Let $a$, $b$, $c$ be the three sides of a triangle, and let $\alpha$, $\beta$, $\gamma$, be the angles opposite them. If $a^2+b^2=1989c^2$, find
Answers
If a, b, c be the three sides of a triangle , let α, β, γ be the angles opposite them and if a² + b² = 1989c² , the value of [tex]\frac{Cot \gamma}{(Cot \alpha + Cot \beta)}[/tex] = 994 .
Let the sides of the triangle ABC be a , b and c .
let h be the altitude of the triangle that meets the side AB at point c ,
From the figure ,
we can write , [tex]Cot\alpha + Cot\beta = \frac{c}{h}[/tex] ;
let area of triangle ABC = K ,
So , h = 2K/c ,
⇒ [tex]Cot\alpha + Cot\beta = \frac{C^{2} }{2K}[/tex] ,.....equation(1)
By following the Similar pattern we can write the similar equations ,
we have ,
⇒ [tex]Cot\beta + Cot\gamma = \frac{a^{2} }{2K}[/tex] ,.....equation(2)
⇒ [tex]Cot\gamma + Cot\alpha = \frac{b^{2} }{2K}[/tex] ,....equation(3)
On adding the equation(2) and equation(3) and subtracting it from the equation(1) , and dividing it by 2 ,
we get ,
⇒ [tex]cot\gamma = \frac{a^{2} + b^{2} - c^{2} }{4K}[/tex];
So , the value of [tex]\frac{Cot \gamma}{(Cot \alpha + Cot \beta)}[/tex] = [tex]\frac{\frac{a^{2} +b^{2} -c^{2}}{4K} }{\frac{c^{2} }{2K} }[/tex];
⇒ [tex]\frac{a^{2} +b^{2} -c^{2} }{2c^{2} }[/tex] ;
On substituting the value of a² + b² = 1989c² ,
we get ,
⇒ [tex]\frac{1989c^{2} - c^{2} }{2c^{2} }[/tex];
⇒ 1988/2 = 994 .
Therefore , the value of [tex]\frac{Cot \gamma}{(Cot \alpha + Cot \beta)}[/tex] = 994 .
The given question is incomplete , the complete question is
Let a, b, c be the three sides of a triangle, and let α, β, γ be the angles opposite them. If a² + b² = 1989c² , find the value of [tex]\frac{Cot \gamma}{(Cot \alpha + Cot \beta)}[/tex] .
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We use the law of cosines to find the angles in the triangle, substitute [tex]$a^2+b^2=1989c^2$[/tex], and add them together to get[tex]$\cos\alpha + \cos\beta + \cos\gamma = 1989$.[/tex]
We can use the law of cosines to find the angles in the triangle:
[tex]$$\cos\alpha = \frac{b^2 + c^2 - a^2}{2bc}$$[/tex]
[tex]$$\cos\beta = \frac{a^2 + c^2 - b^2}{2ac}$$[/tex]
[tex]$$\cos\gamma = \frac{a^2 + b^2 - c^2}{2ab}$$[/tex]
Substituting, we get:
[tex]$$\cos\alpha = \frac{1989c^2 - c^2}{2bc}$$[/tex]
[tex]$$\cos\beta = \frac{1989c^2 - b^2}{2ac}$$[/tex]
[tex]$$\cos\gamma = \frac{1989c^2 - a^2}{2ab}$$[/tex]
Therefore,
[tex]$$\cos\alpha + \cos\beta + \cos\gamma = \frac{1989c^2}{2bc} + \frac{1989c^2}{2ac} + \frac{1989c^2}{2ab} = \frac{1989c^2}{2bc} + \frac{1989c^2}{2ac} + \frac{1989c^2}{2ab} = 1989$$[/tex]
We can use the law of cosines to find the angles in the triangle: [tex]$\cos\alpha = \frac{b^2 + c^2 - a^2}{2bc}$[/tex], [tex]$\cos\beta = \frac{a^2 + c^2 - b^2}{2ac}$[/tex], and [tex]$\cos\gamma = \frac{a^2 + b^2 - c^2}{2ab}$[/tex]. Since [tex]$a^2+b^2=1989c^2$[/tex], we can substitute this value into the equations to get [tex]$\cos\alpha = \frac{1989c^2 - c^2}{2bc}$, $\cos\beta = \frac{1989c^2 - b^2}{2ac}$, and $\cos\gamma = \frac{1989c^2 - a^2}{2ab}$[/tex]. The cosines of the angles of a triangle can be found using the law of cosines. We are given that [tex]$a^2 + b^2 = 1989c^2$[/tex], so we can use this to find the cosines of the angles of the triangle. We substitute this into the law of cosines and solve for the cosines of the angles, which gives us [tex]$\cos\alpha$[/tex], [tex]$\cos\beta$[/tex], and [tex]$\cos\gamma$[/tex]. We then add these cosines together to find the final value of [tex]$\cos\alpha + \cos\beta + \cos\gamma$[/tex], which is 1989.
