Two forces 30-lb and 50-lb are pulling an object at an angle of 30°between them. Find the magnitude of the resultant force. Round answer to 2 decimal places.
Answer: The magnitude of the resultant force is 77.45-lb
Explanation:
Resultant is represented as R
Last year, Kaitlyn had $30,000 to invest. She invested some of it in an account that paid 5% simple interest per year, and she invested the rest in an account that paid 9% simple interest per year. After one year, she received a total of $2580 in interest. How much did she invest in each account?First account:Second account:
Answer:
She invested an amount of $3,000 in the first accont and $27,000 in the second account
Explanation:
Here, we want to get the amount invested in each of the accounts
To get this,let us write the simple interest formula
Mathematically, we have this as:
[tex]I\text{ = }\frac{PRT}{100}[/tex]Let the amount invested in the first account be $x, while that of the second account be $y
P represent the amounts invested
R is the rate of investment
T is the time (1 year)
The sum of these two is the $30000 she has to invest
Mathematically, we have this as:
[tex]x\text{ + y = 30000}[/tex]Let us get the interests on each of the accounts
For the first account, we have the interest as:
[tex]I_1\text{ = }\frac{x\times5\times1}{100}\text{ = }\frac{5x}{100}[/tex]For the second account, we have the interest as:
[tex]I_2\text{ = }\frac{y\times9\times1}{100}\text{ =}\frac{9y}{100}[/tex]The sum of these two is the interest value, which is as follows:
[tex]\begin{gathered} I_1+I_2\text{ = }\frac{5x}{100}+\frac{9y}{100}\text{ = 2580} \\ \\ 5x\text{ + 9y = 258000} \end{gathered}[/tex]So, we have two equations to solve simultaneously
The two equations are:
[tex]\begin{gathered} x\text{ + y = 30000} \\ 5x\text{ + 9y = 258000} \end{gathered}[/tex]We can solve this by substitution
Let us substitute for y
[tex]y\text{ = 30000-x}[/tex]Insert this into the second equation, we have this as:
[tex]\begin{gathered} 5x\text{ + 9(30000-x) = 258000} \\ 5x\text{ + 270000-9x = 258000} \\ 9x-5x\text{ = 270000-258000} \\ 4x\text{ = 12000} \\ x\text{ = }\frac{12000}{4} \\ x\text{ = 3,000} \end{gathered}[/tex]Recall:
[tex]y\text{ = 30000-x = 30000-3000 = 27000}[/tex]What this mean is that:
She invested an amount of $3,000 in the first accont and $27,000 in the second account
whats 2+2 i cant figure it out
Answer: 4
Step by step solution:
[tex]2+2=4[/tex]Write Expression to represent the total area as the sum of the areas of each room
We are given the following areas:
The total area of the square is given by:
[tex]11(7+4)[/tex]If we apply the distributive property we get:
[tex]11(7+4)=11\times7+11\times4[/tex]Which is equivalent to determining the area of the interior rectangle and adding them together.
Answer:
11x7+11x4
Step-by-step explanation:
your welcome <3
PLS HELP ASAP WILL GIVE BRAINLIST
Mr. Emmer gave a test in his Chemistry class. The scores were normally distributed with a mean of 82 and a standard deviation of 4. A student is randomly chosen. What is the probability that the student scores an 88 or below?
Answer:
93.32 %
Step-by-step explanation:
88 - 82 = 6 points
this is 6 /4 = z-score + 1.5
from z score table , this corresponds to .9332 or 93.32 %
Female
Male
Total
10
113
Snellville Stone
Mountain
12
14
26
316
10
20
30
Suwanee
8
16
24
Consider the following table with information about a sample of students from Phoenix High School and where they
live. If a person is randomly selected determine the following probability provided the condition: P(Female | Suwanee).
Total
30
50
80
If a person is randomly selected, the probability provided the condition is P(Female | Suwanee) is 1/3.
What is the probability?Probability is used to determine the odds in favor or against a random event happening. The odds in favor or against an event happening has a probability value that lies between 0 and 1.
The higher the odds of an event happening, the closer the probability value would be to 1. If it is equally likely that the event might happen or not happen, the probability value will be 0.5.
