precalculus problem need help
1. <C= 90 degree
AC = 13.25 unit
<B= 60 degree
2. <C= 90 degree
AC = 13.
<B= 60 degree
1. Using Sine law
sin C/4 = sin 30/2 = sin B/ AC
so, sin C/4 = 1/4
sin C = 1
C= 90 degree
and, <B= 180 - 30- 90= 60 degree
So, sin 30/2 = sin 60/ AC
1/4 AC = √3/2
AC = 2√3
2. Using Sine law
sin 30/ 7.65 = sin B / 15.3
1/15.3 = sin B/15.3
sin B= 1
B = 90 degree
and, <C= 180 - 90 - 30 = 60
So, 1/15.3 = sin 60/ C
C = 13.25
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Find the Constant of proportionality of Henderson Toll Road Cost
The constant of proportionality is equal to 3/10.
What is a proportional relationship?In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:
y = kx
Where:
y represents the miles traveled.x represents the cost ($).k is the constant of proportionality.Next, we would determine the constant of proportionality (k) by using various data points as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 3/10 = 6/20 = 9/30
Constant of proportionality, k = 3/10.
Therefore, the required linear equation is given by;
y = kx
y = 3/10(x)
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an athlete eats 55kg of protein a day while training. How much protein will she eat during 23 days of training?
Answer:
1265 kg of protein
Step-by-step explanation:
If 55kg is eaten in one day then in 23 days there will be x kgs.
To find 'x':
55 x 23 = 1265
Set up and find the meaure of the arc or angle indicated.
Applying the inscribed angle theorem, the measure of the angle is calculated: 35°.
How to Find the Measure of the indicated angle using the Inscribed Angle Theorem?Recall the following based on the inscribed angle theorem:
Measure of an arc = 2(measure of inscribed angle)
Also not that half of a circle is equal to 180 degrees. Therefore, we have:
Measure of arc QR = 180 - 110 = 70 degrees.
Measure of angle QRS = 1/2(measure of arc QR)
Plug in the values:
Measure of angle QRS = 1/2(70)
Measure of angle QRS = 35°
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A store is having a sale on jelly beans and almonds. For 3 pounds of jelly beans and 5 pounds of almonds, the total cost is $27. For 9 pounds of jelly beans and
7 pounds of almonds, the total cost is $51. Find the cost for each pound of jelly beans and each pound of almonds.
Cost for each pound of jelly beans:
Cost for each pound of almonds:
Answer:
Cost for each pound of jelly beans: $2.75
Cost for each pound of almonds: $3.75
Step-by-step explanation:
Let J be the cost of one pound of jelly beans.
Let A be the cost of one pound of almonds.
Using the given information, we can create a system of equations.
Given 3 pounds of jelly beans and 5 pounds of almonds cost $27:
[tex]\implies 3J + 5A = 27[/tex]
Given 9 pounds of jelly beans and 7 pounds of almonds cost $51:
[tex]\implies 9J + 7A = 51[/tex]
Therefore, the system of equations is:
[tex]\begin{cases}3J+5A=27\\9J+7A=51\end{cases}[/tex]
To solve the system of equations, multiply the first equation by 3 to create a third equation:
[tex]3J \cdot 3+5A \cdot 3=27 \cdot 3[/tex]
[tex]9J+15A=81[/tex]
Subtract the second equation from the third equation to eliminate the J term.
[tex]\begin{array}{crcrcl}&9J & + & 15A & = & 81\\\vphantom{\dfrac12}- & (9J & + & 7A & = & 51)\\\cline{2-6}\vphantom{\dfrac12} &&&8A&=&30\end{array}[/tex]
Solve the equation for A by dividing both sides by 8:
[tex]\dfrac{8A}{8}=\dfrac{30}{8}[/tex]
[tex]A=3.75[/tex]
Therefore, the cost of one pound of almonds is $3.75.
Now that we know the cost of one pound of almonds, we can substitute this value into one of the original equations to solve for J.
Using the first equation:
[tex]3J+5(3.75)=27[/tex]
[tex]3J+18.75=27[/tex]
[tex]3J+18.75-18/75=27-18.75[/tex]
[tex]3J=8.25[/tex]
[tex]\dfrac{3J}{3}=\dfrac{8.25}{3}[/tex]
[tex]J=2.75[/tex]
Therefore, the cost of one pound of jelly beans is $2.75.
Mary started a bank account with m dollars. The money increased to 6.2 times the sum of the starting amount and $4. Mary then withdrew 3 times there starting amount. The remaining balance was 348.80. Enter the amount of money, in dollars, Mary used to start the account.