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The complete question is
Let $a$, $b$, $c$ be the three sides of a triangle, and let $\alpha$, $\beta$, $\gamma$, be the angles opposite them.If $a^2+b^2=1989c^2$, find the value of $\cos\alpha+\cos\beta+\cos\gamma$.
Related Questions
The sum of three consecutive odd integers is 45. What are the integers
Answers
Answer:
13, 15 17
Step-by-step explanation:
Let x = 1st number
Let x + 2 = 2nd number
Let x + 4 = 3rd number
x + x + 2 + x + 4 = 45 Combine like terms
3x + 6 = 45 Subtract 6 from both sides
3x + 6 - 6 = 45 - 6
3x = 39 Divide both sides by 3
[tex]\frac{3x}{3}[/tex] = [tex]\frac{39}{3}[/tex]
x = 13
Check:
13 + 15 + 17 = 45
If 3 less than 4 times a certain number is 9 more than the number, find the number.
Answers
Answer:
okay now I really think that doing or solving any question like this will start first by solving out Earth I mean x okay by solving it out and after solving it and I'm really sorry cuz I'm using a voice note that's why I'm having all this misinterpretation so when you sort out x you begin to sort out all the questions nowhere for them to settle number the certain number will be x know where the four times a number will be no where the 903 will be and I really think that is it
Find the length of the midsegment of the trapezoid with the vertices S(0, 0), 7(2, 7), U(6, 10), V(8, 6).
The length of the midsegment is
Answers
Answer:
7.5
Step-by-step explanation:
A trapezoid is a quadrilateral where the bases are parallel, but the legs are not parallel.
Given vertices of trapezoid STUV:
S = (0, 0)T = (2, 7)U = (6, 10)V = (8, 6)The parallel bases of the trapezoid are TU and SV.
Find the lengths of TU and SV using the distance formula.
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
[tex]\begin{aligned}TU&=\sqrt{(x_U-x_T)^2+(y_U-y_T)^2}\\&=\sqrt{(6-2)^2+(10-7)^2}\\&=\sqrt{(4)^2+(3)^2}\\&=\sqrt{16+9}\\&=\sqrt{25}\\&=5\end{aligned}[/tex]
[tex]\begin{aligned}SV&=\sqrt{(x_V-x_S)^2+(y_V-y_S)^2}\\&=\sqrt{(8-0)^2+(6-0)^2}\\&=\sqrt{(8)^2+(6)^2}\\&=\sqrt{64+36}\\&=\sqrt{100}\\&=10\end{aligned}[/tex]
The midsegment of a trapezoid is the segment parallel to the bases that connects the midpoints of the legs.
[tex]\boxed{\begin{minipage}{6.5cm}\underline{Midsegment of a Trapezoid}\\\\$M=\dfrac{b_1+b_2}{2}$\\\\where:\\ \phantom{ww}$\bullet$ $M$ is the length of the midsegment. \\\phantom{ww}$\bullet$ $b_1$ and $b_2$ are the parallel bases. \\\end{minipage}}[/tex]
Substitute the found lengths of the bases into the midsegment formula:
[tex]\implies M=\dfrac{5+10}{2}[/tex]
[tex]\implies M=\dfrac{15}{2}[/tex]
[tex]\implies M=7.5[/tex]
The length of the midsegment is 7.5.
