formula to find the simple interest?The formula to find the simple interest is S.I=P×T×R/100.
Where, P=Principal, T=Time period and R=Rate of interest.
With P=$252, T=2 years and R=8%.
Now, SP=252×2×8/100=$40.32
With P=$400, T=6 months (0.5 years) and R=2%.
Now, SP=400×0.5×2/100=$4
With P=$5000, T=1 year and R=3.5%.
Now, SP=5000×1×3.5/100=$175
With P=$6,240, T=9 months (0.75 years) and R=10%.
Now, SP=6,240×0.75×10/100=$468
Therefore, the interest for each loan is $40.32, $4, $175 and $468 respectively.
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Trevor is holding 5 red balloons and 4 blue balloons. He randomly selects a balloon to give his sister, and then he randomly selects a balloon to give his brother. Are two events dependent or independent? Explain.
A) Dependent. The two siblings will want the same color balloon.
B) Independent. Girls always want red and boys always want blue.
C) Independent. There are a set number of red balloons and blue balloons.
D) Dependent. When the first balloon is taken, it affects the ratio of red to blue balloons.
Answer:
Dependent. When the first balloon is taken, it affects the ratio of red to blue balloons.
Step-by-step explanation:
Whatever color the sister choses is irrelevant, eliminating answers A and B, but it does change the odds. If there are 5 red balloons and 4 blue balloons, if the sister is given a blue balloon, the odds of the brother receiving a red balloon increases (vis versa).
A cone is placed inside a cylinder as shown. The radius of the cone is half the radius of the cylinder. The height of the cone is equal to the radius of the cylinder. What is the volume of the cone in terms of the radius, r?
Answer:
Volume of the cone is [tex]\frac{1}{12}\pi r^{3}[/tex]
Step-by-step explanation:
Formula to find the volume of a cone is V = [tex]\frac{1}{3}\pi r^{2}h[/tex]
Here r is the radius of the cone and h is the height of the cone.
Since radius of cone = [tex]\frac{1}{2}(\text{Radius of cylinder})[/tex]
= [tex]\frac{r}{2}[/tex]
Height of the cone = radius of the cylinder = r
Now we put the values of radius and height of cone in the formula
Volume of cone = [tex]\frac{1}{3}\pi (\frac{r}{2})^{2}(r)[/tex]
= [tex]\frac{1}{3}\pi(\frac{r^{2}}{4})(r)[/tex]
= [tex]\frac{1}{12}\pi r^{3}[/tex]
Therefore, volume of the cone is [tex]\frac{1}{12}\pi r^{3}[/tex]
In a chess variant, a "lord" can move one space at a time, either upward, or to the right, or diagonally up and to the right. how many ways are there for a lord to move from the bottom left to top right corner of the 8 by 8 chessboard?
There are 48639 ways for a lord to move from the bottom left to top right corner of the 8 by 8 chessboard
Further explanationThe probability of an event is defined as the possibility of an event occurring against sample space.
[tex]\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }[/tex]
Permutation ( Arrangement )Permutation is the number of ways to arrange objects.
[tex]\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }[/tex]
Combination ( Selection )Combination is the number of ways to select objects.
[tex]\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }[/tex]
Let us tackle the problem.
This problem is similar to Pascal Triangle.
The Lord can move to the right or up in one way only.
We can put "1" in each box on the bottom and left to represent 1 possible movement.
To get the possibility of movement to another box, we will add the possibility of movement to the left, right, and diagonal squares as shown in Figure 1.
This process is repeated for the next box as shown in Figure 2.
Finally, after this process is repeated until the top right box, we get the results as shown in Figure 3.
There are 48639 ways for a lord to move from the bottom left to top right corner of the 8 by 8 chessboard.
Learn moreDifferent Birthdays : https://brainly.com/question/7567074Dependent or Independent Events : https://brainly.com/question/12029535Mutually exclusive : https://brainly.com/question/3464581Answer detailsGrade: High School
Subject: Mathematics
Chapter: Probability
Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation
If it costs a restaurant $11.90 to produce 2 white chocolate tortes and each torte is cut into 8 slices, how much does each slice cost to make?
Final answer:
To find the cost of each slice of white chocolate torte, divide the total cost to produce two tortes ($11.90) by the total number of slices (16), resulting in approximately 74 cents per slice.