Please be quick I only have an hour to submit. Thank you
Which sequences are geometric? Select three options.
O-2.7, -9, -30, -100, ...
0-1, 2.5, -6.25, 15.625,...
9.1, 9.2, 9.3, 9.4, ...
8, 0.8, 0.08, 0.008, ...
4,-4, -12, -20, ...
Answer:
A. -2.7, -9, -30, -100, ...
B. -1, 2.5, -6.25, 15.625, ...
C. 9.1, 9.2, 9.3, 9.4, ...✔️
D. 8, 0.8, 0.08, 0.008, ...✔️
E. 4, -4, -12, -20, ... ✔️
Hope you understand
Let me know if you need further explaination
Solve the following differential equations
What are the polar coordinates of the point A shown below?
Select the correct answer below:
(−2,5π6)
(2,π3)
(2,−5π6)
(3,π3)
(−3,−π6)
(3,−5π6)
Answer:
(−3,−π/6)
Step-by-step explanation:
Note that the point is on the circle whose radius is labeled 3, so r=3 or r=−3. Of the choices available, only an angle of −π6, drawn from the negative x axis plots at the point A. So θ=−π6, and r must be negative, as the angle is measured from the negative x axis. Thus, the polar coordinates are (−3,−π6).
This query is about identifying the polar coordinates of a specific point on a graph. However, without an accompanying graphical representation, a definitive answer cannot be provided based on the options given. Polar coordinates represent a point using the distance from a reference point and an angle from a reference direction.
Explanation:The question is about polar coordinates, a way of expressing the location of a point in two-dimensional space. Without seeing the actual point A on a graph, it is not possible to definitively determine its polar coordinates from the provided choices. However, it is very crucial to know that polar coordinates represent a point in the plane using the distance from a reference point and an angle from a reference direction. The distance, represented as r, should always be non-negative whereas the angle θ can range from 0 to 2π, or in negative, -π to π. An understanding of these may help you determine the coordinates of the point A in your problem.
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Someone pls help me with this.
The value of angle k is 129⁰.
The value of angle b is 64.5⁰.
What is the value of angle b and angle k?
The value of angle b and angle k is calculated by applying the following principle of intersecting chord theorem.
k + 113 + 118 = 360 (sum of angles in a circle)
k + 231 = 360
k = 360 - 231
k = 129⁰
The value of angle b is calculated by applying the principle of intersecting chord theorem.
b = ¹/₂ arc k
b = ¹/₂ x 129
b = 64.5⁰
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Which Box And Whisker Plot Has GREATEST interguartile range?
picture below
The box and whisker plot that has the greatest interquartile range from the options given is option 3.
What is the Interquartile Range of a data Displayed in a Box and Whisker Plot?In order to calculate the interquartile range of a dataset, we can determine or find the difference between the values at the edges of the rectangular box in a box and whisker plot that displays the data set.
This also implies that we subtract the first quartile from the third quartile.
From the options given, we see that in option 3, the box and whisker plot has the largest interquartile range. This is because: Q3 - Q1 is approximately 9.
9 is higher than the interquartile ranges of the other datasets, therefore, option 3 is the right option.
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awarding 84 points!!! Before playing a game that uses a spinner, you decide to examine the fairness of the spinner. The spinner is divided into 5 equally-sized sectors that are numbered 1, 2, 3, 4 and 5.
You spin the spinner 1000 times and notice that 5 is spun 203 times.
Which statement best describes the fairness of the spinner?
There is not enough information to determine if the spinner is probably fair.
The spinner is probably fair because 5 was spun approximately 200 times.
The spinner is probably not fair because 5 was spun 203 times which is more than expected.
Answer: The spinner is probably because 5 was spun approximately 200 times
Step-by-step explanation:
5/6 having denominator 35
Answer:( 175/6)
Step-by-step explanation: 5*35/6=175/6 sour our numerator is 175/6. So sour answer is (175/6)/35
8y^2+6xy
evaluate the given polynomial at:
x=3, y=1
. Replace the variable(s) in the polynomial with the specific value(s) given and determine the value of the polynomial by performing the indicated operations.