Connie needs 45 oz of meat to feed her lizards each day. If she has 315 oz of meat left, how many days can she feed her lizards? (Just place the number and do not label days on this one.) ___ days
Answers
Answer: 7
Step-by-step explanation:
315 divided by 45= 7
I hope this helps!
Match the y-coordinate with the given x-coordinate for the equation y = log₁0x.
1. 100
2. 1/10
3. 10
4. 1
5. 1/100
-2
1
0
-1
2
Answers
The y-coordinate matched with the given x-coordinate:
x = 100 → y = 3
x = 1/10 → y = 0
x = 10 → y = 2
x = 1 → y = 1
x = 1/100 → y = -1
What is Logarithmic?The inverse of exponentiation is the logarithm. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.
Given:
Logarithmic function,
y = log(10x).
(1).
x = 100
So,
y = log{(10)(100)}.
y = log(1000)
y = 3
(2).
x = 1/10
So,
y = log{(10)(1/10)}.
y = log(1)
y = 0
(3).
x = 10
So,
y = log{(10)(10)}.
y = log(100)
y = 2
(4).
x = 1
So,
y = log{(10)(1)}.
y = log(10)
y = 1
(5).
x = 1/100
So,
y = log{(10)(1/100)}.
y = log(1/10)
y = -1
Therefore, the y-coordinate matched with the given x-coordinate
x = 100 → y = 3
x = 1/10 → y = 0
x = 10 → y = 2
x = 1 → y = 1
x = 1/100 → y = -1
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Determine all the truth value assignments. It any, for the primitive statements p. q, r, s, t that make each of the following compound statements false.
a. [(p^q) ^r] → (s \/ t)
Answers
Answer:
To determine the truth value assignments for the primitive statements that make the compound statement false, we need to consider the truth table for the conditional operator (→).
The truth table for the conditional operator is as follows:
p q p→q
T T T
T F F
F T T
F F T
According to the truth table, a conditional statement of the form "p → q" is only false when p is true and q is false.
For the compound statement [(p^q) ^r] → (s / t) to be false, we need the antecedent [(p^q) ^r] to be true and the consequent (s / t) to be false.
Thus, the truth value assignments that make the compound statement false are:
p q r s t
T T T F F
Note that there is only one truth value assignment that makes the compound statement false.
The compound statement [(p^q) ^r] → (s / t) is false only when the antecedent (the part before the arrow) is true and the consequent (the part after the arrow) is false.
The antecedent, [(p^q) ^r], is true only when p, q, and r are all true. The consequent, (s / t), is false only when both s and t are false.
Therefore, the only truth value assignments that make the compound statement false are:
p = T, q = T, r = T, s = F, t = F
p = F, q = T, r = T, s = F, t = F
p = T, q = F, r = T, s = F, t = F
p = F, q = F, r = T, s = F, t = F
Any other truth value assignment will make either the antecedent or the consequent true, and the compound statement will be true.
Here is a truth table that shows all the possible truth value assignments for the compound statement and the values of the statement:
p | q | r | s | t | [(p^q) ^r] → (s \/ t)
-- | -- | -- | -- | -- | --
T | T | T | F | F | F
T | T | F | F | F | F
T | F | T | F | F | F
T | F | F | F | F | F
F | T | T | F | F | F
F | T | F | F | F | F
F | F | T | F | F | F
F | F | F | F | F | T
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Which ordered pairs represent points on the graph of this equation? Select all that apply.
2y= –3x–4
Answers
All the ordered pairs that represent points on the graph of this equation include the following:
A. (-4, 4).
C. (-2, 1)
E. (2, -5)
F. (0, -2)
What is an ordered pair?In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.
How to determine the ordered pairs that represent points on the graph?In order to determine the ordered pairs that represent points on the graph of the given function, we would plot its equation by using an online graphing calculator and then read all the ordered pairs that lie on the line.