Explanation:
Cost of Each Slice of White Chocolate Torte
To calculate the cost of each slice of white chocolate torte, we start by determining the total cost of producing the tortes. The restaurant's cost is $11.90 for 2 tortes, and each torte is cut into 8 slices. This means there's a total of 2 tortes × 8 slices/torte = 16 slices. Dividing the total cost by the number of slices gives us the cost per slice:
Total cost for 2 tortes: $11.90
Number of slices per torte: 8
Total number of slices: 2 tortes × 8 slices/torte = 16 slices
Cost per slice: $11.90 / 16 slices = $0.74375 per slice
Therefore, each slice costs approximately 74 cents to make.
F. one die is rolled 3 times. what is the chance of getting no 2's?
James buys a shirt and a pair of socks on sale for 25% off. if the price of the shirt before the sale was $24 and he spent a total of $24, what was the original price of the socks?
Answer:
The original price of socks was $8.
Step-by-step explanation:
James buys a shirt and a pair of socks on sale for 25% off.
The price of the shirt before the sale was $24 that means after discount the price was:
[tex]24-(0.25\times24)[/tex] = $18
And James paid a total of $24.
That means the price of socks after discount is = [tex]24-18[/tex] = $6
Let the original price of socks be x. And after 25% discount, it was for $6.
So, [tex]x-0.25x=6[/tex]
=> [tex]0.75x=6[/tex]
x = 8.
Hence, the original price of socks was $8.
I need help pleasss
Rammy has $9.60 to spend on some peaches and a gallon of milk. Peaches cost $1.20 per pound, and a gallon of milk costs $3.60.
The inequality 1.20x + 3.60 ≤ 9.60 models this situation, where x is the number of pounds of peaches.
Solve the inequality. How many pounds of peaches can Rammy buy?
A. x ≥ 8; Rammy can buy 8 pounds or more of peaches.
B. x ≤ 5; Rammy can buy 5 pounds or less of peaches.
C. x ≥ 5; Rammy can buy 5 pounds or more of peaches.
D. x ≤ 8; Rammy can buy 8 pounds or less of peaches.
Rammy can buy 5 pounds or less of peaches that is x ≤ 5. Then the correct option is B.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Rammy has $9.60 to spend on some peaches and a gallon of milk. Peaches cost $1.20 per pound, and a gallon of milk costs $3.60.
The inequality 1.20x + 3.60 ≤ 9.60 models this situation, where x is the number of pounds of peaches.
Then the number of pounds of peaches can Rammy buy will be
1.20x + 3.60 ≤ 9.60
1.20x ≤ 6
x ≤ 5
Rammy can buy 5 pounds or less of peaches that is x ≤ 5. Then the correct option is B.
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Which statement could describe the dog’s movement 5 seconds after the command was given
Answer:
The dog is rather running towards the trainer to receive a treat. So it is the second answer.
m∠WYX = (4x − 8)° and m∠WYZ = 10x°. If ∠WYX and ∠WYZ are complementary, find the measure of each angle.
Answer:
[tex]m\angle WYX=20^{\circ}[/tex]
[tex]m\angle WYZ=70^{\circ}[/tex]
Step-by-step explanation:
We have been given that [tex]m\angle WYX=(4x-8)^{\circ}[/tex] and [tex]m\angle WYZ=(10x)^{\circ}[/tex].
Since ∠WYX and ∠WYZ are complementary, so they will add up-to 90 degrees.
[tex]m\angle WYZ+m\angle WYX=90^{\circ}[/tex]
Substitute the given values:
[tex]4x-8+10x=90[/tex]
Combine like terms:
[tex]14x-8=90[/tex]
[tex]14x-8+8=90+8[/tex]
[tex]14x=98[/tex]
[tex]\frac{14x}{14}=\frac{98}{14}[/tex]
[tex]x=7[/tex]
Let us substitute [tex]x=7[/tex] in measure of each angle as:
[tex]m\angle WYX=(4(7)-8)^{\circ}[/tex]
[tex]m\angle WYX=(28-8)^{\circ}[/tex]
[tex]m\angle WYX=20^{\circ}[/tex]
Therefore, the measure of angle WYX is 20 degrees.
[tex]m\angle WYZ=(10x)^{\circ}[/tex]
[tex]m\angle WYZ=(10(7))^{\circ}[/tex]
[tex]m\angle WYZ=70^{\circ}[/tex]
Therefore, the measure of angle WYZ is 70 degrees.
What is 0.9 x 10 power of negative 2 in scientific notation
plz tell me what 3ab-9ab+7ab
The value of the equation 3ab - 9ab + 7ab is [tex]\boxed{ab}[/tex].