Answer:
Putting the values of x and y in the given polynomial
[tex] = 8({1})^{2} + 6(3)(1)[/tex]
[tex] = 8(1) + 18[/tex]
[tex] = 8 + 18[/tex]
[tex] = 26[/tex]
Hence the value of polynomial is 26
.HELPPPPPPPPPPPPPPPPP
Answer:
[tex]\textsf{Choice A } \quad y = \dfrac{5}{3}x + 1[/tex]
Step-by-step explanation:
Slope intercept form of a line equation is
y = mx + b
where
m = slope
b = y-intercept
A perpendicular line to y = mx + b will have a slope of -1/m
Let's first find the equation for line z in slope-intercept form
Slope m for a line = (y2- y1)/(x2 - x1) where x1, y1 and x2, y2 are two points on the line
Slope of line z is
[tex]m = \dfrac { 2 - (-1) }{-2 - 3} = \dfrac{3}{-5} = - \dfrac{3}{5}[/tex]
So line z will have an equation of the form
[tex]y = -\dfrac{3}{5}x + b[/tex]
We know that a line perpendicular to this line will have a slope of
[tex]- \dfrac{1}{-\dfrac{3}{5}} = \dfrac{5}{3}[/tex]
So the equation of the perpendicular line is
[tex]y = \dfrac{5}{3}x + b[/tex]
Only one of the 4 choices, name choice A has this slope of 5/3
Therefore the correct answer choice is A
There is no need to compute b, the y intercept but if you wanted to, this is how you would do it:
The perpendicular line passes through (3, 6). This means when x = 3, y =6
Substitute these values of x, y into the equation for the perpendicular line and solve for b
[tex]y = \dfrac{5}{3}x + b\\\\\text{When x = 3, y = 6}:\\\\6 = \dfrac{5}{3} \cdot 3 + b\\\\6 = 5 + b\\\\b = 6 - 5 = 1\\\\\text{So, the equation of the perpendicular line is }\\y = \dfrac{5}{3}x + 1[/tex]
This corresponds to Choice A
can someone help really fast look at the directions and just do it in a simpler way if you can please hurry somebody
Answer:
The easiest method to remember when dividing fractions is Keep Change Flip (KCF)
Step-by-step explanation:
I wrote out some examples of KCF. Once you use KCF, you just multiply the fractions normally and then don't forget to write the improper fractions (ex: 12/7) as a mixed number (1 5/7)
If you have any questions about the steps just let me know. I hope this helps ^-^
Answer this for me please
The function values are f(10) = 198 and g(-6) = 24/7; the range of h(x) is 3/5 < h(x) < 31/25 and the inverse function is p-1(x) = -(1 + 3x)/(5 + x)
Calculating the function valuesGiven that
f(x) = 2x^2 - 2
g(x) = 4x/(x - 1)
So, we have
f(10) = 2(10)^2 - 2 = 198
g(-6) = 4(-6)/(-6 - 1) = 24/7
The range of h(x)Here, we have
h(x) = (7x - 4)/5x
Where
1 < x < 5
So, we have
h(1) = (7(1) - 4)/5(1) = 3/5
h(5) = (7(5) - 4)/5(5) = 31/25
So the range is 3/5 < h(x) < 31/25
The inverse of p(x)Here, we have
P(x) = (5x - 1)/(3 - x)
So, we have
x = (5y - 1)/(3 - y)
This gives
3x - xy = 5y - 1
So, we have
y(5 + x) = -1 - 3x
This gives
y = -(1 + 3x)/(5 + x)
So, the inverse function is p-1(x) = -(1 + 3x)/(5 + x)
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A cake recipe calls for the following dry ingredients: 3 ½ cups of flour, 2 ⅔ cups of sugar, and 1 ¾ cups of cocoa. To the nearest cup, how much dry ingredients will be used?
HELO
The amount of dry ingredients used in the cake recipe is approximately 7 cups.
We have,
3 ½ cups of flour, 2 ⅔ cups of sugar, and 1 ¾ cups of cocoa.
Now, first convert all quantity in same unit.
3 ½ cups of flour
= 3 cups + 0.5 cups
= 3 cups and 8 ounces.
and, 2 ⅔ cups of sugar
= 2 cups + 0.67 cups,
= 2 cups and 10.72 ounces.
and, 1 ¾ cups of cocoa
=1 cup + 0.75 cups
= 1 cup and 12 ounces.
So, the total amount
= 3 cups and 8 ounces + 2 cups and 10.72 ounces + 1 cup and 12 ounces = 6 cups and 14.72 ounces
= 7 cups
Therefore, the amount of dry ingredients used in the cake recipe is approximately 7 cups.
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Determine if the question is a Statistical Question
Answer:
satiscal
Step-by-step explanation:
Jon has a rectangular picture that is 54 inches wide and 24 inches tall. He wants to hang it on the wall shown so that it is centered both horizontally and vertically.