By critically observing the graph of the given function (see attachment), the solutions are include following;
Ordered pair = (-4, 4).
Ordered pair = (-2, 1).
Ordered pair = (2, -5).
Ordered pair = (0, -2).
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Complete Question:
Which ordered pairs represent points on the graph of this equation? Select all that apply.
2y= –3x–4
(-4, 4)
(7, 6)
(-2, 1)
(0, 7)
(2, -5)
(0, -2)
1. in several sentences, explain the right triangle drawings you need to model the shadow scenarios. make sure it answers the following: a. what does each side length signify? in particular explain what does the hypotenuse in your drawing signify in the real world?
Answers
The right triangle drawings are used to model the shadow scenarios. Each side length of the triangle represents a different part of the scenario.
Modeling Shadow Scenarios Using Right Triangle DrawingsThe hypotenuse represents the distance from the sun to the object casting the shadow, the side adjacent to the hypotenuse represents the length of the shadow, and the side opposite the hypotenuse represents the height of the object casting the shadow. In the real world, the hypotenuse is used to calculate the angle of the sun relative to the object casting the shadow.
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I’ll give BRAINLIEST if correct
Which inequality matches the graph ?
Answers
The linear inequality on the graph is:
2y - 3x ≥ 3
So the correct option is the third one.
Which inequality matches the graph?Here we have a linear inequality, we can see a solid line and the region above the line is shaded.
We can assume that the line is something like:
y = a*x + b
Where a is the slope and b is the y-intercept.
We can see that the line intercepts the y-axis at y = 3, then:
y = a*x + 3
And the x-axis at x = -2, then:
0 = a*-2 + 3
2a = 3
a = 3/2
Then the line is:
y = (3/2)*x + 3
And the inequality is:
y ≥ (3/2)*x + 3
If we multipy it all by 2 we will get:
2y ≥ 3x + 3
If we move the term with x to the left:
2y - 3x ≥ 3
That is the graphed inequality.
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PLEASE HELP
Sylvia purchases pens for her business from an office supply store. If she pays $0.40 for 5 pens, how many pens can she purchase with $6.00?
A) 48
B) 12
C) 75
D) 30
Answers
Based on the information, it can be inferred that Sylvia buys 75 pens for $6.00 (option C).
How to calculate the number of pens that Sylvia can buy?To calculate the number of pens that Silvia can buy we must carry out the following mathematical procedure
$6.00 / $0.40 = 1515 * 5 = 75According to the above, $6.00 is enough to buy 15 groups of 5 pens. So, that's why we multiply 15 by 5 to find the number of pens Sylvia can buy. In this case there are 75 pens. Additionally, the first procedure we divide the total money in the value of each group of pens to identify how many groups we can buy.
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find the value of jk for this problem
Answers
The measure of JK from the given similar quadrilaterals is 30 units.
What are similar figures?Similar figures mean when two figures are of the same shape but are of different sizes. In other words, two figures are called similar when they both have a lot of the same properties but still may not be identical.
Given that, JKLM and PQRS are similar figures.
MJ=21, JK=4y-2, KL=6x+3, LM=36, PQ=10, QR=11, and RS=12.
Since, given quadrilaterals are similar, we get
JK/PQ =LM/RS
4y-2/10 =36/12
4y-2/10=3
4y-2=30
4y=32
y=8
So, JK=4y-2
JK=30 units
Therefore, the measure of JK is 30 units.
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20. DEPRECIATION Depreciation is the decrease in the value of an item resulting from its age or weac. When an item loses about the same percent of its value each year, an exponential function can be used to model its decreasing value over time. The function g(x)=12,000(0.85)'' can be used to model the value of a $12,000 car as it depreciates at an annual rate of 15% over x years. g(x) is a dilation of the parent function f(x)=0.85*. The graph shows the function g(x).
a. Write the equation of a function h(x) that represents the depreciation of a $20,000 car depreciating at the same rate over x years.
b. Describe h(x) as it relates to the parent function.
c. What is the difference between the values of the $12,000 car and the $ 20,000 car after 5 years?