Further explanation:
There are two properties.
1. The property of addition or property of sum.
2. The property of subtraction.
3. The property of division.
4. The property of multiplication.
Given:
The equation is 3ab - 9ab + 7ab.
Explanation:
Consider the equation S = 3ab - 9ab + 7ab.
The equation contains the two variables that are “a” and “b”.
In the equation we have two operations one is addition and another is subtraction.
Solve the above equation to obtain the value of the equation.
First add 3ab and 7ab.
[tex]\begin{aligned}X&=3ab+7ab\\&=10ab\\\end{aligned}[/tex]
Now subtract 9ab from 10ab.
[tex]\begin{aligned}S&=10ab-9ab\\&=1ab\\&=ab\\\end{aligned}[/tex]
The value of S is ab.
Hence, the value of the equation 3ab - 9ab + 7ab is [tex]\boxed{ab}[/tex].
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Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Number System
Keywords: property, zero, eight, sum, addition, identity, shows, subtraction, number sentence, division, multiplication, variables.
Bailey’s Cakes and Pastries baked a three-tiered cake for a wedding. The bottom tier is a rectangular prism that is 18 centimeters long, 12 centimeters wide, and 8 centimeters tall. The middle tier is a rectangular prism that is 12 centimeters long, 8 centimeters wide, and 6 centimeters tall. The top tier is a cube with edges of 4 centimeters each. What is the volume of each tier and of the entire cake?
1,728 cubic centimeters
2,368 cubic centimeters
2,664 cubic centimeters
64 cubic centimeters
576 cubic centimeters
38 cubic centimeters
16 cubic centimeters
Pairs
the top tier
the middle tier
the bottom tier
the entire cake
Answer:
the top tier is 64 cubic centimeters
the middle tier is 576 cubic centimeters
the bottom tier is 1728 cubic centimeters
the entire cake is 2368 cubic centimeters
Which graph represents the function y – 3 = (x – 4)?
The graph represents the function y = (x - 1), as per linear equation.
What is a linear equation?A linear equation represents an equation that has one or multiple variables with the highest power of the variable is 1.
The given equation is:
y - 3 = x - 4
⇒ y = x - 1
Therefore, for x = 0, y = - 1
for x = 1, y = 0
for x = - 1, y = - 2
Therefore, the graph will pass through points (0, - 1), (1, 0), (- 1, - 2).
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Answer:
its A
Step-by-step explanation:
What is the length of side AC of the triangle?
Enter your answers in the boxes.
Answer:
[tex]AC=25[/tex]
Step-by-step explanation:
From the given figure, it can be seen that [tex]{\angle}A={\angle}C[/tex], thus ΔABC is an isosceles triangle.
Therefore,[tex]AB=BC[/tex]
⇒[tex]5x+5=7x-1[/tex]
Solving the above equation, we get
⇒[tex]5x-7x=-1-5[/tex]
⇒[tex]-2x=-6[/tex]
⇒[tex]x=3[/tex]
Now, substituting the value of x in AC, we have
⇒[tex]AC=6x+7[/tex]
⇒[tex]AC=6(3)+7[/tex]
⇒[tex]AC=18+7[/tex]
⇒[tex]AC=25[/tex]
Thus, the length of the side AC of the given triangle is 25 units.
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Write the converse, inverse, and contrapositive for the following conditional statement. Determine whether the contrapositive is true or false and give reason why it is true or false.
Conditional Statement: If two segments are congruent, then they have the same length.
1.) Converse:
2.) Inverse:
3.) Contrapositive:
4.) Determine if the conditional statement below is TRUE OF FALSE. If False, provide a counterexample?
Conditional Statement:
If m∠A is greater than an acute ∠B, then ∠A must be obtuse.
The converse, inverse, and contrapositive of the given statement are provided. They are logically consistent with the original statement, pointing to the synonymous relationship between congruence and identical length in segments. The additional statement about angles is also factual, as one greater than an acute angle is, by definition, an obtuse.
Explanation:1.) Converse: If two segments have the same length, then they are congruent.
2.) Inverse: If two segments are not congruent, then they do not have the same length.
3.) Contrapositive: If two segments do not have the same length, then they are not congruent.
The contrapositive is true because it is a logical inverse of the original statement, which is also true. In geometry, congruent means being of the same size and shape, which directly implies having the same length.