Please answer as soon as possible this assignment will be due in an hour. Thank you
The values of x and y are given as follows:
x = 3.75 ft.y = 3 ft.How to obtain the dimensions?The dimensions are obtained applying the proportions in the context in the problem.
The conversion rate between feet and inches is given as follows:
1 feet = 12 inches.
Hence the dimensions of the picture are given as follows:
Wide: 54/12 = 4.5 feet.Height: 24/12 = 2 feet.The height of the entire frame is of 8 ft, while y is half the height outside the picture, thus the value of y is obtained as follows:
y = 0.5(8 - 2) = 3 ft.
The value of x is given as follows:
x = 0.5(12 - 4.5)
x = 3.75 ft.
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una barra de carbono de radio 0'1 mm se utiliza pára construir una resistencia. La resistividad de este material es 3.5 x 10- 5 Ω. m. Que longitud de la barra de carbono se necesita para obtener una resistencia de 10Ω?
The length of carbon rod is needed to obtain a resistance of 10 ohms is 0.00897 or 8.97 × 10⁻³ meters.
How to determine the length of carbon rod?In Mathematics and Science, the resistance of any conductor (wire) in terms of length can be calculated by using this formula:
Length = RA/ρ
Where:
R is the resistance.A is the area of conductor.ρ is the resistivity.By substituting the parameters, we have:
Length = Rπr²/ρ
Length = [10 × 3.142 × (0.0001)²]/3.5 × 10⁻⁵
Length = 3.142 × 10⁻⁷/3.5 × 10⁻⁵
Length = 0.00897 or 8.97 × 10⁻³ meters.
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Complete Question:
A carbon bar of radius 0.1 mm is used to build a resistor. The resistivity of this material is 3.5 x 10-5 Ω. m. What length of carbon rod is needed to obtain a resistance of 10 ohms?
Find the measure of arc LN. Fill in the blank with the
number only.
Assume that segments that appear to be tangent are
tangent.
The value of arc LN in the intersecting chords is 100⁰.
What is the value of arc LN?
The value of arc LN is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.
arc LN = 2 x m∠LMN
From the diagram, we have, m∠LMN = 50⁰
The value of arc LN is calculated as follows;
arc LN = 2 x 50⁰
arc LN = 100⁰
Thus, the value of arc LN is based on intersecting chord theorem.
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Prove Vin 20 + los 20 = 1
The prove of the trig identity gives sin²θ + cos²θ = 1.
What is the proof of the trig identity?The proof of the trig identity is determined as follows;
Let's consider a right triangle with one acute angle θ.
Let the hypotenuse have length 1
Let the length of the adjacent side = cosθ
then, the opposite side length = sinθ
Apply Pythagorean theorem, to determine the hypotenuse side;
(sinθ)² + (cosθ)² = 1²
sin²θ + cos²θ = 1
Thus, we have proved the identity.
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A new dictionary in the shape of a rectangular prism will have a thickness of 3 33 inches ( in ) (in)left parenthesis, start text, i, n, end text, right parenthesis. The volume of the dictionary will be 216 in 3 216in 3 216, start text, i, n, end text, cubed. What must be the area of the front cover, a face perpendicular to the thickness, in square inches?
The area of the front cover a face perpendicular to the thickness is 72 in².
Given:
A new dictionary in the shape of a rectangular prism will have a thickness of 3 inches.
The volume of the dictionary will be 216in².
Volume = W×L×H
Surface = volume/ height
= 216/3
= 72 in²
Hence, the area of the front cover of a face perpendicular to the thickness is 72 in².
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Determine the type of probability:
A spinner has 4 equal-sized spaces labeled A, B, C, and D.
The chance of landing in any of the spaces is 1/4, or 25%.
Answer:
Theoretical Probability
Step-by-step explanation:
Total number of possible outcomes
find the equation of the following lines:
parallel to the line joining (1;2) and (-2;-2) and passing through (4;1)
passing through the point (2; -3) and perpendicular to the line joining (2;-3) to (-1;-1)
Answer:
[tex]\textsf{1)}\quad y = \dfrac{4}{3}x-\dfrac{13}{3}[/tex]
[tex]\textsf{2)} \quad y = \dfrac{3}{2}x-6[/tex]
Step-by-step explanation:
To find the equation of a line parallel to the line joining (1, 2) and (-2, -2) and passing through (4, 1), we first need to find the slope of the line joining (1, 2) and (-2, -2).
[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-2}{-2-1}=\dfrac{-4}{-3}=\dfrac{4}{3}[/tex]
Parallel lines have the same slope, so the slope of the parallel line is m = 4/3.