P (Female | Suwanee) is the probability that a person is female given that the person is from Suwanee.
P (Female | Suwanee) = total number of females from Suwanee / total number of people from Suwanee
8 / 24 = 1/3
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Write the correct expression for the following statement.
The quotient of x and three
Answer:
[tex]\frac{x}{3}[/tex] or x/3 or x÷3
I am just all around confused with this. Well explanation needed!
Given:
m∠A = (4x - 2) degrees
m∠B = (11x + 17) degrees
Let's find the value of x if the angles A and B are complementary angles.
Complementary angles are angles that sum up to 90 degrees.
Hence, we have:
m∠A + m∠B = 90
(4x - 2) + (11x + 17) = 90
Let's solve for x.
• Remove the parentheses:
4x - 2 + 11x + 17 = 90
• Combine like terms:
4x + 11x - 2 + 17 = 90
15x + 15 = 90
• Subtract 15 from both sides:
15x + 15 - 15 = 90 - 15
15x = 75
• Divide both sides of the equation by 15:
[tex]\begin{gathered} \frac{15x}{15}=\frac{75}{15} \\ \\ x=5 \end{gathered}[/tex]Therefore, the value of x = 5
ANSWER:
x = 5
Find odds in favor of winning ring and find against winning the ring
We have a randomly selected prize out of 9 objects (4 rings, 4 headsets and 1 camera).
a) We have to calculate the odds in favor of Mary winning a ring.
The odds can be expressed as the proportion (or quotient) between the probabilities of winning a ring and the probabilities of not winning a ring.
This will also be equal to the number of outcomes that will be a ring (4 elements are rings) divided by the number of outcomes that are not a ring (5 elements are not a ring):
[tex]o_{wr}=\frac{4\/9}{5\/9}=4:5[/tex]b) Now, we have to calculate the odds against Mary winning a ring.
This will be the inverse of the previous result, as we have to divide the probability of not winning a ring by the probability of winning.
We can then write:
[tex]o_{nwr}=\frac{5\/9}{4\/9}=5:4[/tex]Answer:
a) 4 : 5
b) 5 : 4
A farmer is going to divide her40 acre farm between two crops. Seed for crop A costs $30 per acre. Seedfor crop B costs $15 per acre. The farmer can spend at most $1050 on seed.If crop B brings in a profit of $70 per acre, and crop A brings in a profit of $180 per acre, how many acres ofeach crop should the farmer plant to maximize her profit?acres of crop Aacres of crop B
Given: A farmer is going to divide her40 acre farm between two crops
To Determine: How many acres of each crop should the farmer plant to maximize her profit
Solution
[tex]\begin{gathered} x=acres\text{ for crop A} \\ y=acres\text{ fro corp B} \end{gathered}[/tex][tex]\begin{gathered} Therefore: \\ x+y\leq40 \\ 30x+15y\leq1050 \\ Profit\text{ functon is} \\ P=70y+180x \end{gathered}[/tex]The graph of the inequalitiesis as shown below
Neglecting the negative axis, the point that will maximize the profit are te points shown above with their coordinates
The coordinates will maximum profits are
[tex]\begin{gathered} Point1:(0,40) \\ Point2:(35,0) \\ Point3:(30,10) \end{gathered}[/tex]Substitute the 3 points into the profit functions to determine thepoint that will given the maximum profit
[tex]\begin{gathered} P=180x+70y \\ Point1 \\ P1=180(0)+70(40) \\ P1=0+2800 \end{gathered}[/tex][tex]\begin{gathered} Point2 \\ P2=180(35)+70(0) \\ P2=6300+0 \\ P2=6300 \end{gathered}[/tex][tex]\begin{gathered} Point3 \\ P3=180(30)+70(10) \\ P3=5400+700 \\ P3=6100 \end{gathered}[/tex]Hence, the point that will maximize profit is (35, 0), which is
35 acres of crop A, and
0 acre of crop B
The tree diagram represents an experiment consisting of two trials
P(A)=
Based on the parameters in the question, the value of probability P(A) is 0.60
How to determine the probability?The given parameters from the tree diagram are:
Probability of event A: P(A only) = 0.6Probability of event A: P(A and C) = 0.3Probability of event A: P(A and D) = 0.7The probability is calculated using the following probability formula
P(A) = P(A and D) + P(A and C)
Substitute the known values in the above equation
P(A) = 0.6 * 0.7 + 0.6 * 0.3
Evaluate the products
P(A) = 0.42 + 0.18
Evaluate the sum
P(A) = 0.60
Hence, the value of the probability of A is 0.60
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PLS HELP DUE TODAY THE IXL
Answer:
Step-by-step explanation:
Answer:
What is 78,600 rounded to the nearest thousand
Answer:
79,000
Step-by-step explanation:
:]
Answer:
79000.