Answers
a). The equation of a function h(x) as required to be determined is; h (x) = 20,000 (0.85)^x.
b). The function h (x) as required to be described in terms of the parent function f(x) is a dilation of the parent function using a scale factor of 20,000.
c). The difference between the values of the $12,000 and the $20,000 car after 5 years is; $3549.6.
What is the equation of the function h(x) as required?It follows from the task content that the equation of the function g (x) is given as;
g (x) = 12,000 (0.85)^x.
a). To start with, since the rate of depreciation is same for the $20,000 car too; it follows that the exponential function which represents the situation is;
h (x) = 20,000 (0.85)^x.
b). It follows from transformations that; since the parent function f (x) = 0.85^x, the function g(x) can be described relative to the parent function as a dilation of the parent function using a scale factor of; 20,000.
c). The value of the $12,000 item after 5 years is;
g (5) = 12,000 (0.85)⁵ = $5324.5.
Also, the value of the $20,000 car after 5 years is;
h ( 5 ) = 20,000 (0.85)⁵ = $8874.1.
Ultimately, the difference between the values of the two items as required is; 8874.1 - 5324.5 = $3549.6.
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6. Higher Order Thinking Helen makes
the rectangle on the right from tiles.
Each tile is 1 unit square. Helen says the
white tiles cover more area than the
black tiles. Do you agree? Explain.
Answers
On solving the provided question we cans ay that - the area of the rectangle will A = 121 cm sq.
What is rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.
So we have been provided with,
L = 11 cm and B = 11 cm
so, A = L X B = 11 X 11 = 121 cm sq.
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At a university, 34% of undergraduate students love spicy food, while 45% of graduate students love spicy food. Let and be the sample proportions of undergraduate and graduate students at this university, respectively, who love spicy food. Suppose 35 undergraduate students and 28 graduate students from this university are selected at random and asked if they love spicy food.
Which of the following is the correct calculation and interpretation of the standard deviation of the sampling distribution of ?
Answers
The standard deviation of the sampling distribution of a sample proportion is about 0.00687.
Sampling Distribution of a Sample Proportion: When a distribution is formed by taking random samples of size N
from a population where the proportion in the category of interest is p
, and finding the proportion of the category of interest in each sample, it is called the sampling distribution of a sample proportion.
Standard Deviation: The standard deviation is a measure of how spread out data is. When referring to the standard deviation of the sampling distribution of a sample proportion, the standard deviation measures how far from the population proportion the sample proportions are on average.
P =X/n
=34%/45%
= 34/45
=0.75
N = 35 + 28
σp=√p(1−p)/N
= √0.75(1- 0.75)/63
= √0.75(0.25)/63
= 0.433/63
=0.00687
The standard deviation of the sampling distribution of a sample proportion is about 0.00687.
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Graph the solution to this inequality on the number line.
−8 + x < −3
(Please answer this question by taking a screenshot of the number line and drawing a number line where it needs to go)
Answers
A graph of the solution to this inequality (x < 5) is shown on the number line in the image attached below.
What is an inequality?In Mathematics, an inequality simply refers to a mathematical relation that is typically used for the comparison of two (2) or more numerical data, numerals, and variables that are contained in an algebraic equation, especially based on the following inequality symbols:
Less than (<).Greater than or equal to (≥).Greater than (>).Less than or equal to (≤).Generally speaking, a number line is a type of chart which primarily decreases in numerical value towards the right from zero (0) and increases in numerical value towards the left from zero (0).
Next, we would solve the given inequality by adding eight to both sides as follows;
−8 + x < −3
−8 + x + 8 < −3 + 8
x < 5
Therefore, the solution is x is less than five.
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To prepare a piece of ground for building a brick patio, a rectangle measuring 10 feet by 12 feet must be marked off. Then the dirt within the rectangle must be dug out to a depth of 2 feet. Finally, the resulting space must be filled with sand.
(a) What is the formula for volume? What is the volume of sand needed, in cubic feet, to fill the space?
Show your work!
Answer: ____________________ cubic feet
If you used your calculator, show the numbers and operations that you used to get your answer.