Substitute the found slope and point (4, 1) into the point-slope formula:
[tex]\begin{aligned} y - y_1 &= m(x - x_1)\\\\y - 1 &= \dfrac{4}{3}(x - 4)\\\\y - 1 &= \dfrac{4}{3}x-\dfrac{16}{3}\\\\y &= \dfrac{4}{3}x-\dfrac{13}{3}\end{aligned}[/tex]
Therefore, the equation of the line parallel to the line joining (1, 2) and (-2, -2) and passing through (4, 1) is:
[tex]\boxed{y = \dfrac{4}{3}x-\dfrac{13}{3}}[/tex]
[tex]\hrulefill[/tex]
To find the equation of a line perpendicular to the line joining (2, -3) and (-1, -1) and passing through (2, -3), we first need to find the slope of the line joining (2, -3) and (-1, -1).
[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-1-(-3)}{-1-2}=\dfrac{2}{-3}=-\dfrac{2}{3}[/tex]
The slopes of perpendicular lines are negative reciprocals, so the slope of the parallel line is m = 3/2.
Substitute the found slope and point (2, -3) into the point-slope formula:
[tex]\begin{aligned} y - y_1 &= m(x - x_1)\\\\y - (-3) &= \dfrac{3}{2}(x - 2)\\\\y+3&= \dfrac{3}{2}x-3\\\\y &= \dfrac{3}{2}x-6\end{aligned}[/tex]
Therefore, the equation of the line perpendicular to the line joining (2, -3) and (-1, -1) and passing through (2, -3):
[tex]\boxed{y = \dfrac{3}{2}x-6}[/tex]
Explain how to simplify this expression: 4a + 19 - 3a - 7
Answer:
1a+12
Step-by-step explanation:
Use the stem-and-leaf plot of Monthly Sales Goals to answer the question that follows.
Monthly Sales Goals (in thousands)
Stem Leaf
1 2 5 5 8
2 4 4 6
3 4 6
4 7 8 9
What is the range of the monthly sales goals? Round to the nearest thousand.
$12,000
$24,000
$37,000
$49,000
The range of the monthly sales goals is; 37,000.
We are given the stem plot :
Stem Leaf
1 2, 5, 5, 8
2 4, 4, 6
3 4, 6
4 7, 8, 9
The largest number is 49 and the smallest is 12. Since is in thousands, the numbers become 49,000 and 12,000.
Range = highest value - the lowest value
Range = 49,000 - 12,000 = 37,000
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Out of 50 students taking a midterm psychology exam, 26 answered the first of two bonus questions, 33 answered the second bonus question, and 2 didn't bother with either
Answer:
This has no answer. Whats the question? Please tell me so I can help you
Is it probability ???
A standard deck of
52
5252 cards contains
4
44 suits: hearts, clubs, diamonds, and spades. Each suit consists of cards numbered
2
22 through
10
1010, a jack, a queen, a king, and an ace.
Bashir decides to pick one card at random from a standard deck of
52
5252 cards. Let
�
FF be the event that he chooses a face card (a jack, queen, or king of any suit) and
�
SS be the event that he chooses a spade.
What is
�
(
�
or
�
)
P(F or S)P, left parenthesis, F, start text, space, o, r, space, end text, S, right parenthesis, the probability that the card Bashir chooses is either a face card or a spade?
The probability that Bashir chooses a card that is either a face card or a spade is 11/26.
To find the probability that the card Bashir chooses is either a face card or a spade, we need to add the probabilities of the two events occurring and then subtract the probability of their intersection (choosing a face card that is also a spade).
First, we need to find the probability of choosing a face card. There are 12 face cards in a deck (4 jacks, 4 queens, and 4 kings), and a total of 52 cards, so the probability of choosing a face card is
P(F) = 12/52 = 3/13
Next, we need to find the probability of choosing a spade. There are 13 spades in a deck (from 2 to ace), and a total of 52 cards, so the probability of choosing a spade is
P(S) = 13/52 = 1/4
To find the probability of choosing either a face card or a spade, we can use the formula
P(F or S) = P(F) + P(S) - P(F and S)
We need to find the probability of choosing a face card that is also a spade (their intersection). There are only 3 face cards that are spades (jack of spades, queen of spades, king of spades), so the probability of choosing a face card that is also a spade is
P(F and S) = 3/52
Now we can plug in the values to get
P(F or S) = P(F) + P(S) - P(F and S)
P(F or S) = 3/13 + 1/4 - 3/52
P(F or S) = 12/52 + 13/52 - 3/52
P(F or S) = 22/52
P(F or S) = 11/26
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