Step-by-step explanation:
Explain the meaning of 5!
a. 1+2+3+4+5
b.5-4-3-1-0
c.0×1×2×3×4×5
d. 5•4•3•2•1
The number 5 in mathematics denotes a quantity or value of 5. Five is the entire number between four and six. Five is the name of the number. Sam the little shows off five fingers.
What does 5 represent?The distance between 5 and 0 is the absolute value of 5. Then you go 1, 2, 3, 4, and 5. To the immediate right of zero, 5 is located. As a result, 5 has an absolute value of 5.
It denotes the sum of all succeeding integers, inclusively from 1 to 5.
That ' s 5! = 5*4*3*2*1 =120.
Also known as five factorials.
What's the name of a five-digit number?Ten-thousands
Answer and justification A five-digit figure is one that is in the tens of thousands. This is due to the fact that 10,000 is the smallest positive whole number with five digits.
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Plant A is 2 inches tall and is growing
at 14 inches per week. Plant B is 12
inches tall but is only growing at
inch per week. How many weeks will it
take for Plant A to be the same height
as Plant B?
It will take Plant A 5 days to be the same height as Plant B and this can be calculated through unitary method of mathematical calculation.
Unitary Method: What is it?The unitary technique used in here involves at first determining the value of a particular single unit, that is thus followed by the value of the necessary number of units.
What is an example of a unitary method?A single or type of a distinct unit is referred to by the word of unitary.
Therefore, the goal of this strategy is to establish values in reference to a single unit.
The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one liter of gas if it travels 44 km on two liters of fuel.
Plant A initial height = 2 inches
Growth rate = 14 inches/ week
= 2 inches/ day
Plant B initial height = 12 inches
Growth rate = 1 inch/ week
After 5 days we can see that plant A will be
2 + (5 x 2) = 12 inches
this is the same height as that of Plant B.
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ANSWERS ASAP PLEASEEEEE
Answer:
y= -3x+3
Step-by-step explanation:
atleast I think so
Identify the types of sampling errors that exist in the following sampling designs:A radio show asks people to phone in their views on whether the United States should house the homeless.The student newspaper plans to make a prediction for the student council election based on a survey of its readers.A new gym chooses to survey the first 20 members who enter the facility one day to determine whether members favor the new elliptical machines. I, voluntary; II, nonresponse; III, convenience I, nonresponse; II, voluntary; III, convenience I, nonresponse; II, convenience; III, voluntary I, voluntary; II, convenience; III, nonresponse I, convenience; II, voluntary; III, nonresponse
We are goinf to analise each case properly
1) As the radio show is asking it could be that their listners do not attend this demand. Then the error would be nonresponse.
2) As the students do the survey based of its readers it depends only of this part of the poblation. Then the error would be voluntary.
3) As the gym ask only to the first 20 members it makes the error would be convenience
So, the correct answer is B.
f(x)=7x-3 for f(x)= -38
Answer:
f(x)= -269
Step-by-step explanation:
f(x)=7x-3
Since we know f(x)= -38, we can substitute x for -38.