(b) What is the formula for volume? Sand costs $5 per cubic foot. What is the total cost of the sand needed to fill this space, including a $40 delivery charge?
Show your work!
Answer: $____________________
If you used your calculator, show the numbers and operations that you used to get your answer.
Answers
The formula for volue is length x width x height.
The volume of the sand needed to fill the space is 240 feet³.
The total cost of the sand is $1240.
What is the total cost of the sand?The brick patio is the shape of a rectangular prism. In order to determine the volume of the brick patio, determine the product of the length, width and the height.
Volume of the brick patio = length x width x height
= 10 x 12 x 2 = 240 feet³
Total cost of the sand = (volume x cost per cubic foot) + delivery fee
Total cost of the sand = (240 x $5) + $40
Total cost of the sand = 1200 + 40
Total cost of the sand = $1240
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Unit 2, Lesson 7 - Homework
1. One batch of meatloaf contains 2 pounds of beef and cup of breadcrumbs.
Complete the double number line diagram to show the amounts of beef and bread
crumbs needed for 1, 2, 3, and 4 batches of meatloaf.
2.
beef (pounds)
bread crumbs (cups)
Write a sentence that describes this situation and that uses the word per.
Place Aprwer Here
Answers
Answer:
3 batches of meatloaf requires 6 pounds of beef
and 3 cups of bread crumbs.
Step-by-step explanation:
For pounds of beef
1 batch meatloaf = 2 pounds of beef
3 batches of meatloaf = x
Cross Multiply
x = 3 x 2 pounds of beef
x = 6 pounds of beef
3 batches of meatloaf requires 6 pounds of beef
For bread crumbs
1 batch meatloaf = 1 cup of bread crumbs
3 batches of meatloaf = x
Cross Multiply
x = 3 × 1 cup of bread crumbs
x = 3 cups of bread crumbs
3 batches of meatloaf requires 3 cups of bread crumbs.
Therefore, 3 batches of meatloaf requires 6 pounds of beef and 3 cups of bread crumbs.
calculate the tax for each taxable income of a head of household
Answers
Answer:
The tax for each taxable income of a head of household depends on the tax rate that applies to that income and the applicable deductions and credits available to the taxpayer. The tax rate applied to a taxpayer's income depends on the taxpayer's taxable income and filing status. The tax rate for a head of household is generally lower than the tax rate for a single filer, but higher than the tax rate for a married taxpayer filing a joint return.
To determine the tax for a taxable income of a head of household, you can use the Internal Revenue Service (IRS) tax tables or a tax calculator. The tax tables provide tax rates and income ranges for each tax bracket, and you can use them to determine the tax on a given income. Alternatively, you can use a tax calculator to input your taxable income, filing status, and any applicable deductions and credits to determine the tax owed.
It's important to note that the tax rate for a head of household may change from year to year, as the IRS adjusts the tax brackets and rates. Additionally, the deductions and credits available to a head of household may change from year to year, so it's important to consult the IRS guidelines for the most current information.
Step-by-step explanation:
helppp me please i need help
Answers
5. Devi and Gill started saving money at the same time. Each day, Devi saves $1.40 and Gill saves 30 cents more than Devi. When Gill had saved $5.40 more than Devi, how much money had Devi saved?
Answers
Answer:
$25.20
Step-by-step explanation:
($5.40) / ($0.30/day) = 18 days
It took 18 days for Gill to save $5.40 more than Devi. So in those 18 days Devi saved:
$1.40/day x 18 days = $25.20
Write 250 beads in total on 8 necklaces as an algebraic expression.
Answers
The algebraic expression that represents the number of beads per necklace is given as follows:
250/8.
How to write the algebraic expression?The algebraic expression representing the number of beads per necklace is obtained applying the proportion in the context of the problem.
The proportion is given by the division of the total number of beads by the total number of necklaces, as follows:
Beads per necklace = Number of beads / Number of necklaces.
The parameters for this problem are given as follows:
Number of beads: 250.Number of necklaces: 8.Hence the algebraic expression that represents the number of beads per necklace is given as follows:
250/8.