4.) The statement: 'If m∠A is greater than an acute ∠B, then ∠A must be obtuse' is true. An acute angle is one that is less than 90 degrees. If ∠A is greater than this, it must be between 91 and 180 degrees, which by definition, makes it an obtuse angle.
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what are the real roots of 2x^3-42x-40
Write 3 and 1 fraction 8 % in simplest form. Justify your answer
Name the corresponding part if RST WXY.
RS =
A. WY
B. WX
C. XY
Name the corresponding part if RST WXY.
Answer:
RS = WX
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1. Samuel bought a cement mixer for $54,205. The value of the cement mixer depreciated at a constant rate per year. The table below shows the value of the cement mixer after the first and second years:
Year 1 2
Value (in dollars) 47,158.35 41,027.76
Which function best represents the value of the cement mixer after t years?
f(t) = 47,158.35(0.87)^t
f(t) = 54,205(0.13)^t
f(t) = 47,158.35(0.13)^t
f(t) = 54,205(0.87)^t
Answer: [tex] f(x)=54205(0.87)^t[/tex]
Step-by-step explanation:
Given: The initial value of cement mixer (A) = $54,205
After one year, the value of mixer = $47,158.35
The constant rate of depreciation (b)=[tex]\frac{47158.35}{54205}=8.7[/tex]
The exponential function represent the value after depreciation of t years is given by :-
[tex]f(t)=A(b)^t\\\\\Rightarrow\ f(x)=54205(0.87)^t[/tex]
Hence, the function best represents the value of the cement mixer after t years will be
[tex] f(x)=54205(0.87)^t[/tex]
A rectangular porch has an area of 75 square feet.The length of the porch is 4 feet longer than the width.What is the width of the porch ?
The width of the porch is 5 feet.
Explanation:Let's denote the width of the porch as x. The length of the porch is then x + 4. The area of a rectangle is given by length x width. So, we can set up the equation x(x + 4) = 75 to find the width of the porch. Expanding the equation, we get x² + 4x = 75. Rearranging the equation, we have x² + 4x - 75 = 0. This quadratic equation can be factored as (x - 5)(x + 15) = 0. Since the width of the porch cannot be negative, we discard the x + 15 = 0 solution. Therefore, the width of the porch is 5 feet.
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In what form is the following linear equation written? 3x-2y=4. A. Point-slope
B. Standard
C. Rise-run
D. Slope-intercept
The answer is Standard.
What is a linear equation with instance?The same old shape for linear equations in variables is Ax+with the aid of=C. as an example, 2x+3y=five is a linear equation in popular shape. whilst an equation is given on this form, it is pretty clean to discover each intercept (x and y). This form is likewise very beneficial while fixing structures of two linear equations.
What are the three sorts of equations?There are three major types of linear equations: point-slope shape, well-known shape, and slope-intercept shape.
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A pizza parlor sold 38 pizzas during a dinner hour. If each pizza contained 8 slices, how many slices of pizza were sold?
A)46 slices
B)304 slices
C)305 slices
D)303 slices
99 subtracted from m is 299. What is the equation for the sentence shown?
The expression of the word problem can be written as M-99=299 where M is 398.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that 99 subtracted from m is 299. The expression for the word problem can be written as:-
M-99=299
M = 299 + 99
M = 398
Therefore, the expression of the word problem can be written as M-99=299 where M is 398.
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What is the value of the underlined digit in the following number?
3.69
9 hundredths
90 hundredths
9 tenths
9 thousandths
If y varies inversely with x and y=3 when x=4,what is the value of y when x=2?
busses run every 9 minutes starting at 6:00 am. you get to the bus stop at 7:16 am. how long will you wait for the bus
Mr. Staley has $62 to buy binders for his mathematics class. How many binders can he buy at $3 each?
Mr. Staley buy 20 binders for his mathematics class.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Mr. Staley has $62 to buy binders for his mathematics class.
And, The cost of each binders = $3
Now,
Since, The cost of each binders = $3
Hence, Number of binders = $62 / $3
= 20.67
Since, We get the remainder 2 and the quotient is 20.
So, we get;
Mr. Staley buy 20 binders for his mathematics class.
Thus, Mr. Staley buy 20 binders for his mathematics class.
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Dennis has 30 plums and 42 apricots. He wants to put the fruit in bags so that each bag has the same number of like fruit.
If Dennis wants to make baskets of fruit sells plums in bags of 12 and apricots in bags of 8, what is the minimum amount of baskets we can make if they are identical?
Please help this due tommorow for me. Thank you!