So:
f(-38)=7(-38)-3
f(-38)= -266-3
f(x)= -269
Answer:
-7x=38+3
-7x=41/-7=5.8
The equation of a line is: y = 4/7x - 12Which equation would have a line that is perpendicular to this line?1. y = - 4/7x - 12. y = - 7/4x - 53. y = 7/4x - 84. y = 4/7x - 2
Let's recall the framework of the equation of a line:
We say that two lines are perpendicular if the slope of one line is minus the multiplicative inverse of the slope of the other one; mathematically, this amounts to the following equation:
[tex]m_1=-\frac{1}{m_2}.\leftarrow\begin{cases}m_1=\text{Slope of one line} \\ m_2=\text{ Slope of the other line}\end{cases}[/tex]In this case, the slope of our line is 4/7. Then the slope (m) of any line perpendicular to it must satisfy
[tex]m=-\frac{1}{\frac{4}{7}}\text{.}[/tex]Solving this equation for m, we get
[tex]\begin{gathered} m=-\frac{1}{\frac{4}{7}}, \\ m=-\frac{\frac{1}{1}}{\frac{4}{7}}, \\ m=-\frac{1}{1}\cdot\frac{7}{4},\leftarrow\text{ Flipping rule when dividing fractions} \\ m=-\frac{7}{4}. \end{gathered}[/tex]AnswerThe answer is 2.
HELPP PLEASE
Choose A
( A is the answer <3)
Solve for x:
X=
76⁰
9x+1
40°
The value of x is 7 and the measure of unknown angle is 64°.
The angles of triangle are given 76°, (9x+1)° and 40°.
What is angle sum property of a triangle?Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
Now, sum of three angles of a triangle is
76°+(9x+1)°+40°= 180°
⇒ 116+9x+1 = 180
⇒ 9x + 117 = 180
⇒ 9x = 63
⇒ x = 7
So, 9x+1=64°
Therefore, the value of x is 7 and the measure of unknown angle is 64°.
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What is the end behavior of the polynomial function?
Drag the choices in to the boxes to correctly describe the end behavior of the function.
The end behaviours of the functions are
f(x) = 6x⁹ - 6x⁴ - 6: As x ⇒ +∝, f(x) ⇒ +∝ and as x ⇒ -∝, f(x) ⇒ -∝f(x) = -3x⁴ - 6x + 4x - 5: As x ⇒ +∝, f(x) ⇒ -∝ and as x ⇒ -∝, f(x) ⇒ -∝How to determine the end behaviours of the functions?Function 1
The equation of the function is given as
f(x) = 6x⁹ - 6x⁴ - 6
Calculate f(∝) and f(-∝)
So, we have
f(∝) = 6(∝)⁹ - 6(∝)⁴ - 6
Evaluate
f(∝) = ∝ - ∝ - 6
So, we have
f(∝) = ∝
Also, we have
f(-∝) = 6(-∝)⁹ - 6(-∝)⁴ - 6
Evaluate
f(-∝) = -∝ - ∝ - 6
So, we have
f(∝) = -∝
This means that
As x ⇒ +∝, f(x) ⇒ +∝ and as x ⇒ -∝, f(x) ⇒ -∝
Function 2
The equation of the function is given as
f(x) = -3x⁴ - 6x + 4x - 5
Evaluate the like terms
f(x) = -3x⁴ - 2x - 5
Calculate f(∝) and f(-∝)
So, we have
f(∝) = -3(∝)⁴ - 2(∝) - 5
Evaluate
f(∝) = -∝ - ∝ - 5
So, we have
f(∝) = -∝
Also, we have
f(-∝) = -3(-∝)⁴ - 2(-∝) - 5
Evaluate
f(∝) = -∝ + ∝ - 5
So, we have
f(∝) = -∝
This means that
As x ⇒ +∝, f(x) ⇒ -∝ and as x ⇒ -∝, f(x) ⇒ -∝
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The model represents an equation. What value of x makes the equation true? Enter your answer in the box below
the value of x are that makes it true
continued - calculating gross payRemember, this is money round to the nearest Penny/hundredths place.
ANSWER:
Regular pay is $383.2
Overtime rate is $14.37
Overtime pay is $114.96
Gross pay is $498.16
STEP-BY-STEP EXPLANATION:
Assuming the overtime multiplier is 1.5 and the standard work week is 40 hours. Therefore, we calculate the regular payment like this:
[tex]RP=40\cdot9.58=383.2[/tex]The overtime rate would be the value of the normal payment times the overtime multiplier, like this
[tex]OTR=9.58\cdot1.5=14.37[/tex]Then we multiply the number of additional hours to the 40 hours allowed, that is, 8 (48 - 40), for which one gives overtime pay
[tex]OTP=8\cdot114.96=114.96[/tex]Now the gross pay would be the sum of the regular payment with the overtime payment:
[tex]GP=114.96+383.2=498.16[/tex]Graph the line 3x + 6y =12.
Use the line tool and select two points on the line.
Answer: First divide everything by 3 to make it simpler. Then subtract 12 on both sides to get the equation "x+2y-12 = 0. You can then graph this.
Step-by-step explanation:
Temperature is usually measured on the Fahrenheit scale (°F) or the Celsius scale (°C). Use the formula F = 1.8C+ 32 to convert from one scale to the other. The highest temperature ever recorded in Virginia Beach, Virginia, was 104°F. Find the temperature in degrees Celsius. 219°C 26°C b. 155°C d. 40°C
Answer:
The temperature in degrees Celsius is;
[tex]40^0C[/tex]Explanation:
Given the formula for converting Temperature from Celsius to Fahrenheit as;
[tex]F=1.8C+32[/tex]Where;
F = temperature in Fahrenheit
C = temperature in Celsius
To convert from Fahrenheit to Celsius, let us make C the subject of formula;
[tex]\begin{gathered} F-32=1.8C \\ C=\frac{F-32}{1.8} \end{gathered}[/tex]To convert 104°F to Celsius, let us substitute the value into the derived formula;
[tex]\begin{gathered} C=\frac{F-32}{1.8} \\ C=\frac{104-32}{1.8} \\ C=40^0C \end{gathered}[/tex]Therefore, the temperature in degrees Celsius is;
[tex]40^0C[/tex]
During a physics lab, students added weights of different masses to aspring. After adding each weight to the spring, they measured how far theweight was from the lab tabletop, in centimeters. Then they graphed thedata and calculated the line of best fit to be y = -1 x + 10.25Weight Distance fromthe Tabletop (cm)108642Effect of Weightson a Spring0 50 100 150 200 250 300Mass (g)What does the x-intercept represent?-XAt 250 grams, the weight will touch thetabletop.With no weight, the spring is 10centimeters above the tabletop.The weight will be 250 centimetersabove the tabletop when the spring hasa mass of 10 grams on it.The spring stretches and the weight is 1centimeter closer to the tabletop forevery 25 grams added to it.
Solution:
Given the graph below:
where the equation of the line of best fit is expressed as
[tex]y=-\frac{1}{25}x+10[/tex]The x-intercept represents:
The correct option is
Find the distance between the two points.(-6, -3) and (194,42)The distance is(Type an exact answer, using radicals as needed.)
distance=205
Explanation
Step 1
the distance between is given by:
[tex]\begin{gathered} \text{distance=}\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2} \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}[/tex]Let
P1(-6,-3)
P2(194,42)
Step 2
apply the formula.
[tex]\begin{gathered} \text{distance=}\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2} \\ \text{distance=}\sqrt[]{(-6-194)^2+(-3-42)^2} \\ \text{distance=}\sqrt[]{(-200)^2+-45^2} \\ \text{distance=}\sqrt[]{40000+2025} \\ \text{distance=}\sqrt[]{42025} \\ \text{distance}=205 \end{gathered}[/tex]I hope this helps you
The measure of an angle and it’s complement differ by 22 degrees. Find the larger angle.
The measure of an angle and its complement differ by 22 degrees and the larger is 56°
What are Complementary Angles?The total of the two angles' measurements determines their complement and supplement. The pair of angles is said to be complimentary if the product of the two angles equals the measurement of a right angle.
1. If the total of two angles equals 90°, the angles are considered to be complements of one another.
2. Let x° and y° be the two angles. Since they complement one another, the two angles' sum will be 90 degrees.
= x + y = 90°. (Assume equation 1 is used.)
3. The two angles differ by 22 degrees, hence the equation will be,
= x - y = 22°. (Put equation 2 in.
4. To determine the values of x and y, solve equations 1 and 2.
Add equations 1 and 2 together.
= x + y + x - y = 90 + 22,
= 2x = 112°,
= x = 56°.
5. In equation 1, change the value of x.
= 56° + y = 90°,
= y = 90 -56,
= y = 34°.
So, the measure of the two angles is 56°, and 34°.
And the larger angle is 56°
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