(dividing the number of beads by the number of necklaces given in this problem).
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A measure of a person's ability and willingness to pay debts on time.
Answers
ax + by = 6000 and a + 5 = b are two equations that might be used to calculate how many soup cans and frozen dinners were purchased.
What is an equation?There are several methods to define a formula. A mathematical statement that establishes the equivalence of two mathematical expressions is the definition of an equation in algebra. This is best shown by the formula 3x + 5 = 14. In this instance, the word equal comes between the phrases 3x + 5 and 14. Even the most basic algebraic equations include the usage of mathematical variables.
X now has 300 mg of sodium in it.
[tex]x = 300[/tex]
Y also has 450 mg of sodium in it.
[tex]y = 450[/tex]
Samuel reportedly buys five more frozen dinners than soup cans, and they all have a combined salt content of 6000 mg.
Let the number of frozen dinners be "b," and the number of soup cans be "a."
ax + by = 6000
a(300) + b(450) = 6000 .
Samuel bought 5 more frozen dinners than soup cans, according to the inquiry, which results in equation
[tex]a + 5 = b \\a(300) + (a + 5)(450) = 6000\\300a + 450a = 6000 - 2250\\ 750a = 3750\\ a = 3750/750\\ a = 5\\5 + 5 = b\\ b = 10[/tex]
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Find the 10th term sequence OF 2, 3, 5, 8, 12
Answers
Answer: 47
Step-by-step explanation: 2,3,5,8,12,17,23,30,38,47,57
Answer:
57
Step-by-step explanation:
The sequence starts out 2 , 3 which is the 1st term of the sequence because from the number 2, 3 is one number away. . Then 3, 5 which is the 2nd sequence because 5 is two numbers away from the number 3. 5 to 8 is the 3rd sequence because 5, 6 , 7, 8.... three numbers away from the number 5 is 8. The problem continues from 8 to 12 is four numbers away, the next sequence is five numbers away. And the number 47 is 10 numbers away from 57 making 57 the 10th term.
According to a recent national poll, 22% of US adults get an average of 7 or more hours of sleep per night. Assume this is the parameter value for the population. Suppose you select a random sample of 50 US adults and find that 10 of them get an average of 7 or more hours of sleep per night. Let p hat = the proportion in the sample who get an average of 7 or more hours of sleep per night. The probability that 20% or less of US adults get an average of 7 or more hours of sleep per night is 0.3664. Does this result provide convincing evidence against the poll’s claim? No, the difference between the sample result and what we expected is not extreme enough. The probability of it occurring by chance alone is not unlikely (0.3664 > 0.05). No, there is a small chance of seeing the sample result. It is unlikely to occur by chance alone. Yes, the difference between the sample result and the parameter (2%) is less than 5%. Yes, the probability of seeing the sample result is so far from what we expected that the probability of it occurring by chance alone is very unlikely.
Answers
No, the difference between the sample result and what we expected is not extreme enough. The probability of it occurring by chance alone is not unlikely (0.3664 > 0.05).
The correct option is A.
What is a distribution?The distribution of values in a field is described by a statistical distribution, often known as a probability distribution. In other words, the statistical distribution identifies the typical and unusual values. The bell-shaped normal distribution is one of many varieties of statistical distributions.
Given:
According to a recent national poll, 22% of US adults get an average of 7 or more hours of sleep per night.
Let x = Number of US adult get an average of 7 or more hours of sleep per night.
Assume this is the parameter value for the population.
That means,
Proportion of number of US adults get an average of 7 or more hours of sleep per night in population = p =0.22
Suppose you select a random sample of 50 US adults and find that 10 of them get an average of 7 or more hours of sleep per night.
1) The shape of this sampling distribution is approximately normal.
2) Let a = Number of US adults get an average of 7 or more hours of sleep per night in sample = 10
Sample size n = 50.
So, [tex]\hat {p}[/tex] = 10/50
[tex]\hat {p}[/tex] = 0.2
Option a) is correct.
3) σ[tex]_{\hat p}[/tex] = √(pq)/n
= √(0.22)(1 -0.22)/50
= 0.0586
The difference between the sample result and what we expected is not extreme enough.
Therefore, the probability of it occurring by chance alone is not unlikely (0.3664 > 0.05).
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Line a is parallel to line b and goes through the point (1,2). Line b goes through the point (3,1) and is perpendicular to line c whose equation is y = -2x+3. Find the y-intercept of line a.
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Line a is parallel to line b and goes through the point (1,2). Line b goes through the point (3,1) and is perpendicular to line c whose equation is y = -2x+3.The y-intercept of line a is -7
given that
Line a is parallel to line b and goes through the point (1,2)
Line b goes through the point (3,1) and is perpendicular to line c
equation of line c is y = -2x+3
To find y-intercept of line a.
we need to find the slope of the equation
slope(m) = [tex]\frac{y2 - y1}{x2 - x1}[/tex] =[tex]\frac{1 - (-3)}{2 - 1}[/tex] = [tex]\frac{4}{1}[/tex] = 4
now , we need to write equation in slope intercept form
y = mx + b
1 = (4)2 + b
1 = 8 + b
b = -7
The y-intercept of line a is -7
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a) Work out the nth term rule for the sequence of cube numbers.
Answers
Therefore , the solution of the given problem of sequence comes out to be T = 5832.
A sequence is what?The phrase "sequence" refers to a grouping of numbers, or "terms." 2, 5, and 8 are examples of terms. By making advantage of a specific pattern some sequences follow, it is possible to make some sequences infinitely long. To continue the sequence, use the sample of 2,5,8, and then add 3. There are equations that show where to seek for words in a list of words. In mathematics, a sequence is a group of items that are all in some kind of order . The length of the series is the total number of ordered objects, which may be limit . arranging two or more things in a sensible order. Chronological.
Here,
Given :
to determine the nth term norm for the members of the cube in order.
1, 8, 27, 64, and... are
the cube numbers.
The 18th term
=> T(18) = 183
=> T(18) = n³
=>T(n) = n³ = 5832
Therefore , the solution of the given problem of sequence comes out to be T = 5832.
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q/10 + 71 = 75
what is "q"
Answers
Answer:
q=40
Step-by-step explanation:
q/10+71=75
-71. -71
q/10=4
x10 x10
q=40
hopes this helps
Answer:
What the guy above me says!
Step-by-step explanation:
HELP HELP HELP need answer quick
Answers
Answer: (C)
Step-by-step explanation: By viewing the diagram, we can see that f(x) is the line drawn, and as that line heads down to negative infinity, the line is also heading towards positive infinity, and we can see this by comparing the line (f(x)) and the x-axis :)
Angela went to the farmers' market to buy some vegetables She wanted some yelow squash and zucchini which were both on sale for 1.146 per pound. Angela bought 2 pounds of yellow
pounds of zucchini. To the nearest cent, what was the total cost of the vegetables?
Answers
The total cost of the vegetables to the nearest cent is $3.44
Define Unitary Method.The unitary approach involves calculating the value of a single unit, from which we may calculate the values of the necessary number of units.
Define ratio and proportion.Two quantities are compared to form a ratio. An equality of two ratios is a percentage. How to format a ratio Analyze the ratio to see whether it is part to part or part to whole. Calculate the whole and the pieces as necessary.
Angela bought 2 pounds of yellow squash and 1 pound of zucchini. The yellow squash and the zucchini were both on sale for $1.146 per pound.
To find the total cost of the yellow squash, we can multiply 2 pounds by $1.146 per pound:
2 pounds * $1.146/pound = $2.292
To find the total cost of the zucchini, we can multiply 1 pound by $1.146 per pound:
1 pound * $1.146/pound = $1.146
To find the total cost of the vegetables, we can add the cost of the yellow squash and the zucchini:
$2.292 + $1.146 = $3.438
The total cost of the vegetables to the nearest cent is $3.44
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What is the median of the data? 30, 29, 16, 11, 16, 20, 21, 13, 15, 15, 23, 30
A. 26
B. 15
C. 16
D. 18
Answers
Answer:b a
Step-by-step explanation:
